Abstract

An approach for the numerical simulation of cyclic symmetry conditions on non-conformal curvilinear meshes using spectral element method is presented. The multi point constraints (MPC) method [1,2] is used to set the imposed displacement constraints and the Direct elimination method in matrix form is used to add them to the system of equations with mass and stiffness matrices. When forming MPC conditions on non-conformal meshes, it is proposed to rotate the surfaces on which the conditions of cyclic symmetry are set, and then search for the projection of the master-node onto the slave-surface by the method used in the search for contact pairs [4]. Further, the constraint equations are combined together for the original (not rotated) node and its projection. The conditions 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 freedom is described. A direct elimination method is proposed to exclude the dependent degrees of freedom from the finite element system of linear equations. The influence of a symmetrization matrix additional to the stiffness matrix and containing the condition of equality of normal stresses is considered. Algorithm was implemented in CAE FIDESYS [5]. As an example of application of the developed algorithm, solutions of several problems with cyclic symmetry are considered. The proposed approach makes it possible to specify conditions of cyclic symmetry, which are fulfilled exactly, in contrast to penalty methods. And at the same time, the developed algorithm allows the use of non-conformal curvilinear grids, which simplifies a mesh generation process and provides high accuracy in the discretization of complex geometric CAD-models. The reported study was funded by Russian Science Foundation project - 19-77-10062. References: [1] Abel J and Shephard M 1979 An algorithm for multipoint constraints in finite element analysis Int. J. Numer. Meth. Engng 14 pp 464?467 [2] Felippa C 2004 Introduction to finite element methods. Chapter 8 Multifreedom constraints I. Colorado, Department of Aerospace Engineering Sciences and Center for Aerospace Structures University of Colorado Boulder pp 1-17 [3] Kukushkin A, Konovalov D, Vershinin A and Levin V Numerical simulation in CAE Fidesys of bonded contact problems on non-conformal meshes 2019 J. Phys.: Conf. Ser. 1158 032022 [4] Zienkiewicz O and Taylor R 2014 The Finite Element Method for Solid and Structural Mechanics Seventh Edition (Amsterdam: Elsevier) [5] www.cae-fidesys.com