Some Methods of Solving Problems of Non-Linear Thermo-Viscoelasticity
The formulation of the problems of non-linear thermo-viscoelasticity, including also coupled problems is given. For that purpose application of thermodynamics of irreversible processes to the visco-elastic media is analysed. Certain methods of subsequent approximations are presented for the solution of problems of non-linear theory of thermo-viscoelasticity, among other "rapidly convergent" method. The rate of convergence of these methods is analysed. Numerical methods are also considered, mainly the method of nets and the method of finite elements.
[On coupled problems of mechanics of a continuum, Selected works: «Elasticity and non-elasticity»],
[Plasticity (Foundations of the general theory)],
P. LÉVY, Problèmes corcrets d'analyse fonctionnelle, Deuxième edition, Paris 1951.
M. B. GURTIN, Eli STERNBERG, On the linear theory of viscoelasticity, Arch. Ration Mech. and Analys, 11, 4, 291 - 356, 1962.
C. TRUESDELL, W. NOLL, The non-linear field theories of mechanics, Handbuch der Physik, Band III/3, 1965.
[Equa-tions of state in the non-linear theory of viscoelasticity],
[Mathematical theory of non-linear viscoelasticity. Selected works: «Elasticity and non-elasticity»],
[Fundamental equations and theorems for a certain model of a physically non-linear medium],
[Quasi-linear theory of viscoelasticity and the perturbation method],
[A contribution to the problem of non-linear theory of viscoelästicity],
H. LEADERMAN, F. MC CRAKIN, O. NAKADA, Large longitudinal retarted elastic deformation of rubberlike network polimers, Trans. Soc. Rheology, N 7, 1963.
[The uniqueness theorem of coupled thermo-viscoelasticity],
[On the method of elastic solutions],
[The convergence of the method of elastic approximations in non-linear viscoelastincity],
[Some problems of existence and approximate solution for quasi-linear elliptic equations and sets of equations in S. L. Sobolev's spaces],
I. BABUSKA, I. HLVACEK, On the existencense and uniqueness of solution in the theory of viscoelasticity, Arch. Mech. Stos., 1, N 18, 1966.
[On a new method for solution of some quasi-static problems in non-linear continuum mechanics],
[Equations of mathematic physics],
[Equations of mathematic physics],
[Introduction into the theory of difference schemes],
[Introduction into the theory. of difference schemes],
[Method of small steps for solving multi-dimensional problems of theoretical physics],
[Difference methods for solving boundary-value problems],
[Fundamental notions of numerical analysis],
[Numerical solutions of problems of the theory of elasticity],
[Solution of boundary value problems of the plane theory of elasticity by means of digital and analogue computers
[Numerical methods in the theory of viscoelasticity],
[Difference methods for solving certain nonstationary systems. Selected works: «Applied mathematics and programming>],
[Numerical application of variational methods],
O.C. ZIENKIEWICZ, Y. K. CHEUNG, The finite element method in structural and continuum mechanics, Mc Graw-Hill Publ. Comp. Lim., NY, 1967.
J. T. ODEN. The finite element method in non-lineare continuum mechanics, Mc Graw-Hill Company, N.Y., 1972.
[Dependence of a solution in the theory of elasticity on the elastic constants],
[Computation of viscoelastic systems according to the numerical elastic method],
[Problem of coupling in the mechanics of polymers],
R. C. PETROF, S. GRATCH, Wawe propagation in a viscoelastic material with temperature-dependent properties and thermomechanical coupling, J. Appl. Mech., Series E, 31, 3, 1964.
[Numerical method for solving coupled problems of thermo-viscoelasticity],
[Algorithms in the theory of elasticity and the strain theory of plasticity],
[Algorithm system for solving, by means of an electronic computer, problems of the theory of elasticity and plasticity. Selected works: «Problems of numerical and applied ma thematics»,]