A mechanical approach to solve two-dimensional static electrical and magnetic fields: Applications to contact between conductors under electrical load

A general approach has been developed to obtain analytical solutions to the boundaryvalue problems for a two-dimensional conductor under static electric and magnetic fields. This approach is based on a "congruity principle" between a solution of Maxwell's equation and the corresponding linear elastic plane stress solution with constant mean stress or plane strain solution with constant mean in-plane stress. It also leads to a new avenue to construct analytical solutions of antiplane strain boundary-value problems using plane stress/strain solutions, or vice versa, in linear elastic theory. This approach has been applied for such engineering problems as contact between two conducting solid bodies under electrical load.