Abstract
AbstractThe initial–boundary value problems in the linear theory of elasticity is considered. Based on the method of integrodifferential relations (MIDR) two dynamical variational principles is proposed and discussed. It is shown that the Hamilton principle as well as the corresponding complementary principle stated for dynamic boundary value problems follow out the variational formulations proposed. To minimize the nonnegative functional under algebraic and differential constraints a regular finite element algorithm is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. A 3D problem of lateral motions of a rectilinear elastic prism with a rectangular cross section are considered. The numerical results are presented and discussed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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