Combined Mortar Finite Element Method Using Dual Lagrange Multiplier and BDD-MPC Method for Large-scale Assembly Structures

  • MIYAMURA Tomoshi
    Department of Computer Science, College of Engineering, Nihon University
  • YANO Yu-ki
    Department of Computer Science, Graduate School of Engineering, Nihon University

Bibliographic Information

Other Title
  • 大規模アセンブリ構造問題のための双対Lagrange乗数を用いたモルタル有限要素法とBDD-MPC法の組み合わせ手法

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Description

<p>A numerical method is proposed in the present paper for structural analysis of large-scale assembly structures. The mortar finite element method (FEM) has been developed for assembling structural components modeled by finite elements and a set of constraints in a weak form, which is formulated using Lagrange multipliers. In the dual Lagrange multiplier method proposed by Wohlmuth, a set of biorthogonal shape functions is used to discretize Lagrange multipliers. One of the present authors proposed a method to incorporate multi-point constraints (MPCs) into the balancing domain decomposition (BDD) method, which was proposed by Mandel. The method, which is called the BDD-MPC method in this paper, can solve large-scale structural problems having many MPCs at high speed using parallel computers. The proposed method for large-scale assembly structures combines the above two methods, i.e., the mortar FEM using the dual Lagrange multipliers and the BDD-MPC method. A numerical integration method using back ground cells for integrating the constraints in a weak form is also proposed. In this method, square and fine integration cells are arranged as a grid without considering the shapes of surface elements on the surfaces to be connected. The integration method is verified by investigating the levels of details of divisions of both meshes to be connected and the integration cells. In the illustrative example of two cubes that are connected by the dual Lagrange multipliers, very fine mesh division is necessary to obtain a solution with sufficient accuracy. It is demonstrated that the BDD-MPC method is a powerful tool to solve such a problem. Computation performances of the method are also investigated.</p>

Journal

Details 詳細情報について

  • CRID
    1390296841718707712
  • DOI
    10.11421/jsces.2023.20230005
  • ISSN
    13478826
    13449443
  • Text Lang
    ja
  • Data Source
    • JaLC
  • Abstract License Flag
    Disallowed

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