A new finite element approach for solving three-dimensional problems using trimmed hexahedral elements

In this paper, a novel finite element approach is presented to solve three-dimensional problems using trimmed hexahedral elements generated by cutting a simple block consisting of regular hexahedral elements with a computer-aided design (CAD) surface. Trimmed hexahedral elements, which are polyhedral elements with curved faces, are placed at the boundaries of finite element models, and regular hexahedral elements remain in the interior regions. Shape functions for trimmed hexahedral elements are developed by using moving least square approximation with harmonic weight functions based on an extension of Wachspress coordinates to curved faces. A subdivision of polyhedral domains into tetrahedral sub-domains is performed to construct shape functions for trimmed hexahedral elements, and numerical integration of the weak form can be carried out consistently over the tetrahedral sub-domains. Trimmed hexahedral elements have similar properties to conventional finite elements regarding the continuity, the completeness, the node-element connectivity, and the inter-element compatibility. Numerical examples for three-dimensional linear elastic problems with complex geometries show the efficiency and effectiveness of the present method.