Snap-through instability of helicoidal composite imperfect beams surrounded by nonlinear elastic foundation

Bernstein polynomials are exploited, for the first time, in investigation of the nonlinear bending and snap -through instability phenomena of geometrically imperfect bioinspired composite beams with helicoidal orien-tation scheme. The curved bioinspired beam subjected to different types of lateral loading and embedded on three parameters elastic foundations is considered in formulation and analysis. The nonlinear equilibrium equation of the system based on Euler-Bernoulli beam hypothesis, von K ' arm ' an nonlinear strain, and initial imperfect curvature is developed. The equilibrium equation portrayed by nonlinear fourth order integro-differential equation is solved by Bernstein polynomials method and closed form solution of the load -deflection relationship is obtained. The accuracy of the present model and solution procedure is examined by comparing our results with previous results. The developed model is exploited to present the influence of lamination scheme, amplitude of initial imperfection and elastic foundation constants on the nonlinear bending and snap-through/reverse snap-through behaviors in detail. The numerical results show that the Bernstein polynomials approach can capture successfully the nonlinear equilibrium path and overcoming limit (turning) points, which usually appear in the nonlinear response of curved structures. The developed model can be used in design and control the snap-through response and open opportunities for this type of structures in many real applications.