A novel quasi-smooth manifold method with enriched interpolation for wave propagation and structural dynamics

In this paper, a quasi-smooth manifold element with enriched interpolation (QSME-E) is developed for accurate and efficient elastodynamic analysis. The proposed formulation includes a three-dimensional (3D) tetrahedral 8-node quasi-smooth manifold element (Tetra-8 QSME) and a two-dimensional (2D) triangular 4-node quasi-smooth manifold element (Tri-4 QSME). For both elements, nodal displacements and their gradients are introduced as degrees of freedom (DOFs) to enrich the approximation space and achieve cubic completeness of the displacement approximation. Based on the variational principle, the governing equations are discretized within a Galerkin framework, and a high-precision three sub-step time integration scheme is employed for transient simulations. A weakly-coupled geometry mapping strategy together with a compatible numerical integration procedure is also introduced for curved boundaries. The performance of the proposed method is demonstrated through a set of benchmark problems, as well as representative examples involving wave propagation and structural dynamics. Numerical results demonstrate that the QSME-E achieves higher accuracy than conventional finite elements for wave propagation in both 2D and 3D cases, as well as in transient structural dynamic analyses.