Solving of boundary value problem of the theory of elasticity in displacements using conservation laws

S. I. Senashov, O. V. Gomonova

M. F. Reshetnev Siberian State University of Science and Technologies, Krasnoyarsk

Abstract: New conservation laws are constructed for the equations of the linear theory of elasticity in the three-dimensional case. Using these laws, for the first time, a boundary value problem in displacements was solved in the general case for an arbitrary body of finite dimensions. The solution is obtained in quadratures along the outer boundary of the body. It is shown that three fixed harmonic functions are sufficient to solve considered problem.

Keywords: boundary value problem, theory of elasticity, conservation laws.

UDC: 539.374

Received: 01.06.2023
Revised: 05.07.2024
Accepted: 15.04.2024

DOI: 10.37972/chgpu.2024.59.1.011