Face-to-face multi-point constraint method in 3D problems by numerical integration based on geometrical triangulation

The purpose of this study is to establish a method to obtain face-to-face multi-point constraint (MPC) conditions that connect two nonconforming meshes in 3D problems. In this study, the formulation of the MPC conditions proposed by El-Abbasi and Bathe is employed, which considers the compatibility of deformation and the distribution of constraint traction on the connecting surface. The MPC conditions are expressed as a coefficient matrix by an integration of the product of shape functions over a connecting surface. The integration domain is divided using the Delaunay triangulation so that each integration domain contains just a polynomial. Then, the integration is numerically and precisely evaluated. Two examples are presented to verify the computational accuracy and validate the triangulation for numerical integration. In the first example, it has been confirmed that the numerical integration values calculated via the Delaunay triangulation coincide with the corresponding theoretical values. In the second example, a simple elastic problem in which two rectangular parallelepiped domains are connected by the face-to-face MPC has been solved. It has been confirmed that the displacement, the constraint traction and the first principal stress on the connecting surface are more accurate than those obtained with a node-to-face MPC. Additionally, we have found that Gaussian integration using a small number of integration points gave rise to unexpectedly inaccurate numerical results. © 2020 by the Japan Society for Computational Engineering and Science.