Approximate formulation of a coupled dynamical problem of thermoviscoplasticity for thin-walled shells of revolution under harmonic load (Q2754752)

The suggested scleronomic approach is based on the assumption that under harmonic deformation of elements of a solid, the variation of stresses and plastic deformations is also close to harmonic law. Thus behavior of material is described by means of complex shear moduli and plasticity coefficient depending on effective strain. The problem formulation includes complex analogue of geometric equations, equations of motion, relationships of plasticity and averaged heat conduction equations supplemented by the corresponding boundary and initial conditions. Plasticity relationships do not contain terms depending on thermal and plastic strains. The formulated problem is solved using an iterative technique analogous to the method of variable parameters in elasticity. Al elementary iteration consists in solution of a linearized mechanical problem and a heat conduction problem.