ЗАСТОСУВАННЯ МЕТОДУ ГРАНИЧНИХ ЕЛЕМЕНТІВ ДЛЯ РОЗРАХУНКУ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ПРИ КРУЧЕННІ ТОНКОСТІННИХ РАМ АВТОМОБІЛІВ

Abstract

Currently, the main method of calculating the stress-strain state (SSS) is the finite element method (FEM), implemented in software packages such as ANSYS, Solid Works, MATLAB, and others. It is established that if the SSS structure is described by rod functions, then the finite element method gives accurate results. If the state of the object is described by other functions, then MSE can give only approximate results of SSS calculation. Therefore, in this work, the authors applied a more accurate method of calculating the SSS of thin-walled car frames – the numerical analytical method of boundary elements (NA BEM). The purpose of the study is to apply a more accurate method of calculating the SSS of thin-walled car frames with the help of BEM. The scientific and practical direction of the work is that the technology of a more accurate method of calculating the SSS of thin-walled car frames - NA BEM is applied. The research methodology is the construction of mathematical models for the calculation of thin-walled car frames – NA BEM. When designing thin-walled metal structures, SSS is described by hyperbolic functions, and FEM, in principle, cannot provide accurate results for calculating SSS of thin-walled structures. Therefore, in the work, it is proposed to apply the technology of the boundary element method, which is free from the shortcomings of FEM technologies, to calculate SSS torsion of thin-walled car frames. The paper presents the matrix functions of the solution of the differential equations of the finite torsion of thin-walled frames, which were used to calculate the SSS of the rod torsion of thin-walled car frames. A more accurate SSS calculation of thin-walled car frames has been performed. This, in turn, will make it possible to determine the exact dimensions of the cross-section of thin-walled car frames. The result of the conducted research is the construction of accurate models of the stress-strain state during torsion of thin-walled car frames. Systems of linear equations of the SSS calculation algebra of limited torsion of two inseparable beams, which are models of car frames, are given. The calculation of frames for compressed torsion is presented. Отримані точні результати розрахунку SSS обмеженого кручення рам автомобілів, що представлені у вигляді таблиць і епюр. Keywords: FEM, BEM, thin-walled car frames.