Finite-Element Method for Three-Dimensional Problems of Elastic Structures Buckling Theory

The study tested the three-dimensional problems of elastic structures buckling theory. In the research we applied the tensor statement of these problems offered by Yu.I. Dimitrienko before. The three-dimensional problems of elastic structures buckling theory are studied less than the two-dimensional problems of buckling theory. Nowadays, numerical methods of their solution are not known. The work gives the variation statement of the three-dimensional problem of elastic structures buckling theory. According to this statement, we proposed the final-element method for solving the buckling problems which is reduced to finding the eigen values of the linear algebraic equations system with a global symmetric stiffness matrix. As a result, we developed the program module implementing the offered final-element method within the SMCM program complex developed in Scientific and Educational Center "SIMPLEX" at Bauman Moscow State Technical University with the use of the CSIR storage scheme of the sparse matrixes and a bi-conjugate gradient method. We carried out the test calculation for the rectangular plate buckling problem under the longitudinal compression. The comparison of the final-element solution of this problem according to the three-dimensional theory and Timoshenko plates theory has shown high precision of the developed numerical method when determining critical loads. At the same time, the three-dimensional theory allows for more exact forms of eigen functions of stability loss.

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