Behavior of a rhombus frame of nonlinear elastic material under large deflection

The large-deflection spring behavior of an inextensible thin rhombus frame is studied in this work. The frame has a rectangular cross-section and supports two equal and opposite diagonal forces that act on its two opposite corners with a given apex angle γ. Both geometrical and material nonlinearities have been considered in the study. The beam was assumed to be made of a material having a nonlinear stress–strain relationship of the Ludwick type.A semi-analytical solution has been formulated for the relation between the large displacement at the corners of the frame and the applied forces. The deformed shapes and the nonlinear secant stiffnesses of the rhombus frame were plotted against applied loads. The frame behavior was fully investigated for different apex angles and nonlinear elastic material constants, n.In order to check the accuracy and efficiency of the proposed analytical solution, a large-displacement finite-element analysis utilizing the multi-purpose computer program ADINA was performed. Each side of the rhombus frame was divided into 10 moment–curvature beam elements. Results obtained using the analytical solution were identical to the results obtained using the software ADINA.