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Application of Spectral Element Method for Solving Problems With a Cyclic Symmetry at Unstructured Nonconformal Curvilinear Meshesтезисы доклада
- Авторы: Vershinin A.V., Levin V.A., Kukushkin A.V., Konovalov D.A.
- Сборник: Proceedings of NAFEMS World Congress 2021
- Тезисы
- Год издания: 2021
- Место издания: NAFEMS NAFEMS Ltd
- Первая страница: 378
- Последняя страница: 378
- Аннотация: An approach for the numerical simulation of cyclic symmetry conditions on non-conformalcurvilinear meshes using spectral element method is presented. The multi point constraints(MPC) method is used to set the imposed displacement constraints and the Direct eliminationmethod in matrix form is used to add them to the system of equations with mass and stiffnessmatrices. When forming MPC conditions on non-conformal meshes, it is proposed to rotate thesurfaces on which the conditions of cyclic symmetry are set, and then search for the projection of themaster-node onto the slave-surface by the method used in the search for contact pairs. Further, theconstraint equations are combined together for the original (not rotated) node and its projection. Theconditions of equality of displacements and equality of normal stresses are imposed at cyclic surfaces.An algorithm for transforming constraints to identify the principal and dependent degrees of freedomis described. A direct elimination method is proposed to exclude the dependent degrees of freedomfrom the finite element system of linear equations. The influence of a symmetrization matrixadditional to the stiffness matrix and containing the condition of equality of normal stresses isconsidered. Algorithm was implemented in CAE FIDESYS.As an example of application of the developed algorithm, solutions of several problems with cyclicsymmetry are considered. The proposed approach makes it possible to specify conditions of cyclicsymmetry, which are fulfilled exactly, in contrast to penalty methods. And at the same time, thedeveloped algorithm allows the use of non-conformal curvilinear grids, which simplifies a meshgeneration process and provides high accuracy in the discretization of complex geometric CADmodels.The reported study was funded by Russian Science Foundation project - 19-77-10062.
- Добавил в систему: Вершинин Анатолий Викторович