FIG. 1.
Results from Elastica3D were a good match to analytical and FEM solutions of whisker bending. (a) A nondimensional plot of whisker bending is reproduced from Mattiasson26 figure 5.2, and results from Elastica3D are overlaid. The value on the y-axis is determined by the magnitude of the applied force (Fapplied) and the arc length at which the force was applied (sapplied). The values on the x-axis show the amount of deflection at the point of contact in the x- and y-directions (u and w, respectively) normalized to sapplied. The blue lines reproduce Mattiasson's values, and the colored regions bordered by black and red lines represent the results from Elastica3D. The coloring within the regions is determined by the angle of deflection, which is directly related to the values u/sapplied and w/sapplied. The coloring emphasizes that larger angles of deflection result in larger errors. The black lines are the deflections when sapplied was set to its smallest value (10 mm or 29% of the whisker arc length), and the red lines are the deflections for a much larger value of sapplied (30 mm or 86% of the whisker arc length). When sapplied was greater than 30 mm, the whisker was not able to deflect through as large an angle and, therefore, does not extend out as far along the x-axis. The green dots and boxes mark three specific examples in which the identical force was applied to the FEM model and Elastica3D. Boxes mark the analytical solution, and dots mark the Elastica3D solution. (b) This diagram depicts the variables used in (a). The gray line is the undeflected straight, cylindrical whisker, and the blue line is the whisker shape once the force has been applied. The values of u and w show the amount of deflection at the point of applied force in the x and y directions, respectively. (c) A comparison of the FEM solution and the Elastica3D solution for a tapered whisker with intrinsic curvature. The undeflected whisker shape is shown in gray. Results for the deflected whisker shape from the FEM (blue) and Elastica3D model (black) are indistinguishable in the plot. The 3D contact points from the two models are plotted in blue and gray and are also indistinguishable. 3D, three-dimensional; FEM, finite element model.