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An investigation of the stability of numerical solutions of the equations of viscoelasticity
Author(s) -
Booker J. R.,
Small J. C.
Publication year - 1977
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/nme.1620111206
Subject(s) - laplace transform , mathematics , viscoelasticity , laplace transform applied to differential equations , finite element method , stability (learning theory) , numerical stability , mathematical analysis , elasticity (physics) , inverse laplace transform , integral equation , two sided laplace transform , volterra integral equation , numerical analysis , computer science , engineering , physics , fourier analysis , structural engineering , fourier transform , machine learning , fractional fourier transform , thermodynamics
In this paper the correspondence principle is used to reduce the equations of viscoelasticity to the equations of elasticity by means of a Laplace transform. The finite element technique is used to approximate these equations in Laplace transform space. The approximating equations are then inverted to obtain a set of simultaneous Volterra integral equations. It is then shown how the introduction of certain auxiliary variables can be used to develop an integration scheme which considerably reduces computer storage requirements. The conditions under which this integration scheme is conditionally stable and unconditionally stable are both investigated and illustrated by means of examples.