Abstract
The extended Somigliana identity for thermomagnetoelectroelastic anisotropic dielectric solids is deduced. This identity does not impose restrictions on the dimensionality of the problem. The volume integral caused by the interaction of physical fields (internal temperature field and electric and magnetic loads) is reduced to the surface integral. The physical meaning of all kernels appearing in the obtained integral formula is clarified. The differential equations for the kernels are presented. The influence of external factors is taken into account with the help of convolution-type integrals, which should be found only for boundary points of the body. The obtained results are characterized both by theoretical significance and the possibilities of their practical application to the construction of the integral equations of three-, two-, and one-dimensional problems of the thermomagnetoelectroelasticity of anisotropic dielectrics and, hence, for the corresponding numerical realizations of the direct method of boundary elements.
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