Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials

Abstract

Purpose

For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs.

Design/methodology/approach

Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods.

Findings

In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints.

Originality/value

The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

Citation

Zhang, W.X., Liu, R.G. and Bai, Y. (2017), "Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials", Engineering Computations, Vol. 34 No. 4, pp. 1314-1331. https://doi.org/10.1108/EC-02-2016-0063