Inverse Problem of Elastic-plastic Deformation of a Free Thick-walled Cylindrical Shell Taking Into Account the Nonlinear Law of Hardening
Year: 2024
Type: article
Abstract: The inverse problem of elastoplastic deformation of a thick-walled cylindrical shell of finite length under internal pressure is solved. For a given displacement of the outer surface of the shell, it was necessary to construct a numerical technique to determine the internal pressure providing this displacement. The problem being solved is a boundary value problem of a mixed type. The cylindrical shell under study is in a plane stress state and a volumetric deformed state. The mathematical formulation of the problem was based on the provisions of the deformation theory of plasticity. The strain state of the shell was described using nonlinear Hencky strains. The constructed model of elastic-plastic deformation of the shell took into account the compressibility of the material and the nonlinear law of hardening. The numerical calculation method is based on the method of variable elasticity parameters using the method of successive approximations, taking into account changes in the geometry of the shell during deformation. To assess the adequacy of the constructed numerical method for solving the inverse problem, a comparative calculation of the direct problem of elastoplastic deformation using the finite element method in the ANSYS 19.0 software package was carried out. The results obtained for radial and circumferential stresses, stress intensity, radial displacements of the boundary surfaces of a cylindrical shell at internal pressure calculated when solving the inverse elastoplastic problem showed sufficient consistency. The stress distribution patterns in the cylindrical shell wall according to the method of variable elasticity parameters and the finite element method are qualitatively the same. The differences in the quantitative results obtained according to the two approaches are no more than 10%. The proposed calculation method can be used in the field of aircraft engineering in order to calculate the required pressure when deforming cylindrical shells to the required geometry, taking into account the physical and geometric nonlinearities of the material under the condition of monotonic loading.
Authors: I.K. Andrianov, S.I. Feoktistov
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
Funder: Russian Science Foundation
OpenAlex ID: W4403333393