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A three-dimensional finite element formulation for thermoviscoelastic orthotropic media. (English) Zbl 0888.73067
Summary: This paper develops a numerical algorithm for the solution of the uncoupled, quasistatic initial boundary value problem involving orthotropic linear viscoelastic media undergoing thermal and/or mechanical deformation. The constitutive equations, expressed in integral from involving the relaxation moduli, are transformed into an incremental algebraic form prior to development of the finite element formulation. This incrementalization is accomplished in closed form and results in a recursive relationship which leads to the need of solving a simple set of linear algebraic equations only for the extraction of the finite element solution. Use is made of a Dirichlet-Prony series representation of the relaxation moduli in order to derive the recursive relationship and thereby eliminate the storage problem that arises when dealing with materials possessing memory. Three illustrative example problems are included to demonstrate the method.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74K15 Membranes 74E10 Anisotropy in solid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010)
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