caa a22 4500 605522146 CHVBK 20210128100743.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10958-015-2275-y doi (NATIONALLICENCE)springer-10.1007/s10958-015-2275-y Generalized Somigliana Identity for Thermomagnetoelectroelastic Anisotropic Bodies [Elektronische Daten] [Ya. Pasternak, H. Sulym, R. Pasternak] 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. Springer Science+Business Media New York, 2015 Pasternak Ya Lutsk National Technical University, Lutsk, Ukraine aut Sulym H. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine aut Pasternak R. Lutsk National Technical University, Lutsk, Ukraine aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/5(2015-03-01), 677-690 1072-3374 205:5<677 2015 205 10958 https://doi.org/10.1007/s10958-015-2275-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2275-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Pasternak Ya Lutsk National Technical University, Lutsk, Ukraine aut NATIONALLICENCE 700 1- Sulym H. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine aut NATIONALLICENCE 700 1- Pasternak R. Lutsk National Technical University, Lutsk, Ukraine aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 205/5(2015-03-01), 677-690 1072-3374 205:5<677 2015 205 10958