plane-deformed state

A methodology for constructing a solution to the two-dimensional dynamic problem of thermoelasticity in stresses for a rectangular beam is proposed.  The system of stress equations describing the plane-deformed state of the beam under nonstationary thermal and mechanical loadings is chosen as the initial one.  The methodology is based on the approximation of the distributions of all components of the dynamic stress tensor by cubic polynomials along the thickness coordinate of the beam.  As a result, the system of initial two-dimensional nonstationary equations for these

The method for solving a two-dimensional dynamic thermoelasticity problem in stresses for a strip with a rectangular cross-section is proposed.  The initial system of equations in stresses, which describes the plane-stress state of the strip, is selected.  A solution method is developed based on approximating the distributions of all components of the dynamic stress tensor using cubic polynomials with respect to the thickness coordinate of the strip.  This reduces the original system of two-dimensional unsteady equations to a system of one-dimensional unsteady equations