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

Summary

Non-probabilistic convex models need to be provided only the changing boundary of parameters rather than their exact probability distributions; thus, such models can be applied to uncertainty analysis of complex structures when experimental information is lacking. The interval and the ellipsoidal models are the two most commonly used modeling methods in the field of non-probabilistic convex modeling. However, the former can only deal with independent variables, while the latter can only deal with dependent variables. This paper presents a more general non-probabilistic convex model, the multidimensional parallelepiped model. This model can include the independent and dependent uncertain variables in a unified framework and can effectively deal with complex ‘multi-source uncertainty’ problems in which dependent variables and independent variables coexist. For any two parameters, the concepts of the correlation angle and the correlation coefficient are defined. Through the marginal intervals of all the parameters and also their correlation coefficients, a multidimensional parallelepiped can easily be built as the uncertainty domain for parameters. Through the introduction of affine coordinates, the parallelepiped model in the original parameter space is converted to an interval model in the affine space, thus greatly facilitating subsequent structural uncertainty analysis. The parallelepiped model is applied to structural uncertainty propagation analysis, and the response interval of the structure is obtained in the case of uncertain initial parameters. Finally, the method described in this paper was applied to several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.

Multidimensional parallelepiped model—a new type of non-probabilistic convex model for structural uncertainty analysis

An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems

Ballistic reliability study on SiC/UHMWPE composite armor against armor-piercing bullet

A modified meshless local Petrov–Galerkin (MLPG) method is presented for elasticity problems using the moving least squares (MLS) approximation. It is a truly meshless method because it does not need a mesh for the interpolation of the solution variables or for the integration of the energy. In this paper, a simple Heaviside test function is chosen to overcome the computationally expensive problems in the MLPG method. Essential boundary conditions are imposed by using a direct interpolation method based on the MLPG method establishes equations node by node. Numerical results in several examples show that the present method yielded very accurate solutions. And the sensitivity of the method to several parameters is also studied in this paper.

Dean Hu

Papers

Multidimensional parallelepiped model—a new type of non-probabilistic convex model for structural uncertainty analysis

An arbitrary boundary with ghost particles incorporated in coupled FEM-SPH model for FSI problems

Ballistic reliability study on SiC/UHMWPE composite armor against armor-piercing bullet

A modified meshless local Petrov-Galerkin method to elasticity problems in computer modeling and simulation

Evidence-theory-based structural static and dynamic response analysis under epistemic uncertainties