stress tensor components

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

A methodology to construct solutions for two-dimensional quasi-static thermomechanical problems for bodies with plane-parallel boundaries (2D-QS thermomechanical problems) is proposed.  This approach begins with selecting equations for the plane quasi-static thermoelasticity problem in terms of stresses.  The methodology approximates the distribution of non-zero stress tensor components through the body's thickness using cubic polynomials, with coefficients expressed in terms of integral characteristics of the stress tensor components over the thickness variable and the