Kozub V. Finite element analysis using parallel technologies

The introduction substantiates the choice of the topic of the dissertation, formulates the goal, task, object, subject of research, reveals the scientific novelty and practical significance of the obtained results. Data on the approval of research results and their coverage in scientific publications are given. The first chapter analyzes the current state of research on the topic of the work. A review of publications was made, parallel programming methods for modeling and forecasting in problems of solid mechanics were analyzed. When applying the method of finite elements, the process of solving the problem consists of the following stages: formation of initial data; forming and solving a system of equations; procedure for outputting results. Various approaches are used to increase the performance of the finite element method parallelization: the use of modified algorithms of systems of equations, the use of decomposition of the computational domain. In each case, there is a need to provide additional boundary conditions for the convergence of the method. In most of the existing packages of application programs of the finite element method, the calculation is carried out according to the traditional sequential scheme. Parallelization of computing processes for already existing software architecture requires the development of algorithms for the use of parallel computing at the stage of forming systems of solving equations. In the second chapter, the peculiarities of the construction of solving equations describing the processes of deformation under the action of power and thermal loads are considered. Based on the relations of the three-dimensional theory of elasticity and thermoelasticity of isotropic and anisotropic bodies, matrices of stiffness and thermal conductivity of the finite element were constructed. The developed technique is universal and has a number of features, namely: independence of the order of solving equations from the structure of layered bodies; the possibility of setting the values of the corresponding thermophysical characteristics of isotropic or anisotropic layers of layered bodies; the possibility of using three-dimensional finite elements in the modeling of physical and mechanical processes occurring in structures of arbitrary geometric shape under real operating conditions. The application of the proposed method allows solving problems of thermomechanics of structures in a three-dimensional setting. In the third section, an approach to the use of parallel calculations in the finite element method within the subsystems of the "MIRELA+" application program package was developed. A method of parallelization of the calculation of matrix components of systems of finite element solving equations is proposed. An algorithm for the parallel calculation of the finite element stiffness matrix for the problems of elastic deformation of structures, as well as the procedure for calculating the parameters of the stress state based on the results of the finite element solution, was developed and implemented. Algorithms for solving nonlinear problems of mechanics and problems of thermoelasticity using parallel calculations have been developed. The solutions of practical problems of elasticity and thermoelasticity are given in the fourth chapter. The solution for layered structures with anisotropic layers is considered. To solve the related problem of thermoelasticity of a layered anisotropic structure, the relations for determining the thermophysical parameters of the layers are obtained. The stress-strain state of structures was calculated according to the traditional scheme and using parallel calculations. The influence of the use of parallel technologies on the performance of finite element solving of mechanics problems was studied. The scientific novelty of the work, its practical significance and prospects for further development are given in the conclusions. The following scientific results were obtained in the dissertation work: for the first time, algorithms for parallel calculations of stiffness matrices of finite elements based on the moment scheme of finite elements for problems of elasticity were developed; for the first time, parallel algorithms for calculating thermal conductivity matrices for solving thermal conductivity problems were developed; algorithms of parallel calculations were further developed when applied to solving linear and nonlinear problems; for the first time, an application using parallel computing algorithms was developed as part of the "MIRELA+" application program package for solving problems of thermal elasticity of structures. The software implementation of the given problem-solving technique is written in the Fortran 2018 programming language based on the Intel Fortran Compiler using the parallel programming library in OpenMP shared memory systems.