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A THREE‐DIMENSIONAL FINITE ELEMENT FORMULATION FOR THERMOVISCOELASTIC ORTHOTROPIC MEDIA
Author(s) -
ZOCHER M. A.,
GROVES S. E.,
ALLEN D. H.
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19970630)40:12<2267::aid-nme156>3.0.co;2-p
Subject(s) - orthotropic material , finite element method , mathematics , algebraic equation , viscoelasticity , relaxation (psychology) , moduli , mathematical analysis , boundary value problem , simple (philosophy) , quasistatic process , nonlinear system , materials science , structural engineering , physics , engineering , psychology , social psychology , philosophy , epistemology , quantum mechanics , composite material
This paper is concerned with the development of 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 form 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. © 1997 John Wiley & Sons, Ltd.