Multi-objective optimization of snap-through instability of helicoidal composite imperfect beams using Bernstein polynomials method

This paper deals with the multi-objective optimization problems of snap-through instabil-ity of geometrically imperfect simply supported helicoidal composite beam with nonlinear orientation schemes. The objective function is to maximize the load required to initiate snap-through and minimize the instability region. It is assumed that the curved bioin-spired beam is embedded on nonlinear elastic foundation and is subjected to different types of lateral loads. The presented formulation is based on Euler-Bernoulli theory, non-linear higher order strain, and imperfect curvature. Bernstein polynomials (BPs) method is employed to solve the nonlinear nonhomogeneous fourth order integro-differential gov-erning equation. Developed model can considered the effect of imperfection, lamination scheme, and elastic foundation on the nonlinear deflection and snap-through behaviors of helicoidal composite structures. Analytical closed form formula of the nonlinear load-deflection relationship is developed. The analytical relation is validated by comparing it with exact solution and numerical results available in literature. Multi-objective particle swarm optimization (MOPSO) algorithm is employed to determine Pareto-optimal set for limiting load and region of instability. In these analyses, optimal lamination parameter, am-plitude of imperfection and elastic foundation constants are found for helicoidal composite beam, and the results are presented as 2D Pareto-optimal design points. (c) 2023 Elsevier Inc. All rights reserved.