SOME NEW RESULTS IN CONSRUCTING OF 3-D GREEN’S MATRICES

Abstract eng:
This article describes a new method of how to construct effectively the Green’s Matrices in 3D theory of elasticity. The suggested method is based on the new general integral representations for Green’s matrices, their kernels being the Green’s functions for so called incompressible influence elements. I general cases of boundary conditions the problem of Green’s matrices construction leads to the boundary integral equations. As an example, the fist basic problem of the theory of elasticity is considered leading to the boundary integral equation of Liechtenstein’s type. For certain wide classes of the mixed problems in Cartesian co-ordinate one theorem is presented. This theorem expressed the Green’s matrices in a form of integral formulas containing only the Green’s functions for the Poisson’s equation. As examples of effective application of suggested method, two new boundary value problems for the octant and for semiwedge are solved. The Green’s matrices of these problems were obtained in elementary functions, that is very important for their numerical implementations. The suggested method can be developed for regions of any system of orthogonal curvilinear co-ordinates, both in elastostatics and elastodynamics, and as a result, the list of known Green’s matrices can be essentially enlarged.

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