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The Initial Value Problem for the General Dynamic Equations in Nonlinear Elasticity Theory
Author(s) -
Beckert H.
Publication year - 1982
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19820620802
Subject(s) - quasistatic process , elasticity (physics) , mathematics , nonlinear system , mathematical analysis , dynamic problem , convergence (economics) , dynamic equation , initial value problem , simple (philosophy) , mathematical optimization , physics , quantum mechanics , thermodynamics , philosophy , epistemology , economics , economic growth
In this paper the initial value problem for the general dynamic equations in an elastic continuum is solved. At first, we introduce a new form for these equations and define a simple approximation for the solutions of our problem along a difference scheme in the time direction calculating the changing stress configurations as in the authors theory for quasistatic deformations in nonlinear elasticity [1], [2]. The convergence of this approximation to the solution of the initial value problem above is proved. In the last chapter this theory is generalized to include damping material.