Solution of dynamic problems for piecewise-homogeneous bodies of finite dimensions by the method of R-functions (Q2754701)
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scientific article; zbMATH DE number 1668357
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solution of dynamic problems for piecewise-homogeneous bodies of finite dimensions by the method of R-functions |
scientific article; zbMATH DE number 1668357 |
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4 November 2001
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elastodynamics
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piecewise-homogeneous solid
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variational method
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finite differences
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minimization of functional
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Solution of dynamic problems for piecewise-homogeneous bodies of finite dimensions by the method of R-functions (English)
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An algorithm for solving problems of non-stationary dynamics of elastic solids, based on simultaneous application of the R-function method, the variational method and the finite difference approach, is suggested. The essential point of the approach is constructing some expressions for the displacements that would be defined inside the elastic solid, contain some arbitrary functions and satisfy boundary conditions (identically with respect to those functions) and conditions at the interfaces. Corresponding expressions for boundary conditions in stresses, in displacements and in the mixed boundary-value problem are given. In all cases, undefined components of solutions are determined by expanding them in some complete systems of functions (e.g., orthogonal polynomials or splines). The coefficients of expansions are found in the process of minimization of some functional.
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