Layerwise/FSDT comparative studies on nonlinear transient response of SMA hybrid composite beam

Abstract

A comprehensive study is provided to compare the results of layer-wise theory (LWT) with one of the renowned equivalent single layer beam theories (ESLs) known as First-Order shear deformation beam theory (FOBT) on the study of transient nonlinear dynamic response of an SMA reinforced composite beam. Considering von Karman strain–displacement formulations, the governing equations of forced vibrations under transient impulsive loads are formulated by LWT and ESL methods. In order to simulate the constitutive behavior of SMA wires, the 3D SMA model developed by Panico and Brinson is adopted and reduced to a 1D model which enables one to reproduce pseudo-elastic (PE), martensite transformation/orientation and in particular ferro-elastic (FE) effects. General transient transverse loading is considered and the governing equations are discretized by combined method of differential–integral quadratures (DQ-IQ). Based on Newmark time marching technique, an incremental solution algorithm is developed for the problem in which nonlinear governing equations are solved by Newton–Raphson method. The results are assessed by comparing with available literature. Moreover, the FOBT and layerwise solutions are compared with each other and the effects of layup geometry and boundary conditions upon the composite beam responds are explored. The influence of volume fraction of SMA-wire reinforcements and the FE/PE behaviors of the wires upon the diverging results of FOBT/LWT analyses are studied in detail.