Thick-walled spherical shell problem

Introduction. Cylindrical and spherical shells are extensively used in engineering. They face internal and/or external pressure heat. Stresses strains distribution elastoplastic has been studied by many scientists. Numerous works involve the use of von Mises yield conditions, maximum shear stress, reduced stress. These condi- tions do not include dependence on first invariant stress tensor sign third deviator. In some cases, it is possible to obtain numerical-analytical solutions for stresses, displacements de- formations bodies with cylindrical symmetry under axisymmetric thermal force action. Materials Methods. The problem state a thick-walled shell solved within framework theory small deformations. A plasticity condition proposed, which takes into account three independent invariants, also considers deviator translational hardening material. disconnected thermoelastoplastic being solved. To estimate stresses region elastic shell, an equivalent introduced, similar selected function. construction vector hodograph as method verification state. Results. analytical solution linear functions. obtained when strength- ening material taken account. Analytical graphical relationships between parameters action or states sphere determined. For combined load, variants plastic generated at inner outer boundaries these boundaries. Discussion Conclusions. calculation results have shown that taking compressibility limit temperature can significant impact strain hollow sphere. this case, leads fact only drop but values boundaries, vary limited range. formulation problem, there action, does completely pass research provide predicting behavior object (a sphere) experiences centrally symmetric distributed power influences.