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

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

Particle methods in ocean and coastal engineering

Fluid-structure interaction (FSI) is a class of mechanics-related problems with mutual dependence between the fluid and structure parts and it is observable nearly everywhere, in natural phenomena to many engineering systems. The primary challenges in developing numerical models with conventional grid-based methods are the inherent nonlinearity and time-dependent nature of FSI, together with possible large deformations and moving interfaces. Smoothed particle hydrodynamics (SPH) method is a truly Lagrangian and meshfree particle method that conveniently treats large deformations and naturally captures rapidly moving interfaces and free surfaces. Since its invention, the SPH method has been widely applied to study different problems in engineering and sciences, including FSI problems. This article presents a review of the recent developments in SPH based modeling techniques for solving FSI-related problems. The basic concepts of SPH along with conventional and higher order particle approximation schemes are first introduced. Then, the implementation of FSI in a pure SPH framework and the hybrid approaches of SPH with other grid-based or particle-based methods are discussed. The SPH models of FSI problems with rigid, elastic and flexible structures, with granular materials, and with extremely intensive loadings are demonstrated. Some discussions on several key techniques in SPH including the balance of accuracy, stability and efficiency, the treatment of material interface, the coupling of SPH with other methods, and the particle regularization and adaptive particle resolution are provided as concluding marks.

Smoothed particle hydrodynamics (SPH) for modeling fluid-structure interactions

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

A particle-element contact algorithm incorporated into the coupling methods of FEM-ISPH and FEM-WCSPH for FSI problems

In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion.

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

A linear smoothed quadratic finite element for the analysis of laminated composite Reissner–Mindlin plates

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.

Detao Wan

Papers

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

A particle-element contact algorithm incorporated into the coupling methods of FEM-ISPH and FEM-WCSPH for FSI problems

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

A linear smoothed quadratic finite element for the analysis of laminated composite Reissner–Mindlin plates

A fully smoothed finite element method for analysis of axisymmetric problems