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Multi-operator boundary value problems of viscoelasticity of piecewise-homogeneous bodies

Research paper by Valeriy Matveenko, Nikolay Trufanov

Indexed on: 07 Sep '11Published on: 07 Sep '11Published in: Journal of Engineering Mathematics



Abstract

This article deals with multi-operator boundary value problems in viscoelasticity, in particular problems concerning composite bodies which, being inhomogeneous as a whole, are composed of different homogenous viscoelastic materials. It is shown that by application of the Volterra principle, the solution of the viscoelastic problem for a piecewise-homogeneous body can be readily reduced to a purely mathematical problem of involving the construction linear operators which, in most cases, are very complicated functions of several independent operators characterizing the viscoelastic properties of the structural elements. The solutions to the specified class of problems are found using two effective methods: (1) a version of the approximate method of quasi-constant operators using partial approximations and (2) the method of constructing a solution as a series expansion in powers of the Il’yushin hereditary operators. This article presents a detailed description of the methods and gives several examples of their numerical evaluation.