Basic Relations for Complex Potentials of Electromagnetoviscoelasticity and Their Use in Solving Problems of the Action of Concentrated Forces

The main relations for complex potentials of a plane problem of electromagnetic viscoelasticity, their general representations for singly and multiply connected domains, and boundary conditions for their determination are presented. Using these functions, solutions are obtained for problems of concentrated effects (mechanical forces, electric charges, and magnetic dipoles), exact for a singly connected plate, and approximate, with high accuracy of satisfying the boundary conditions, for a multiply connected plate. The results of numerous studies are described for a plate with one or two circular holes or rectilinear cuts-cracks, with a hole and a cut, with two cuts, and the cases are considered when the contours of the holes intersect or the cuts go to the contour of the hole. The patterns of influence of the geometric characteristics of the holes and cuts, the physical-mechanical and electromagnetic properties of the plate materials, and also the time after applying external forces on the values and nature of the distribution of stresses and inductions are established.