Three-dimensional approximated isogeometric analysis via Bernstein–Bézier tetrahedron

Precise simulation of realistic physical phenomena and maintaining high efficiency will be the ultimate goal of computational mechanics. As an effort of such endeavor, an isogeometric analysis (IGA) was proposed by integrating finite element analysis (FEA) and computer-aided design. IGA efficiently predicts a physical behavior with higher fidelity than the original FEA. However, an application to various geometries will be cumbersome owing to the absence of an appropriate pre-processor. To alleviate such limitation, various reinforcements have been attempted, including a finite element (FE)-based IGA. Derived from those initiatives, alternatives will be suggested herein by using a Bernstein–Bézier FE. To obtain approximate \(C^1\) $C^1$ continuity for a general tetrahedral FE, an approximated Worsey–Piper element split will be presented. Also, Bézier mesh generation will be adopted for an enhanced geometric representation. The present attempt will be validated by comparing the results for various curved geometry. Furthermore, the present method will be applied to a much more complicated configuration to demonstrate the geometric applicability.