The smoothed finite element methods (S-FEM) are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the meshfree methods. Studies have proven that S-FEM models behave softer than the FEM counterparts using the same mesh structure, often produce more accurate solutions, higher convergence rates, and much less sensitivity to mesh distortion. They work well with triangular or tetrahedral mesh that can be automatically generated, and hence are ideal for automated computations and adaptive analyses. Some S-FEM models can also produce upper bound solution for force driving problems, which is an excellent unique complementary feature to FEM. Because of these attractive properties, S-FEM has been applied to numerous problems in the disciplines of material mechanics, biomechanics, fracture mechanics, plates and shells, dynamics, acoustics, heat transfer and fluid–structure interactions. This paper reviews the developments and applications of the S-FEM in the past ten years. We hope this review can shed light on further theoretical development of S-FEM and more complex practical applications in future.

Smoothed Finite Element Methods (S-FEM): An Overview and Recent Developments

Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)

Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications

In ocean engineering, the applications are usually related to a free surface which brings so many interesting physical phenomena (e.g. water waves, impacts, splashing jets, etc.). To model these complex free surface flows is a tough and challenging task for most computational fluid dynamics (CFD) solvers which work in the Eulerian framework. As a Lagrangian and meshless method, smoothed particle hydrodynamics (SPH) offers a convenient tracking for different complex boundaries and a straightforward satisfaction for different boundary conditions. Therefore SPH is robust in modeling complex hydrodynamic problems characterized by free surface boundaries, multiphase interfaces or material discontinuities. Along with the rapid development of the SPH theory, related numerical techniques and high-performance computing technologies, SPH has not only attracted much attention in the academic community, but also gradually gained wide applications in industrial circles. This paper is dedicated to a review of the recent developments of SPH method and its typical applications in fluid-structure interactions in ocean engineering. Different numerical techniques for improving numerical accuracy, satisfying different boundary conditions, improving computational efficiency, suppressing pressure fluctuations and preventing the tensile instability, etc., are introduced. In the numerical results, various typical fluid-structure interaction problems or multiphase problems in ocean engineering are described, modeled and validated. The prospective developments of SPH in ocean engineering are also discussed.

Smoothed particle hydrodynamics and its applications in fluid-structure interactions

Meshless Local Petrov--Galerkin (MLPG) method for the unsteady magnetohydrodynamic (MHD) flow through pipe with arbitrary wall conductivity

A fully smoothed finite element method is developed to model axisymmetric problems by incorporating a special integral into the Cell-based, Node-based and Edge-based Smoothed Finite Element Method (CS-FEM, NS-FEM, ES-FEM), respectively. The special integral is done by combining Gauss divergence theorem with the evaluation of an indefinite integral, which can be used for treatment of the axisymmetric term in strain matrix and shape function in mass matrix. Applying the special integral and smoothing technique, all the domain integrals in stiffness matrix and mass matrix can be smoothed and rewritten as boundary integrals of smoothing cells. Then the stiffness matrix and mass matrix of element are computed by a simple summation over the smoothing cells. In this work, the proposed method is extended to static and structure dynamic analysis of axisymmetric problems. Numerical examples show that the proposed method can yield good performance even for extremely irregular elements.

A fully smoothed finite element method for analysis of axisymmetric problems

Modified cylindrical smoothed particle hydrodynamics (MCSPH) approximation equations are derived for hydrodynamics with material strength in axisymmetric cylindrical coordinates. The momentum equation and internal energy equation are represented to be in the axisymmetric form. The MCSPH approximation equations are applied to simulate the process of explosively driven metallic tubes, which includes strong shock waves, large deformations and large inhomogeneities, etc. The meshless and Lagrangian character of the MCSPH method offers the advantages in treating the difficulties embodied in these physical phenomena. Two test cases, the cylinder test and the metallic tube driven by two head-on colliding detonation waves, are presented. Numerical simulation results show that the new form of the MCSPH method can predict the detonation process of high explosives and the expansion process of metallic tubes accurately and robustly.

Dean Hu

Papers

A fully smoothed finite element method for analysis of axisymmetric problems

Simulation of explosively driven metallic tubes by the cylindrical smoothed particle hydrodynamics method

Soft Robotic Surface Enhances the Grasping Adaptability and Reliability of Pneumatic Grippers

Design, Characterization and Optimization of Multi-directional Bending Pneumatic Artificial Muscles

An approach based on level set method for void identification of continuum structure with time-domain dynamic response