Abstract
The article presents an algorithm for solving linked problems of thermoelasticity of elastomeric structural elements on the basis of a moment scheme of finite elements. To model the processes of thermoelastic deformation of structures with initial stresses the incremental theory of a deformed solid is used. At each step of deformation, the stiffness matrix is adjusted using an incremental geometric stiffness matrix. The use of triple approximation of displacements, deformations and volume change function allows to consider the weak compressibility of elastomers. The components of the stress tensor are calculated according to the Duhamel-Neumann law. To solve the problem of thermal conductivity, a thermal conductivity matrix considering the boundary conditions on the surface of a finite element is constructed. A sequential approximation algorithm is used to solve the thermoelasticity problem. At each stage of the solution, the characteristics of the thermal stress state are calculated. Based on the obtained components of stress and strain tensors, the intensity of internal heat sources is calculated as the dissipative energy averaged over the load cycle. To calculate the dissipative characteristics of the viscoelastic elastomer the parameters of the Rabotnov’s relaxation nucleus are used. Solving the problem of thermal conductivity considering the function of internal heat sources allows you to specify the heating temperature of the body. At each cycle of the algorithm, the values of the physical and mechanical characteristics of the thermosensitive material are refined. This approach to solving thermoelastic problems is implemented in the computing complex "MIRELA+". Based on the considered approach, the solutions of a number of problems are obtained. The results obtained satisfactorily coincide with the solutions of other authors. Considering the effect of preload and the dependence of physical and mechanical properties of the material on temperature leads to significant adjustments to the calculated values.
Highlights
In solving related problems of thermoelasticity of elastomeric structural elements, various theories and approaches are used, which are based on the relations of the thermoelasticity obtained by many researchers [1,2,3,4,5,6] and others
We can identify a number of processes, thermomechanical state, during which, it changes over time, but from a certain point in time, the system comes to a stationary state, which does not depend on time
An algorithm for solving the related problems of thermoelasticity of elastomeric elements is built on the basis of the moment scheme of finite elements
Summary
In solving related problems of thermoelasticity of elastomeric structural elements, various theories and approaches are used, which are based on the relations of the thermoelasticity obtained by many researchers [1,2,3,4,5,6] and others. Let us consider the process of determining the temperature of dissipative heating of elastomeric structures as a solution of the linked problem of thermoelasticity for a stable mode of cyclic deformation and heat exchange with the environment. In this case, the solution of the quasi-static thermoelasticity problem requires the solution of several problems: determination of the function of internal sources in an elastic - hereditary body (solution of the thermoelasticity problem) at the initial temperature; calculation of the temperature field under given boundary conditions (solving the problem of stationary thermal conductivity); solving the problem of thermoelasticity for the final temperature of self-heating. Analysis of the results shows that the increase in the initial deformation significantly affects the temperature of dissipative heating
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