A finite element scheme with the aid of a new carving technique combined with smoothed integration

An efficient scheme is proposed that can generate appropriate meshes for three-dimensional complex domains, leading to accurate solutions in finite element analysis. After preparing a structured mesh with hexahedral elements, the surface information of an arbitrary domain is soaked into the mesh. The elements around the surface are trimmed according to the surface information, and then they are replaced by polyhedral elements while the interior of the domain remains occupied by the original hexahedral elements. The scheme is further extended to manage complex domains with discontinuities in geometry and material properties such as a polycrystalline structure comprised of multiple materials or grains, as well as highly curved domains with a single material. Subsequently, the generated mesh, composed of the polyhedral elements on the surface and the hexahedral elements in the interior, is directly applied for finite element analysis in conjunction with smoothed integration in the strain smoothing technique. Because the smoothed integration does not require the shape function derivatives, the efficient analysis can be conducted without explicitly defined shape functions of the polyhedral elements. The smoothed integration can improve the accuracy of the numerical solutions as well. The present study focuses on reporting a new idea on a finite element scheme using the polyhedral elements with the smoothed integration, rather than providing a general and systematic approach; however, it has a great potential to deal with general and practical problems. Through numerical examples, it is shown that the proposed scheme provides accurate solutions in a simple and efficient manner.