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Matrix differential equation and higher‐order numerical methods for problems of non‐linear creep, viscoelasticity and elasto‐plasticity
Author(s) -
Bažant Z. P.
Publication year - 1972
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.1620040104
Subject(s) - viscoelasticity , creep , plasticity , ordinary differential equation , mathematics , constitutive equation , finite element method , matrix (chemical analysis) , mathematical analysis , differential equation , materials science , structural engineering , physics , engineering , thermodynamics , composite material
The constitutive equation is assumed in a very general form which includes as special cases non‐linear creep, incremental elasto‐plasticity as well as viscoelasticity represented by a chain of n standard solid models. Subdividing the structure into N finite elements, the problem of structural analysis is formulated with a system of 6 N ( n + 1) ordinary non‐linear first‐order differential equations in terms of the components of stresses and strains in the elements. This formulation enables one to apply Runge–Kutta methods or the predictor–corrector methods.