Dynamic analysis of pseudoelastic SMA beam

The main goal of this work is to present a formulation of initial-boundary-value problem for the Bernoulli-Euler beam made of pseudoelastic shape memory alloy (SMA). The procedure of formulation of 1D constitutive relations based on the analysis of the proposed rheological model is presented in detail. The relationships to be obtained are of explicit type and were formulated within the notion of non-smooth mechanics using the so-called differential successions of constitutive equations. The system of partial differential equations is discretized with respect to spatial coordinates using the finite difference method. This procedure leads to the system of ordinary differential equations with respect to the time coordinate, which was solved using the Runge-Kutta method. The problem was coded within MATLAB system. A numerical example of a beam structure subjected to concentrated Heaviside-type loading was analysed.