An effective approach for analyzing thermoelastostatic states of 3D-objects

M. A. Lavrentieva, L. Levina, V. B. Penkov

Lipetsk State Technical University

Abstract: The state of a homogeneous, heat-conducting, linearly elastic, isotropic equilibrium medium is described by the equations of heat conduction, Cauchy, equilibrium, and the DuhamelNeumann law. Sets of characteristics that constitute the internal and boundary state of the body are identified. Scalar products defining the spaces of internal and boundary states as Hilbert spaces have been introduced. Their isomorphism is established. Universal algorithms for forming the bases of spaces have been assigned, allowing the application of the boundary state method in the settings of boundary value problems, the solution of which may not allow decomposition. The problem of the 'sausage' has been formulated and solved, in which a body enclosed in a shell experiences a stressed state due to the difference in temperature deformations of fibers of coupled media. Illustration and commentary of the results of the calculation have been performed.

Keywords: boundary state method, BSM, internal state of the body, boundary state, thermoelasticity, thermoelastostatics.

UDC: 539.3

Received: 10.12.2023
Accepted: 20.12.2022

DOI: 10.37972/chgpu.2023.58.4.004