Analysis of structures with arbitrary kinematic boundary conditions by the semi-analytical finite element method

Abstract

The successful application of FEM to the analysis of structures is largely due to the efficiency of the use of modern software packages, in connection with which the role of program systems that implement the solution process increases. The correct organization of the computing complex, the choice of optimal algorithms for solving systems of linear and nonlinear equations largely determine the possibilities of the method in terms of the structural complexity of the objects under consideration, the accuracy of the results obtained, and the complexity of setting nonlinear problems. Therefore, there is an increased interest in the development of fairly universal computing complexes based on FEM. One of the effective software complexes is the "Strength" system, designed to conduct comprehensive research in the field of mechanics of a deformable solid, the basic principles of construction of which are used in this work in the implementation of a semi-analytical version of the FEM.
 In this work, solutions of a significant number of control problems of deformation of massive and thin-walled prismatic bodies under different boundary conditions and loads are obtained. In the process of solving new problems, the estimation of the convergence of results was carried out on the basis of a sequential increase in finite elements and contained terms of decomposition, an increase in the accuracy of systems of linear and nonlinear equations, and the accuracy of satisfaction with natural boundary conditions was checked. The developed effective method for solving new complex problems of deformation of prismatic bodies is implemented in the form of complex programs and can be used in design and construction practice in construction, mechanical engineering and other fields of technology.