Nonlinear Static Stability of Imperfect Bio-Inspired Helicoidal Composite Beams

The objective of this manuscript is to develop, for the first time, a mathematical model for the prediction of buckling, postbuckling, and nonlinear bending of imperfect bio-inspired helicoidal composite beams with nonlinear rotation angle. The equilibrium nonlinear integrodifferential equations of imperfect (curved) helicoidal composite beams are derived from the Euler–Bernoulli kinematic assumption. The differential integral quadrature method (DIQM) and Newton-iterative method are employed to evaluate the response of imperfect helicoidal composite beams. Following the validation of the proposed model, numerical studies are performed to quantify the effect of rotation angle, imperfection amplitude, and foundation stiffness on postbuckling and bending behaviors of helicoidal composite beams. The perfect beam buckles through a pitchfork bifurcation. However, the imperfect beam snaps through the buckling type. The critical buckling load increases with the increasing value of elastic foundation constants. However, the nonlinear foundation constant has no effect in the case of perfect beams. The present model can be exploited in the analysis of bio-inspired structure, which has a failure similar to a metal and low interlaminar shear stress, and is used extensively in numerous engineering applications.