A novel 10-node tetrahedral quasi-smooth manifold method and its application in statics analysis of complex geometric structures

In this paper, a novel 10-node tetrahedral quasi-smooth manifold element (QSME) is proposed based on the high-order interpolation approximation methodology. Its calculation procedure for static analysis is established based on the Galerkin variational framework. To address the characterization challenge of complex geometric boundaries, a quasi-smooth boundary-conforming mesh partitioning technique, are specifically developed for the 10-node tetrahedral QSME. The numerical integration scheme is customized for the proposed QSME to ensure high computation accuracy for problems of complex boundary. Compared to traditional finite element (FE), the QSME exhibits higher-order continuity, achieving C¹-continuous displacement field at nodes. This inherent smoothness eliminates the requirement for post-smoothing procedures when calculating nodal stress/strain. The linear dependence (LD) issues rooted in traditional high-order partition-of-unity (PU) methods are resolved in the proposed QSME, which is rigorously verified through LD test. Some representative numerical simulation examples demonstrate that the proposed QSME method is highly efficient for statics analysis of complex geometry.