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

Applications of the symplectic method in quasi-static analysis for viscoelastic functionally... PurposeFor 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/approachFirstly, 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.FindingsIn the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints.Originality/valueThe paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

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

Zhang, W.X.; Liu, R.G.; Bai, Y.
Engineering Computations , Volume 34 (4): 18 – Jun 12, 2017
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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0264-4401
DOI
10.1108/EC-02-2016-0063
Publisher site
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Abstract

PurposeFor 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/approachFirstly, 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.FindingsIn the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints.Originality/valueThe paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

Journal

Engineering Computations – Emerald Publishing

Published: Jun 12, 2017

References

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