Thermoviscoelastic analysis of composite structures using a triangular flat shell element

Abstract

To accurately model the structural response of fiber-reinforced polymer-matrix composites, it is necessary to account for viscoelastic behavior of the polymer matrix. Therefore, the geometrically linear dynamic analysis capability of a recently developed triangular flat shell element for elastic composite structures is extended here to include thermoviscoelasticity. The flat shell element is the combination of the discrete Kirchhoff theory plate bending element and a membrane element similar to the Allman triangle, but derived by transforming the linear strain triangle element. Linear viscoelastic composite materials are modeled, resulting in the relaxation moduli being expressed as Prony series. Hygrothermorheologically simple materials are considered for which a change in the hygrothermal environment results in a horizontal shifting of the relaxation moduli curves on a log timescale, in addition to the usual hygrothermal loads. The resulting hereditary integral terms are evaluated using a recursion relationship requiring only the previous two solutions. The Newmark method is used to incorporate the inertia terms. Numerical examples are presented to demonstrate the accuracy of the present formulation when compared with correspondence principle solutions and results available in the literature.