Abstract
The integrodifferential approach incorporated in variational technique for static and dynamic problems of the linear theory of elasticity is considered. A families of statical and dynamical variational principles, in which displacement, stress, and momentum fields are varied, is proposed. It is shown that the Hamilton principle and its complementary principle for the dynamical problems of linear elasticity follow out the variational formulation proposed. A regular numerical algorithm of constrained minimization for the initial-boundary value problem is worked out. The algorithm allows us to estimate explicitly the local and integral quality of numerical solutions obtained. As an example, a problem of lateral controlled motions of a 3D rectilinear elastic prism with a rectangular cross section is investigated.
Published Version
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