Numerical modelling in problems of thermal control for three-layer structures with defects

Abstract

This article describes solutions to the direct and inverse problems of the three-dimensional non-stationary heat conduction problem in a three-layer structure, using the finite element method for the direct problem and the gradient descent method for the inverse problem. A comparison of the FEM-solution and the analytical solution for a solid with a simple geometry is presented. Here are presented solutions of the direct and inverse three-dimensional non-stationary heat conductivity problem for a free three-stage turbine. The accuracy of the found and exact solutions is compared.

Modeling the stress-strain state of variable-thickness composite shells and plates

“…For a variable thickness shell, the coordinate X 3 takes the values −a − (X 1 , X 2 ) < X 3 < a + (X 1 , X 2 ), where X 3 = a ± (X 1 , X 2 )equations of the outer and inner surface of the shell. The function h = a + (X 1 , X 2 ) + a − (X 1 , X 2 ) is the thickness of the shell and in this work is a variable depending on the coordinates X 1 , X 2 .…”

“…Variable thickness can be used to increase strength in specific areas of the wall or bottom [1], without unnecessary mass cost to the rest of the structure. In addition, variable thickness can occur in the presence of object defects [2,3], for example, when a structure is made during curing [4,5]. Accounting for variable thickness can improve the quality of the product and reduce the cost of manufacturing structures.…”

“…Figure(2) shows the graphs of the distribution of forces, moments and shear forces for a plate with constant (green line) and variable thickness (red line).…”