A viscoelastic efficient higher-order plate theory

Abstract

An efficient higher-order plate theory for viscoelastic materials is developed to obtain the accurate and efficient time-dependent mechanical behaviors of composite laminates. In-plane displacement fields are constructed by superimposing a cubic varying displacement field on a linear zigzag varying field. Time-dependent relaxation modulus has the form of Prony series which can be determined by the master curve based on experimental data. The constitutive equation which has the form of Boltzmann superposition integral for linear viscoelastic materials is simplified by convolution theorem in the Laplace transformed domain to avoid direct integration as well as to improve both computational accuracy and efficiency. Moreover, by using linear elastic stress-strain relationship in the corresponding Laplace domain, the transverse shear stress free conditions at the top and bottom surfaces and the transverse shear stress continuity conditions at the interface between layers can be satisfied conveniently to reduce the number of primary unknown variables. To validate the present theory, the viscoelastic responses in the real time domain are obtained through various numerical inverse Laplace transforms. The numerical results for graphite/epoxy GY70/339 material are obtained and compared with the solutions of elastic composite laminated plates.