Calculation of bending plates by finite element method in stresses

[摘要] The finite element models for plate bending problems are constructed on the basis of the approximations of moments fields. The bending and twisting moments are approximated in the finite element area by piecewise constant functions. The solution is based on the functional of the additional energy. The algebraic equations of equilibrium of nodes of grid of finite elements are formed using the principle of possible displacements and are included in the functional with the help of Lagrange multipliers. The calculations of square clamped and hinged supported plates on the action of uniformly distributed load are performed. It is shown that the presented method of calculating bent plates by the finite element method in stresses has the property of convergence of the displacements from above.

[发布机构] Polytechnic Institute, Vyatka State University (PI of VSU), Moskovskaya street 36, Kirov; 610000, Russia^1

[学科分类] 土木及结构工程学

[关键词] Algebraic equations;Bending plates;Distributed loads;Piece-wise-constant functions;Plate bending problems;Twisting moment