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The standard finite element method (FEM) is known for its “over-stiff” behavior, which leads to the pollution error in acoustic and acoustic-structural problems. In this paper, a generalized mass-redistributed smoothed FEM (MR-SFEM) is proposed to analyze the acoustic and acoustic-structure interaction problems. In the new MR-SFEM, the generalized mass matrix reconstitution technology is used for both the structural and acoustic discretized system based on the SFEM, which can provide a perfect balance of the discretized system matrix both in the structure and acoustic domain. The global equations of acoustic-structural interaction problems are established by coupling the MR-SFEM for the structure and for the acoustic domain. Some numerical examples of acoustic and acoustic-structure interaction problems have been used to assess the present formulation, and the results show that the present method has much better performance in terms of accuracy, convergence, and efficiency than those obtained using the standard FEM, edge-based FEM (ES-FEM), and face-based FEM (FS-FEM).

An edge-based smoothed tetrahedron radial point interpolation method (ES-T-RPIM) is formulated for the 3D acoustic problems, using the simplest tetrahedron mesh which is adaptive for any complicated geometry. In present ES-T-RPIM, the gradient smoothing operation is performed with respect to each edge-based smoothing domain, which is also serving as building blocks in the assembly of the stiffness matrix. The smoothed Galerkin weak form is then used to create the discretized system equations. The acoustic pressure is constructed using radial point interpolation method, and two typical schemes of selecting nodes for interpolation using RPIM have been introduced in detail. It turns out that the ES-T-RPIM provides an ideal amount of softening effect, and significantly reduces the numerical dispersion error in low- to mid-frequency range. Numerical examples demonstrate the superiority of the ES-T-RPIM for 3D acoustic analysis, especially at mid-frequency.

This paper presents an explicit smoothed finite element method (SFEM) for elastic dynamic problems. The central difference method for time integration will be used in presented formulations. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. In present method, the problem domain is first divided into elements as in the finite element method (FEM), and the elements are further subdivided into several smoothing cells. Cell-wise strain smoothing operations are used to obtain the stresses, which are constants in each smoothing cells. Area integration over the smoothing cell becomes line integration along its edges, and no gradient of shape functions is involved in computing the field gradients nor in forming the internal force. No mapping or coordinate transformation is necessary so that the element can be used effectively for large deformation problems. Through several examples, the simplicity, efficiency and reliability of the smoothed finite element method are demonstrated.

This paper presents a curvature-constructed method (CCM) for bending analysis of thin plates using three-node triangular cells and assumed piecewisely linear deflection field. In the present CCM, the formulation is based on the classic thin plate theory, and only deflection field is treated as the field variable that is assumed piecewisely linear using a set of three-node triangular background cells. The slopes at nodes and/or the mid-edge points of the triangular cells are first obtained using the gradient smoothing techniques (GST) over different smoothing domains. Three schemes are devised to construct the curvature in each cell using these slopes at nodes and/or the mid-edge points. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential rotational boundary conditions are imposed in the process of constructing the curvature field, and the translational boundary conditions are imposed in the same way as in the standard FEM. A number of numerical examples, including both static and free vibration analyses, are studied using the present CCM and the numerical results are compared with the analytical ones and those in the published literatures. The results show that outstanding schemes can obtain very accurate solutions.