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A SEMI-ANALYTICAL METHOD FOR SOLUTION OF THE LINEAR VISCOELASTICITY PROBLEMS

A SEMI-ANALYTICAL METHOD FOR SOLUTION OF THE LINEAR VISCOELASTICITY PROBLEMS,Yuri CHORNOIVAN

A SEMI-ANALYTICAL METHOD FOR SOLUTION OF THE LINEAR VISCOELASTICITY PROBLEMS  
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Developing the ideas of work (1) �k onsidered is the problem of stress-strain state determination for linearly viscoelastic anisotropic body in case when the solution of the corresponding elastic problem can be found numerically. It is proposed to find viscoelastic solution using continued fraction approximation of the stress or strain at hand as a function of elastic constants. This approximation can be obtained numerically by any efficient numerical method (e.g. BEM). If only the Volterra principle is valid the solution can be found using resolvent operators' algebra. The possible error minimization is made via method of rational approximation by Stoer. An algorithm of the solution as well as estimation of the possible error is presented. The advantages of the proposed technique applied to contact and fracture problems of linear viscoelasticity are discussed. As an example the solution of the stress concentration determination problem for orthotropic viscoelastic plane with rigid circular inclusion is given as well as the comparison with the earlier results obtained from the analytical solution.
Published in 2007.
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