Simulating the Solution to an Unsteady Problem of Thermoelastic Strain of Bodies with a Hole
Abstract
The solution to unsteady problems of thermo-elasticity is considered in the article using the finite element method (FEM). The statement of the problem is based on the Fourier form of heat conduction and the equations of mechanics of a deformable rigid body. The nonlinearity of the formulated problem is due to the dependence of the elastic characteristics of the material on the deformation temperature. The Galerkin method is used to directly obtain the finite element equations from the available set of differential equations in the domain. Forming an unsteady heat conduction problem, the authors obtained a system of differential equations in which the time derivative is replaced by a finite difference. So, the initial problem is simplified into a set of linear algebraic equations (LAE), which are solved using Newton’s method. Solving the boundary value problem involves two main steps: first, figuring out the temperature distribution, and then using that to determine the displacements and stresses within the thermos-elastic medium. By means of a computational experiment, the solution to the problem of compression of a copper plate with a central circular hole is investigated. Temperature isotherms are given at different time points. As the finite time increases, the heat flux from the boundary of the hole propagates over the entire area of the plate. The distribution of values of the components of normal and shear stresses in the vicinity of the hole under applied compressive external loads and temperatures is analyzed.