Progresses and Challenges of Composite Laminates in Thin-Walled Structures: A Systematic Review

Abstract

Most engineering technologies, gadgets, and systems have been developed around the use of sophisticated materials. Composite laminates have found widespread application in various significant and innovative industries, such as aviation, maritime transportation, automobiles, and civil engineering. Recent studies have revealed that composite materials are extensively utilized in automotive, undersea, and structural applications. Extensive efforts have been dedicated to exploring the structural components constructed from composite materials due to their importance in engineering. While composite materials offer certain advantages over their metallic counterparts, they also present analysts and designers with intricate and challenging issues. Hence, this Review aims to highlight noteworthy studies on composite materials and their engineering applications, specifically focusing on structural components. Furthermore, this Review includes a comprehensive summary of the application of composite laminates, accompanied by a critical analysis of the existing literature in this field. By presenting this information, the Review intends to provide a valuable resource and guideline for researchers interested in leveraging composite materials for engineering structures.

1. Introduction

Composite materials are made up of two or more different components of materials. Components when combined offer attractive attributes for a particular use. The customary combination of sand and concrete reinforced steel bars and cementing materials are two well-known examples of composite materials. Modern composite materials with high strength and high modulus fibers embedded in a matrix are most frequently employed as fiber-reinforced composites. Composites contain either metallic or nonmetallic fibers and matrix materials. Common metals such as aluminum, copper, iron, nickel, steel, and titanium are used to make fibers, as well as organic ingredients such as glass, carbon, boron, and graphite. New material systems are constantly being developed.¹ The definition of semiproducts, the order of stacking, the processing technique, or the topology of the structure are only a few of the many parameters that make up a composite structure’s comprehensive description. The mechanical performance of the structure (mass, cost, rigidity, resistance, durability, etc.), production (cost, production delay, etc.), and environmental impact are all influenced by these factors.²

For structural applications, fiber-reinforced composite materials are frequently created as a thin layer known as lamina. The layers are then stacked to the desired thickness and characteristics to produce structural elements. To attain the appropriate strength and stiffness for a particular application, the fiber orientation in each lamina and the layer stacking order can be selected. The research on composite materials for structural use has several components, including the creation of material systems, characterizing the material systems, doing an analysis, and designing structural components, as well as the production of such components, to mention a few. Common examples of composite materials include the conventional sand and cement mix and the reinforced steel bars inserted into concrete. Often the morphology of the composite is such that one material, the matrix, surrounds the other.³ The surrounding material may, for instance, be spherical, fibrous, or disc shaped. Fiber composites are the most typical type of structural material. The matrix retains the fibers in position, distributes load among them, and shields them from harm from the outside, which makes it advantageous to surround the fibers with it. Polymers, such as epoxy, are frequently utilized as matrix materials in the case of structural fiber composites. Figure 1 shows the basic composition of composite materials.

Figure 1.

Composition of composite materials.

This paper starts with a basic introduction to composite materials in section one and then presents various applications of composite materials in structural engineering in section two. Then, the structural analysis of composite materials is explained considering the critical factors in section three. Next, some useful optimization techniques are explained in section four which are coeffective and energy-saving approaches. After that, based on the existing literature work of this paper a critical analysis is presented and highlights the research gap in section five. Finally, a conclusion is made of this Review in section six.

2. Composite Materials in Engineering Structures

Due to their outstanding strength, stiffness, light weight, and resistance to corrosion, composite laminates are utilized extensively across a variety of industries. To produce a composite material with superior qualities to more conventional materials such as metals or plastics, they often offer a combination of various components, typically fibers (such as carbon fiber, glass fiber, or aramid fiber) embedded in a matrix (such as epoxy, polyester, or thermoplastic). Various sectors, including aerospace, architecture, automotive, energy, infrastructure, marine, military, sports, and recreation, employ composite materials. While composite technology has a long history spanning thousands of years, its application in civil engineering is relatively recent, dating back just a few decades.⁴ Composite materials have mainly been used in civil engineering in recent decades, which can be briefly summarized in conjunction with Figure 2.

Figure 2.

Applications of composite materials.⁵ Copyright 2023, with permission from Elsevier.

Since the early 1940s, composite materials have been used in the defense sector. Due to their high strength-to-weight ratio and resilience to corrosive substances and weather, composites have found use in several industries.⁶ To manufacture durable concrete members, the construction industry has been working hard to find materials that can survive hostile environments. Unfortunately, the usage of steel as a concrete reinforcement material hastens the decay of structures. The introduction of composite materials offers construction companies the opportunity to construct environmentally friendly concrete infrastructure. Composite materials, including fiber-reinforced composites, aggregate composites, and natural fiber-reinforced composites, have been utilized in various industries to build engineering structures.⁷ Composite laminates, such as fiber-reinforced metal laminates (FRMLs), are commonly employed in aerospace structures.⁸ These laminates combine different structural engineering components, such as polymers, metals, ceramics, and glasses, at a macroscopic level, resulting in composite materials with unique properties.

The arrival of new, affordable, and high-performance structural composites may have ushered in a new era in construction engineering. Studies have shown that reinforcing concrete beams with fiber-reinforced plastics (FRPs) through internal or external bonding can enhance the load-bearing capacity and stiffness of existing structures.⁹ Pultruded FRP sections have the potential to replace steel in numerous load-bearing structures.¹⁰ Major original equipment manufacturers (OEMs) in the aviation industry, such as Airbus and Boeing, have showcased the vast possibilities of using composite materials extensively. The knowledge and application of composites in architecture is expanding significantly. In large-scale projects, composites provide performance and value to architects and designers, and their application in commercial and residential buildings is rising. The automotive sector has a long history with composites and is the main market for them. Composites not only enable ground-breaking vehicle designs but also aid in making cars lighter and more fuel-efficient. Automobiles need dependable, synchronized mechanisms with parts that can tolerate temperature changes, corrosion, and friction. A variety of automotive elements, including headlight housings for forward-facing lights, under-the-hood electrical and heat-shielding components, external body sections, and interior structural and cosmetic components, frequently use composite materials. Table 1 summarizes the applications of composite materials in various industries.

Table 1. Applications of Composite Materials.

no.	industry	applications
1	space	radar and satellite structures
2	aircraft	primary and secondary parts of structures
3	automobiles	body and other critical parts
4	civil infrastructures	truss-type structures, bricks, columns, and beams
5	wind turbine blades	rotor blades, nose cone, and some other parts
6	sports	table tennis boards, tennis, badminton, golf clubs, baseball bats, hockey sticks and others

2.1. Composite Laminates

The loss of stiffness observed in laminated composites, such as carbon fiber-reinforced polymer matrix composites, is a substantial physical and mechanical response that occurs during the progression of damage and failure under various conditions, including continuous or cyclic loads. To accurately study the mechanical properties of composite laminates, it is crucial to replicate the initiation and subsequent development of this type of damage phenomenon.¹¹ In this regard, a proposed approach based on energy-based stiffness degradation,¹² rooted in the cold dark matter (CDM) theory, aims to predict the progressive failure characteristics of Al-carbon fiber/epoxy composite laminates. This method provides insight into the evolution process of damage within the material.

In simple terms, the CDM theory suggests that a sizable fraction of the universe’s stuff is made up of cold dark matter. Dark matter is a category of matter that is invisible and challenging to directly detect because it does not interact with light or other electromagnetic radiation. Dark matter particles that move slowly (at low velocities) in comparison to the speed of light are referred to as cold dark matter.

According to the CDM theory, galaxies and galaxy clusters were formed along with other large-scale astronomical objects in the universe. After the Big Bang, it is believed to have first formed as microscopic clusters or particles, and over the course of billions of years, it has been gravitationally drawing in ordinary matter (atoms).

The distribution of matter on enormous dimensions, the rotational velocities of galaxies, and the patterns in the cosmic microwave background radiation can all be explained by the existence of cold dark matter. The “glue” that holds galaxies and galaxy clusters together and prevents them from scattering owing to the outward expansion of the universe is thought to be the gravitational pull of cold dark matter.

Delamination and matrix microcracking are frequent first steps in the failure of laminated resin matrix composite materials. Interlaminar stresses are the driving force behind these three-dimensional damage mechanisms. An analytical strategy that offers accurate stress estimations in crucial areas is a crucial component to comprehending and, eventually, predicting breakdowns in composite materials. Traditional laminate theories, which are predicated on global displacement assumptions, are insufficient for this task. Furthermore, in the original formulations, the interlaminar stresses are frequently overlooked. Solutions based on these theories are therefore unable to produce realistic stress distributions. A recent theoretical study demonstrates that bending-related behavior is influenced by several nonclassical factors. Included in them are transverse normal strain and section warping, as well as their related nonclassical surface-parallel stress contributions. When these nonclassical factors are considered, the stress prediction ability of a bending theory is greatly enhanced.¹³

Ozaslan et al.¹⁴ experimentally and numerically performed stress analysis and strength prediction for carbon/epoxy laminates with holes in particular orientations. Considering their locations and the direction of the load, the interaction between the holes was investigated. For various hole orientations, the maximum laminate stress at the border of the holes was identified. By considering the location of the maximum tension at the hole edges, the critical zone was identified. Bogetti and Gillespie conducted a study on thermosetting composite laminates, focusing on the analysis of process-induced stress and deformation.¹⁵ They employed a methodology to predict the development of residual stress during the curing process. Li et al.¹⁶ further investigated the curing deformation of thermosetting resin composites by creating two transient models: the viscoelastic model and the linear elastic model. These models, simulated using COMSOL multiphysics, consider the complex interplay between physical and chemical changes during the composite’s curing process and the time-dependent nature of material performance factors.

Both viscoelastic and linear elastic models are used to analyze the mechanical behavior of materials, but they have different approaches to capturing the material’s response to applied forces over time. In accordance with the assumption of linear elastic models, the material deforms instantly and completely returns to its original shape after the applied force is removed.

According to Hooke’s Law, which claims that deformation is exactly proportional to applied force, these models are based on that principle. Stress (force applied per unit area) and strain (deformation) have a linear connection. Within the elastic limit, the material in linear elastic models has a constant Young’s modulus (a measure of stiffness) and a linear stress–strain relationship. Because they are straightforward and analytically manageable, linear elastic models are useful in a wide range of engineering applications. However, they are unable to adequately characterize materials with temperature- or time-dependent behavior.

The time-dependent behavior of materials, in addition to their elastic response, is taken into consideration by viscoelastic models. Both viscous (time-dependent) and elastic (instantaneous) characteristics are present in these materials. When a constant load or stress is applied to a viscoelastic material, it first deforms quickly, much like an elastic material. But as time passes, it keeps changing shape and acting viscous. To simulate the behavior of the material, viscoelastic models include a time-dependent element, such as a dashpot or a spring-dashpot combo. The material can display both instantaneous and time-dependent deformation thanks to these components, which also provide a temporal delay to the reaction. Viscoelastic models can depict processes such as hysteresis (energy loss during cyclic loading), creep (gradual deformation under constant load), and stress relaxation (decrease in stress over time under constant strain).

Dai et al.¹⁷ proposed a numerical model that couples multiple physics aspects of the curing process in thermosetting resin composites. They adopted the modified “cure hardening instantaneously linear elastic (CHILE)” model and the viscoelastic model to predict residual stress and deformation during curing. Examining delamination mechanisms in composite laminates subjected to low-velocity impact, Zhao et al. utilized ultrasonic-guided waves to detect and monitor delamination in composite double cantilever beams (DCBs).¹⁸ They established an experimental setup for ultrasonic-guided wave-based damage detection using piezoelectric sensors and processed the response signals using Hilbert transform (HT), Fourier transform (FFT), and wavelet transform (CWT) techniques.¹⁹ Hassan and Tamer²⁰ explored how composite laminates with a specific arrangement of thin and thick plies in a predetermined sequence behave when used in bolted joint.

To accurately assess composite structures under dynamic conditions or simulate manufacturing processes involving high strain rates, it is important to develop a constitutive model that considers these effects. Eskandari et al. developed a phenomenological approach to account for continuum damage in composites under high strain rates, incorporating the viscoplastic behavior of the material.²¹ They investigated the deformation of composite structures under dynamic conditions. Kharghani et al. studied the deflection and maximum tensile strain of composite laminates under bending conditions, employing different equivalent single-layer and layer-wise theories based on polynomial form functions.²² The Rayleigh–Ritz approximation approach and the concept of minimal potential energy were used to determine the unknown coefficients of the displacement field. The outcomes were compared with experimental studies and three-dimensional finite element analysis. In modeling design-critical impact loading events on laminated composite structures, accurately capturing the rate-dependency of the composite material is crucial. A study examined the rate dependence of the strain-energy release rate for high-rate loading conditions and the failure of fibers in tension.²³

Manufacturing techniques for thin-walled constructions and composite laminates have significantly improved. However, the field of materials science and engineering is always developing, thus further advancements might have occurred since then. One of the earliest and most basic processes for creating composite laminates is hand lay-up. The process entails physically laying down layers of fiber reinforcement (such as carbon fiber or fiberglass) in a mold before saturating them with resin. Although labor- and time-intensive, this technology is still utilized for prototypes or low-volume production. The computer-controlled equipment used in automated tape lay-up (ATL) and automated fiber placement (AFP) is used to precisely lay down preimpregnated composite tapes or tows of fibers onto a mold or mandrel. Compared to hand lay-up, these techniques provide greater accuracy, repeatability, and production speed. While AFP is utilized for intricate designs, ATL is appropriate for flat or slightly curved surfaces.²⁴

Dry fibers are inserted in a mold during the closed-mold resin transfer molding (RTM) process, and resin is then injected under pressure to impregnate the fibers. This process creates composite laminates of the highest quality, with a flawless surface finish and precise dimensions. RTM is frequently utilized in sectors such as aerospace and automotive to create huge, complicated structures.²⁵ Manufacturing cylindrical or axisymmetric composite structures such as pipelines, pressure containers, and rocket engine casings frequently uses filament winding. In this technique, continuous fibers (filaments) are resin-impregnated and wound in a preset pattern onto a revolving mandrel. The composite construction that is produced has a great strength to weight ratio.²⁶ These are but a few illustrations of how manufacturing techniques for composite laminates and thin-walled structures have advanced. Further developments are being made in the industry because of ongoing research and development, including advancements in cost effectiveness, material characteristics, and process automation.

2.2. Thin-Walled Composite Structures

The thin-walled member is one of the systems that use the material to resist buckling the most effectively. The thin-walled section can be easily molded into a variety of shapes with a high shape factor and less used material because it is composed of multiple thin-walled parts. However, the thin-walled member suffers from serious drawbacks common to formed plates, such as local buckling. In most cases, when a thin-walled column is subjected to a compressive force, the component plates of the member buckle before collapsing.²⁷ As everyone is aware, a thin-walled structure is one whose thickness is significantly less than its height and width. Due to its unique properties, including having significant strength and stiffness with low weight, it is a load-bearing profile with a wide range of applications in current technology, including aerospace, automotive, and construction industries.²⁸ Different forms of thin-walled structures are used depending on the application in the industries. For example,²⁹ studies T-shaped thin-walled with various geometry that is used in aircraft as ribs. Next, Rozylo and Debski³⁰ conducted an experiment on composite thin-walled Z-shape structures. Thin-walled structures are intriguing since they can improve other members of the structure.

Due to their numerous benefits, including low density, high strength, and flexible manufacturing, fiber-reinforced composite materials, such as glass fiber-reinforced polymer (GFRP), carbon fiber-reinforced polymer (CFRP), and others, have become increasingly popular in recent years. Today, a variety of industrial industries, such as aviation, manufacturing, and structural engineering, utilize these materials.³¹ Due to the rising need for lightweight and efficient buildings, engineers and scientists have utilized composite materials in a range of applications. By incorporating distinct particular strengths and thermomechanical features that are not possible with standard materials, the composite material design aims to attain superior performance.³² The physical characteristics of composite materials are greatly influenced by the orientation of the fibers. Due to these characteristics, the shell stiffness affects the critical buckling load.³³ The thin-walled structures can be any size and shape based on the application. The most promising shapes of thin-walled structures for lightweight infrastructure commonly use the C-section, I-section, T-section, and L-section of beams (Figure 3).

Figure 3.

Sample of thin-walled sections.

3. Structural Analysis

A laminated composite material consists of different layers of matrix and fibers. Its properties can vary alot with each layer or ply’s orientation, material property and the number of layers itself. There are different analysis methods for the structures; in particular, the finite element method was found to be a more successful analyzing method of the structures considering different modes of shape analysis.^34,35 Additionally, specific analysis of modes is available to define the stresses and strains via buckling analysis, failure mode, etc.

3.1. Buckling Analysis

Buckling is a flaw mostly brought on by a member’s lateral deflection when an axial force is applied. This makes the column bend due to its frailty. Rapidity makes this style of failure dangerous. The length, strength, and other characteristics of a column determine whether it will buckle. Long columns may experience elastic buckling in relation to their thickness.³⁶

Prebuckling, critical-buckling, and postbuckling are the three main states of work that characterize a typical thin-walled composite structure in an ideal model. Prebuckling states occur when the applied force is less than the critical buckling point for the structure. In this state, there is little deflection and only slight compression of the structures. The maximum axial load that the structure can support before buckling is known as the critical load. The system reaches equilibrium at critical load, which also serves as the bifurcation point between the two states of prebuckling and postbuckling. The linearity of a structure terminates at this point, and nonlinearity should be considered after the applied load exceeds the bifurcation point. Finally, a postbuckling condition is one in which bending-related deformation increases. In a postcritical state with severe overloading present, structural integrity is lost, leading to damage. The first stage of moving the structure into a postcritical condition of operation is reaching the bifurcation point. Postcritical activity is characterized by specific effects on the axial compression of the structure. Therefore, the general factor that defines the proper exploitation of the structure in connection to the loading process is buckling and carrying capacity. The postcritical equilibrium trend is steady, and the rise in compressive load is followed by an increase in wall deflection, so the structure may continue to function even after buckling.

In general, linear-buckling analysis and nonlinear-buckling analysis are the two types of analysis that are frequently employed to analyze the buckling on thin-walled structures. The critical buckling load for a plate is determined using the eigenvalue buckling analysis, also referred to as the linear analysis or Euler’s buckling analysis. A load factor or load multiplier will be generated by ABAQUS when a system is subjected to an arbitrary load to reach the bifurcation point. ABAQUS will apply the critical buckling load by multiplying the input load, regardless of whether the applied load is smaller or greater than the critical buckling load. The linear buckling analysis, also known as eigenvalue buckling analysis, forecasts the potential buckling capacity of an ideal linear elastic system. The classical Euler solution, for instance, can be discovered from the eigenvalue buckling analysis of a column given the flaws and nonlinearities. A nonlinear static analysis of rising loads is used in the nonlinear buckling analysis to identify the load level at which the system becomes unstable. As a result, the nonlinear buckling analysis can be used to generate a more accurate method.³² In short, linear analysis is much simpler to conduct while nonlinear analysis offers a robust solution compared to linear. Also, Abadi et al.³⁷ enhance the way unidirectional fiber-reinforced laminates bend by combining an optimization process for nearly uniform configurations with the possibilities offered by varying ply orientations.

3.2. Failure Mode

When a thin-walled structure is compressed, it typically fails because of a loss of stability. Local, distortional, and global buckling are the three main modes or classes that are used to categorize buckling processes. Extreme deformation and eventual failure will result from any of these processes.³⁸ The instabilities of thin-walled compressed members include local, flexural torsional buckling, distortional, and their interaction. The main mode of failure of the column is local and distortional buckling. As reported,³⁹ local buckling in a thin-walled element does not lead to failure. However, distortional buckling, which is shown by displacement of the unit normal to its plane, happens at intermediate columns. Flexural buckling is typically what causes long columns to collapse. This mode exhibits excessive deformation along a weaker primary axis. To considerably increase the compression member’s overall effectiveness, this mode of failure may be diminished or eliminated.

Other names for distortion buckling include stiffener failure and local-torsional failure. In members with edge-stiffened components, it is a mode defined by the rotation of the flange at the flange or web junction. It is straightforward to understand how local buckling action works: as the width-to-thickness (w/t) ratio rises, the local buckling stress falls. Therefore, the engineer can use this information to design for local buckling.⁴⁰ Local instability causes the webs and flanges to buckle like plates, changing the column’s cross-section. The critical stress of buckling is frequently independent of the length of the column when the length of the largest plate element in the cross column is equal to or greater than three times that of the width. Failure modes can be acted at any layer and direction in the composite laminates when it is having the compressive buckling load in the thick-walled structures. Examples are shown in Figure 4. The figure shows the maximum possible types of the compressive failure mode.

Figure 4.

Failure modes of fiber composites (a) Elastic microbuckling, (b) fiber kinking, (c) fiber crushing, (d) shear band formation, (e) matrix cracking, and (f) buckle delamination.⁴¹ Reprinted under the Creative Commons (CC) License (CC BY 4.0).

3.3. Effect of Cutout

To save weight and to allow for assessment and construction services, thin-walled parts are frequently sliced open. Due to the transfer of stresses caused by this perforation, the structural member’s ultimate strength and elastic stiffness may be altered. Typically, as a section of the structure is lost, the critical load of a thin-walled member with cutouts should drop. However, due to its size, this type of structure is vulnerable to buckling, which is made worse by the existence of gaps. The buckling behavior of structural members having perforations is directly influenced by the kind, size, position, and quantity of the perforations.⁴² Thin-walled perforated channel beams under compression loads were the subject of the study. To examine their effect on the beam’s buckling strength, three parameters, the geometry of the apertures, the opening ratios, and the spacing proportion, were chosen. Using the Taguchi technique and ANOVA, the authors aimed to find the ideal combination of the aforementioned factors in a perforated thin-walled construction for aluminum 6061-T6. According to their findings, a hexagonal form with an opening ratio of 1.7 and a spacing ratio of 1.3 provides the best buckling strength.

Rozyło and Wrzesinska⁴³ determined impact on buckling, by examining the thin-walled members with I-section cross-member-changeable hole length and diameter. They claimed that the length has no discernible influence on buckling. However, the dimension of the holes does alter the member’s capacity to support greater loads. It has been determined that the size of the critical load that a member may apply increases with diameter. In contrast to previous research,⁴² this report does not specify a maximum hole width or number of holes. In addition to his study of the relationship between slenderness ratio and stability, Guo⁴⁴ examined the impact of perforations on thin-walled members. It was determined that for a single hole in the structure, the buckling overall stability coefficient decreased as hole size increased. In contrast, for thin-walled members with numerous circular holes, stability rises as hole spacing increases. According to his research, adding additional holes has no discernible impact on stability when smaller holes are present. This was made evident by including the subject’s dimensions, as shown in Figure 5.

Figure 5.

Description of hole spacing and opening ratio in thin-walled structure.⁴² Reprinted under the Creative Commons (CC) License (CC BY 4.0).

Cutouts of various sizes and shapes are frequently employed in composite plates as access ports for mechanical or electrical systems, for damage assessment, or as doors and windows. Additionally, they can be applied to lighten the structure’s total weight.⁴⁵ According to the author’s research shown in Figure 5, elliptical cutouts have the highest critical buckling load up to 45°, but circular cutouts have the highest value beyond 45°. In addition, they also found that the greater the cutout area, the lower the critical buckling load.⁴⁵ The findings presented by Khan et al.⁴⁶ indicate that the hybrid laminate demonstrates reduced sensitivity to notches compared to CFRP and KFRP laminates. This is attributed to a slower decrease in strength with increasing hole size. The researchers demonstrated that, following the introduction of holes, the hybrid laminate exhibited greater specific strength and strain in comparison to CFRP and KFRP laminates. This was attributed to the lower density of Kevlar fibers and the occurrence of gradual damage mechanisms that postponed the ultimate failure of the hybrid composite.

3.4. Effect of Fiber Orientation

It is good to know the effect of fiber orientation on critical buckling. The study found that different fiber orientations gives different critical buckling loads.⁴⁵ The theoretical calculations and finite element analysis used the mechanical properties of laminated glass–polyester composite plates. From the composite plies, eight-ply laminates with eight stacking sequences are created. Fiber orientations of 0, 15, 30, and 45 deg were present in each of the six-ply layers. It was found that in this study, the buckling load is lowest when the fiber angle is 45° and increases as the orientation angle increases. Figure 6 shows the example of fiber direction considering eight layers of composite laminates.

Figure 6.

Example of fiber orientation.⁴⁷ Reprinted under the Creative Commons (CC) License (CC BY 4.0).

According to a published study,³³ the critical buckling stress tended to increase when the fiber orientation changed. Additionally, this research version demonstrates no differences regarding the influence of thickness, with the same pattern being shown in the results as they repeat the process for thicker models. After all, it is important to recognize that each research study uniquely uses materials. One study⁴⁵ used laminated glass–polyester composite plate material in their experiments but another³³ used FRP. From these two publications, we may therefore conclude that various composite materials also influence the critical buckling stress on thin-walled parts.

Due to the popularity of structures, numerous types of research have been done to examine the gaps that are present and so enhance the use of columns, beams, shells, and laminate structures in various sectors. Generally, the critical buckling load of a thin-walled member is then estimated using linear analysis, and after buckling, the researcher examines the column’s behavior in nonlinear stages to determine the ultimate load. Additionally, once the experiment or simulation is completed for a specific thin-walled member, multiple types of failure might be seen. Using Euler’s equation, we may anticipate the mode of buckling. The supporting option employed to support the column is another aspect that adds attention to this subject. As we comprehend Euler’s classic, different supports result in various responses. This is because different buckling coefficients will be used based on the kind and dimensions of the supports. According to reviews of prior literature, the performance of perforated thin walls tends to decline as the size of the holes rises. To determine the acceptability of the cutout diameter for a specific thin-walled structure, optimization is therefore required. Additionally, since a smaller distance between the holes reduces the critical stress for buckling, it is also required to optimize this value. Finally, a variety of factors, including fiber orientation, composite type, and thickness, influence the buckling performance of thin-walled composite structures.

This is a list of specific laminated composites that can be analyzed for the effects of buckling analysis, failure mode, the effect of cutouts, and the effect of fiber orientation:

• 1.Carbon fiber reinforced polymer (CFRP) composites
• 2.Glass fiber reinforced polymer (GFRP) composites
• 3.Aramid fiber reinforced polymer (AFRP) composites
• 4.Hybrid laminates (combination of different fiber types, such as carbon and glass fibers)
• 5.Natural fiber reinforced polymer (NFRP) composites

These specific laminated composites can be subjected to analysis to understand their behavior and characteristics in terms of buckling analysis, failure mode (such as delamination or fiber breakage), the effect of cutouts (different shapes, sizes, and orientations), and the effect of fiber orientation (angle ply or cross-ply configurations). Analyzing these composites can provide insights into their structural performance and guide the design and optimization of thin-walled composite structures.

4. Soft Computing Approaches

Utilizing laminates increases design flexibility and provides greater control to modify the material to satisfy regional design specifications. However, compared to isotropic materials, the laminate design presents a far greater challenge in terms of sizing, optimization, and rules for spatial variation.⁴⁸ Mathematical optimization is an obvious method for the design of laminated composite structures due to the possibility of achieving an effective design that satisfies the overall criteria and the challenge of choosing values from a vast set of limited design variables.⁴⁹

4.1. Genetic Algorithms

At the University of Michigan in the 1970s, John Holland is credited with coming up with the concept of a genetic algorithm. Holland was more interested in developing artificial systems based on the laws of natural selection than systems that are based on a particular thought process. These artificial systems could be built with the use of computer software and used in several areas that place a strong emphasis on design, optimization, and machine learning. Neural networks and genetic algorithms are entirely separate ideas with quite different applications. To identify ideal or nearly ideal solutions to search and optimization issues, genetic algorithms are search-based optimization algorithms. On the other hand, neural networks are mathematical models that represent the mapping between intricate inputs and outputs. Genetic algorithms are search techniques that use a population of designs and mimic biological evolution. Figure 7 shows some basic differences between genetic algorithms and neural networks.

Figure 7.

Genetic algorithm and neural networks.

Genetic algorithms are ideally adapted to solve the combinatorial challenge of designing composite laminates. However, even for a single laminate, thousands of tests may be needed for genetic optimization. As a result, it is crucial to adapt common genetic algorithms to the unique issues related to composite laminates. Stacking sequence optimization issues are ideally suited for genetic algorithms. They cope with combinatorial issues with ease and provide many potential solutions with ease. Their primary drawback is that dozens or even millions of analyses are typically needed. The vast number of necessary analyses is not a concern because the computational costs of a single study are typically relatively inexpensive for many laminate design problems. Figure 8 shows the pictorial representation of a genetic algorithm.

Figure 8.

Generic Algorithm

Reference (50) presents a method for the design optimization of composite laminated structures. A genetic algorithm (GA), connected to the finite element method (FEM) for structural analysis, is used to carry out the optimization process. Bagheri et al. carried out⁵¹ the multiobjective optimization of ring-stiffened cylindrical shells using the GA method. The objective functions look for the shell’s largest fundamental frequency and lowest structural weight while being constrained by four factors: structural weight, axial buckling force, and radial buckling load. The shell thickness, the number of stiffeners, the size and height of the stiffeners, the eccentricity distribution order of the stiffeners, and the spacing distribution order of the stiffeners are the six design factors included in the optimization process. It has been demonstrated in the past that the extended finite element formulation (XFEM) and GAs work very well together to find structural defects. This method converges to the real defect by modeling the forward problem using the XFEM and using a GA as the optimization strategy. Reference (52) suggests various improvements to the XFEM-GA method, most notably a unique genetic algorithm that quickens the scheme’s convergence and reduces entrapment in local optima.

A composite laminate can be created using different combinations of straight-fiber layers or as a matrix that embraces fibers that are placed along curved routes. The former is referred to as a constant stiffness design, whereas the latter is referred to as a variable stiffness design. Reference (53) focuses on the variable stiffness design of composite laminates. Reference (54) compares three popular genetic algorithms: the neighborhood cultivation genetic algorithm (NCGA), the archive-based micro genetic algorithm (AMGA), and nondominate sorting genetic algorithm II (NSGA-II). It considers three alternative beginning population tactics. Their performance was compared in terms of solution, computation time, and generational number. To optimize the reaction of a composite laminate subject to impact, a GA was used.⁵⁵ The two impact scenarios that are discussed are the high-velocity impact of a spherical impactor on a rectangular plate and the low-velocity impact of a thin laminated strip. By adjusting the ply angles in both situations, the GA sought to minimize the peak deflection and penetration, respectively.

In a study by Karakaya and Soykasap,⁵⁶ biaxial in-plane compressive stresses were applied to a composite panel that was simply supported on four sides and subjected to the genetic algorithm and generalized pattern search algorithms to determine the best stacking order. Hybrid composite structures (HCSs) are made of alternating layers of metal sheets and fiber-reinforced polymer. By combining a multiobjective GA and a resilient design technique, a new methodology may be used to enhance the mechanical properties and responsiveness of HCSs for off-design scenarios.⁵⁷ The approach of optimum design for laminated composite structures utilizing the GA and FEM for single-material and hybrid laminates is covered in ref (58). For 3-D finite element analysis, eight-nodded layered elements have been used. To determine the best combination of laminate sequences for hybrid composite structures, an optimization approach using a distributed/parallel multiobjective genetic algorithm is connected with an analysis tool for composite structures.⁵⁷

The objective of the study reported in ref (2) was to assess the impact of various parameters in the context of composite structure optimization. It was performed on all potential orientations and the makeup of the component materials. A genetic algorithm was used to solve issues with optimizing simple plates and structures that were modeled using finite elements. Because of their computational cost, nonelites approach, and requirement to provide a sharing parameter, multiobjective evolutionary algorithms (EAs) that use nondominated sorting and sharing have drawn significant criticism. Deb et al.⁵⁹ proposed a nondominated sorting genetic algorithm II (NSGA-II), a multiobjective EA (MOEA) that overcomes all three of the aforementioned issues. In order to determine how to distribute glass fiber reinforced polymer and concrete in a hybrid deck system and carbon fiber reinforced polymer and steel in a hybrid cable system, Cai and Aref⁶⁰ created a GA-based optimization approach. The goal of the work by Shrivastava et al.⁶¹ was to use a traditional GA in conjunction with a CAE solver to reduce the weight of multilaminate aerospace structures. Structural weight minimization is a multiobjective optimization issue that must also satisfy the design constraints for strength and stiffness.

Sliseris and Rocens⁶² suggested a new optimization method for composite plates with discretely variable stiffness. There are three main steps to it. The first phase involves analyzing the best continuous variable bending and shear stiffness of the plate while reducing structural compliance and stress field variations. The second phase involves using a GA to solve a minimization problem to optimize the size of discrete domains. Park et al.⁶³ proposed novel strategies to decrease the number of fitness function assessments in GAs used for the transdisciplinary optimization of composite laminates.

4.2. ML Algorithms

In composite structure design, structural analysis is commonly employed. Typically, the mechanical properties of different designs are evaluated numerically using finite element analysis (FEA). However, this approach often involves expensive multiphysics computational calculations. The goal is to produce lighter laminates with increased strength while reducing costs and efficiently collecting data for composite optimization. Nevertheless, a major drawback of numerical simulation is the high computational cost associated with setting up model properties and solving complex differential equations. To expedite the FEA process, one approach is to leverage ML and optimization techniques, which have demonstrated great success in various industries, including manufacturing and materials design. ML can work directly on predefined input parameters and automatically predict simulation results, eliminating the need for manual design of composite structures and FEA setups. ML enables researchers to assess the importance of different features and quickly modify design parameters due to its rapid and accurate prediction of FEA outcomes. This technique can potentially be applied to simulate composite laminate structures as well. Many studies have focused on utilizing ML and surrogate modeling techniques to predict the mechanical properties of composite laminates, such as strength and modulus. These methods provide result-oriented predictions that specify design characteristics. However, they may present challenges when attempting to predict process-oriented outcomes, such as the displacement field of an entire structure. ML plays a crucial role in anticipating failure modes, such as delamination, in the fracture process of composite materials. These ML applications can be combined with popular optimization techniques such as genetic algorithms. Figure 9 illustrates the various types of machine learning employed in this context.

Figure 9.

Types of machine learning.

A groundbreaking study⁶⁴ marked the first instance of utilizing machine learning approaches to predict the statistical design allowable for composite laminates. The study employs four machine algorithms (XGBoost, Random Forests, Gaussian Processes, and Artificial Neural Networks) to predict the notched strength of composite laminates and their statistical distribution, considering uncertainties related to material properties and geometric features. In another research effort,⁶⁵ a structural health monitoring system for smart composite structures was developed using signal processing, deep learning algorithms, and optimization theory. Smart composite fabrics, embedded with piezoelectric ribbon sensors, are integrated into composite laminates to enable self-monitoring capabilities. Saberi et al.⁶⁶ employed a deep learning approach using artificial neural networks to determine the free vibration parameters of rectangular bistable composite plates. This marks the first instance of applying deep learning to analyze the behavior of such plates.

To optimize and expedite the design process of composite laminates, Sorrentino⁶⁷ presented a theory-guided ML model that combines the Hashin failure theory (HFT) and the classical lamination theory (CLT). The model utilizes a training data set generated through finite element simulations that incorporate the HFT and CLT. Rather than directly mapping the relationship between the laminate’s strength and stiffness and its ply angles, a multilayer interconnected neural network (NN) system is constructed, following the logical progression of composite theories. Table 2 provides an overview of the types of machine learning algorithms employed in recent studies.

Table 2. Machine Learning Algorithm Used.

reference	machine learning mechanism
(64)	XGBoost, Random Forests, Gaussian Processes, and Artificial Neural Networks
(65)	signal processing, deep learning algorithms
(67)	theory-guided ML model that integrates the HFT and CLT
(68)	ML based on convolutional NN architecture
(69)	FEA and ML

To develop a reliable tool capable of automatically analyzing void content in optical microscope images without requiring parameter tuning, a machine-learning approach based on a convolutional neural network architecture was proposed.⁶⁸ Zhang et al.⁶⁹ introduced a method that combines FEA with machine learning to assess various mechanical properties of composite laminates. This approach is applied to three examples, including the determination of failure factors and critical buckling eigenvalues in open-hole laminates. A data-rich framework was proposed in⁷⁰ to accurately describe the macroscopic strain-softening response of laminated composites under compressive loading. The framework begins by simulating compact compression tests of quasi-isotropic IM7/8552 carbon fiber-reinforced polymers using an efficient continuum damage FE model to create a substantial virtual data set for training ML models. Two ML approaches are then trained and compared: one employs a theory-guided neural network architecture to address the forward FE problem, while the other utilizes recurrent neural networks with long short-term memory (LSTM) architecture. Table 3 provides a summary of different optimization techniques used in recent studies, along with their respective objectives.

Table 3. Optimization Techniques.

reference	algorithm	objective
(51)	genetic algorithm	to look for the shell’s largest fundamental frequency and lowest structural weight
(53)	genetic algorithm	variable stiffness design of composite laminates
(55)	genetic algorithm	optimize the reaction of a composite laminate subject to impact
(57)	genetic algorithm	to determine the best combination of laminate sequences for hybrid composite structures
(56)	genetic algorithm	to determine the best stacking order
(64)	machine learning	the statistical design allowable for composite laminates are being predicted
(65)	machine learning	to develop a system for monitoring the structural integrity of intelligent composite structures
(66)	machine learning	the characteristics of free vibrations in rectangular bistable composite plates are identified.
(68)	machine learning	to offer a reliable tool capable of automatically analyzing the void content in optical microscope images without requiring manual parameter adjustments
(70)	machine learning	to accurately characterize the overall strain-softening behavior of laminated composites under compressive loads

5. Critical Analysis of the Review

Todoroki and Ishikawa⁷¹ introduced a novel experimental design method to obtain the response surface of the buckling load in laminated composites. The paper proposes and thoroughly investigates this innovative approach to experimental design. Since lamination parameters cannot be directly applied to most analytical tools, these tools typically require stacking sequences as input data. Therefore, the present study suggests a new D-optimal set of laminates for stacking sequence optimizations to maximize the buckling stress of a composite cylinder. Using D-optimality, a set of stacking sequences is selected from a group of candidate stacks that form the new experimental design. The study demonstrates that this D-optimal set of laminates proves valuable in designing trials of response surfaces to maximize the buckling load. Soares et al.⁷² developed discrete models for sensitivity analysis and optimization of thick and thin multilayered angle ply composite plate structures. The models utilize an improved shear deformation theory that accounts for nonlinear variations in the displacement field. These models are employed to analyze the response and optimize the performance of the composite plate structures.

The goal of the study in ref (73) was to make large composite plastic parts’ production procedures and structural design as efficient as possible. The primary focus is on reinforcing the plastic-prepared shell by adjusting the reinforcement layer’s material concentrations and adding layers of glass–fiber composite material of varying thicknesses. By concurrently reducing cost and production time, the part’s ultimate attributes are established. The process of multistage optimization has been used. The study in ref (74) used a parallel/distributed evolutionary algorithm to optimize the stacking sequence design for multilayered composite plates. In order to improve the lay-up of the skin of an I-stiffened composite panel and increase its damage resistance in the postbuckling regime, an automated optimization approach was provided.⁷⁵ To construct laminated composite beams with the most stiffness and the least amount of weight, the best fiber orientations and laminate thicknesses were identified.⁷⁶ Beam finite elements are used to assess the structural reaction, properly accounting for the impact of cross-section geometry and fiber orientation.

Due to increasing environmental concerns and the demand for sustainable engineering materials, the use of biofibers as a substitute for synthetic fibers in composites has gained popularity. Megahed et al.⁷⁷ focused on reducing the weight and cost of a symmetric laminated composite beam while maintaining a certain lower bound constraint on its natural frequency. Optimal designs of hybrid composite beams are explored under various boundary conditions. Marouahi et al.⁷⁸ proposed an experimental methodology to investigate the durability of FRP (fiber reinforced polymer) composites used in civil and structural engineering. Carbon-based composites, including carbon epoxy and carbon vinyl ester, undergo accelerated aging tests to simulate real working conditions in the natural environment. The tests involve thermal, hygrometric, chemical, thermochemical, hydrothermal, and freezing–thawing cycles over an 18-month period.

The use of D-optimal designs and ANN to predict the deflection and stresses of a square laminated composite plate made of carbon fiber reinforced plastic CFRP under uniform loading was discussed.⁷⁹ D-optimal designs are employed in finite element calculations to train and test the ANN model while considering variations in fiber orientations and lamina thickness. Sayyad et al.⁸⁰ applied a generalized higher-order shell theory to determine closed-form solutions for static bending and free vibration analysis of laminated composite and sandwich spherical shells. The study in ref (81) utilized an iterative method to study the free edge interlaminar stresses in composite laminates subjected to extension, bending, twisting, and heating loads. The stresses are obtained by applying the complementary virtual work and extended Kantorovich approach, satisfying the traction-free criteria at free edges and top/bottom surfaces of the laminates through iterative application of static and kinematic continuity conditions.

Analysis of interlaminar stresses near the free edges of general cross-ply composite laminates was conducted using a layer-wise theory.⁸² The study in ref (83) demonstrated the capability of a multiparticle finite element to simultaneously predict global and local reactions for generic materials. A repeatable experiment to estimate the tensile strength distribution in FRP bars was presented,⁸⁴ along with the associated test procedure and outcomes.. Khatir et al.⁸⁵ proposed a new method based on ANN and particle swarm optimization (PSO) for damage estimation in laminated composite plates using the Cornwell indicator (CI). Madeira et al.⁸⁶ discussed the optimal design of laminated sandwich panels with a viscoelastic core, aiming to reduce weight and material costs while increasing modal damping. Regarding waste utilization, research was conducted on the use of waste materials in concrete.⁸⁷ Waste products from manufacturing activities, service sectors, and municipal solid wastes pose significant environmental challenges. The study in ref (88) examined the possibility of utilizing recycled plastic bottles (RPET) and woven plastic bags (RWS) as reinforcement for recycled aggregate concrete (RAC), aiming to explore sustainable alternatives to traditional concrete reinforcement.

Through the twin screw extrusion technique, efforts have been undertaken¹⁰ to examine the behavior and properties of the recycled PA6 polymer to increase its recyclability (as the primary recycling process). Table 4 presents the summary of recent work in this field.

Table 4. Critical Analysis of the Literature Review.

reference	methodology	objective
(71)	implementing a novel D-optimal collection of laminates for optimizing stacking sequences	to maximize the buckling stress of a composite cylinder
(72)	employing an enhanced shear deformation theory that considers a nonlinear variation in the displacement field	discrete models are created to analyze the sensitivity and optimize the thickness and thinness of the materials. multilayered angle ply composite plate structures
(73)	adjusting the reinforcement layer’s material concentrations and adding layers of glass-fiber composite material of varying thickness	reinforcing the plastic prepared shell
(74)	using a parallel/distributed evolutionary algorithm	to optimize the stacking sequence design for multilayered composite plates
(76)	identifying the best fiber orientations and laminate thicknesses	to construct laminated composite beams with the most stiffness and the least amount of weight
(79)	employing D-optimal designs in experimental design (DOE) and artificial neural networks (ANN)	to forecast the deflection and stresses of a square laminated composite plate made of carbon fiber reinforced plastic (CFRP) that is being loaded uniformly
(80)	generalized higher-order shell theory is used	to obtain closed-form solutions of higher order for analyzing the static bending and free vibration of laminated composite and sandwich spherical shells
(81)	an iterative method has been used	to study the free edge interlaminar stresses of composite laminates
(85)	proposed approach utilizing artificial neural network (ANN) and particle swarm optimization (PSO) method	estimating damage in laminated composite plates using the Cornwell indicator (CI) method

5.1. Research Gap

The design of composite thin-walled structures needs careful consideration of structural and mechanical parameters because each parameter for a given structure will result in a distinct set of buckling loads. As composites is not a specialized industry and offers virtually limitless possibilities to combine and build the item, the design of composites adds another level of complexity. Because they are either designed for any kind of structures. As a result, present work either has an approach that is too general or too component specific. Therefore, proposing and using more efficient design for c-section thin-walled composite channel. The extensive literature survey conducted in this study clearly indicates that the optimization of laminated composites under various loading conditions remains an active and ongoing area of research. It is evident that new techniques for optimizing laminated composites reveal a promising opportunity for enhancing the analysis, especially when considering different components of a composite structure to achieve the most optimal design. Most of the existing optimization efforts have centered around genetic algorithms, while the utilization of modern machine learning approaches for optimization remains scarce in the literature. This highlights a significant gap that can be explored and leveraged to further improve the optimization process for laminated composites. Furthermore, the literature review reveals a limited amount of research focused on the thermal buckling of laminated thin-walled structures with holes. Additionally, the optimization of such structures has been largely unexplored and lacking in the existing body of literature. These findings underscore the importance of investigating and optimizing these specific types of structures to advance our understanding and design capabilities in this field.

6. Conclusion and Recommendations

Composite materials are composed of multiple materials that collaborate to achieve properties that would be unattainable for the individual components alone. Currently, both major and secondary constructions extensively utilize composite laminates. Composite laminates offer numerous advantages, including design flexibility, cost-effectiveness, enhanced productivity, chemical resistance, consolidated functionality, corrosion resistance, durability, and more. This Review emphasizes the significance of composite materials and explores their diverse applications. Furthermore, it delves into optimization methods such as genetic algorithms and machine learning algorithms, providing a comprehensive explanation of their relevance. Moreover, this Review serves as a guide for scientists seeking to implement composite laminates in engineering structures. It offers detailed descriptions and analyses of the literature concerning composite material applications. Additionally, it presents an overview of research areas within the field of composite materials. By identifying research gaps, researchers can gain insights and identify opportunities for new ideas, especially during the early stages of this research domain. In conclusion, these research gaps provide valuable perspectives and indices to facilitate advancements in various research areas related to composite materials. They serve as a catalyst for researchers to develop innovative ideas, particularly in the nascent phases of this research field.

The authors declare no competing financial interest.