Edge-based Smoothing Technique Research Articles

An edge-based smoothed numerical manifold method and its application to static, free and forced vibration analyses

As a partition of unity (PU) method, the numerical manifold method (NMM) is able to solve continuous and discontinuous problems in a unified manner. However, the accuracy obtained through the traditional NMM (t-NMM) is far from satisfactory, because the strain distribution is constant in each manifold element. To improve the performance of the t-NMM without adding extra nodes or DOFs, the edge-based smoothing technique, which has been applied in the edge-based finite element method (ES-FEM), is incorporated into the t-NMM, resulting in an edge-based smoothed numerical manifold method (ES-NMM). Formulation of the ES-NMM for static, free and forced vibration analyses are presented in great detail. The numerical examples of static, free and forced vibration problems show that the ES-NMM possesses several advantages over the t-NMM, including the close-to-exact stiffness, superconvergence, and ultra-accuracy.

A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner–Mindlin plates

Probabilistic analysis is becoming more important in mechanical science and real-world engineering applications. In this work, a novel generalized stochastic edge-based smoothed finite element method is proposed for Reissner–Mindlin plate problems. The edge-based smoothing technique is applied in the standard FEM to soften the over-stiff behavior of Reissner–Mindlin plate system, aiming to improve the accuracy of predictions for deterministic response. Then, the generalized nth order stochastic perturbation technique is incorporated with the edge-based S-FEM to formulate a generalized probabilistic ES-FEM framework (GP_ES-FEM). Based upon a general order Taylor expansion with random variables of input, it is able to determine higher order probabilistic moments and characteristics of the response of Reissner–Mindlin plates. The significant feature of the proposed approach is that it not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also overcomes the inherent drawbacks of conventional second-order perturbation approach, which is satisfactory only for small coefficients of variation of the stochastic input field. Two numerical examples for static analysis of Reissner–Mindlin plates are presented and verified by Monte Carlo simulations to demonstrate the effectiveness of the present method.

A Copula-based perturbation stochastic method for fiber-reinforced composite structures with correlations

Under most circumstances, there are correlations among random variables for composite structures, and these correlations can have a considerable effect on the reliability analysis result. Consequently, a Copula-based perturbation stochastic method is proposed to amend the disability of traditional perturbation stochastic method on correlation problems. As a statistical tool, Copula function meets the intrinsic demand of fiber-reinforced composite structures on variable’s correlation and allows the choice of joint cumulative distribution functions (CDFs) to be separate from the marginal CDFs. With the aid of change-of-variable technique, Copula is introduced straightly into the framework to describe the relevance without any special transformation. Besides, the probability curves and reliability index of multi-variables of Gaussian and non-Gaussian can be achieved easily. Furthermore, in order to significantly improve the efficiency and capability to resist the mesh distortion compared with the traditional stochastic FEM, strain matrices are reconstructed by the edge-based smoothing technique. The overall uncertain condition coupled by stochastic fiber orientations, material parameters, and external loads is analyzed. Several examples are provided to verify the validity of the method.

A stochastic perturbation edge-based smoothed finite element method for the analysis of uncertain structural-acoustics problems with random variables

Among the current methods in predicting the response of structural-acoustics problems in mid-frequency regime, some problems such as low accuracy and inability to deal with the uncertainties still need to be solved. To eliminate these issues, a novel stochastic perturbation edge-based smoothed FEM method (SP-ES-FEM) is proposed for the analysis of structural-acoustics problems in this work. The edge-based smoothing technique is applied in the standard FEM approach to soften the over-stiff behavior of structural-acoustics problems aiming to improve the accuracy of deterministic response predictions. Then, this approach, for the first time, intends to introduce the first-order perturbation technique into the edge-based smoothed FEM theory frame especially for the probabilistic analysis of structural-acoustics problems. The response of the coupled systems can be expressed simply as a linear function of all the pre-defined input variables by using the change of variable techniques. Due to the linear relationships of variables and response, the probability density function and cumulative probability density function of the response can be obtained based on the simple mathematical transformation of probability theory. The proposed approach not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also can handle the randomness well in the systems. Two numerical examples for frequency response analysis of random structural-acoustics are presented and verified by Monte Carlo simulation, to demonstrate the effectiveness of the present method.

An edge-based smoothed XFEM for fracture in composite materials

In this work, an edge-based smoothed extended finite element method (ES-XFEM) is extended to fracture analysis in composite materials. This method, in which the edge-based smoothing technique is married with enrichment in XFEM, shows advantages of both the extended finite element method (XFEM) and the edge-based smoothed finite element method (ES-FEM). The crack tip enrichment functions are specially derived to represent the characteristic of the displacement field around the crack tip in composite materials. Due to the strain smoothing, the necessity of integrating the singular derivatives of the crack tip enrichment functions is eliminated by transforming area integration into path integration, which is an obvious advantage compared with XFEM. Two examples are presented to testify the accuracy and convergence rate of the ES-XFEM.

Bending and vibration responses of laminated composite plates using an edge-based smoothing technique

In this paper, bending and vibration analysis of laminated composite plates is carried out using a novel triangular composite plate element based on an edge-based smoothing technique. The present formulation is based on the first-order shear deformation theory, and the discrete shear gap (DSG) method is employed to mitigate the shear locking. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and edge-based smoothing domains are used for the numerical integration to improve the accuracy and the convergence rate of the method. The present formulation is coded and used to solve various example problems of bending and free vibration of laminated composite plates. It is found that the present method can provide excellent results with a wide range of thickness and is free of shear locking.