Meshfree System Research Articles

Efficient 3D analysis of laminate structures using ABD-equivalent material models

Laminate composites are widely used in automotive, aerospace, and increasingly in consumer industries, due to their reduced weight and superior structural properties. However, structural analysis of complex laminate structures remains challenging. 2D finite element methods based on plate/shell theories may be accurate and efficient, but they generally do not apply to the whole structure and require identification and preprocessing of the regions where the underlying assumptions hold. Fully automated structural analysis using solid 3D elements with sufficiently high order basis functions is possible in principle, but is rarely practiced due to the significant increase in the cost of computational integration over a large number of laminate plies.We propose a procedure to replace the original laminate by much simpler new virtual material models. These virtual material models, under the usual assumptions made in lamination theory, have the same constitutive relationship as the corresponding 2D plate model of the original laminate, but require only a small fraction of computational integration costs in 3D FEA. We describe implementation of 3D FEA using these material models in a meshfree system using second order B-spline basis functions. Finally, we demonstrate their validity by showing agreement between computed and known results for standard problems.

Offshore Structural Dynamic Analysis Considering Soil-Structure Interaction by a Coupled BEM and Meshfree Method

An investigation of dynamic offshore structure considering soil-structure interaction by a coupled approach based on boundary element and meshfree methods is presented. The moving Kriging interpolation is used for generating the shape functions because of possessing the Kronecker delta property, which makes easier in imposing the essential boundary conditions. The governing elastodynamic equations are transformed into a standard weak formulation. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard implicit Newmark time integration scheme. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details. A two dimensional plane strain offshorefoundation model has been used for the time history analysis to compute the stresses and displacements against earthquake and wave loading considering the effect of soil-structure interaction. As a consequence, it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods.

The complex variable meshless local Petrov–Galerkin method for elastodynamic problems

The complex variable meshless local Petrov–Galerkin (CVMLPG) method is further developed for structural dynamic analyses of two-dimensional (2D) solids. The complex variable moving least-square (CVMLS) approximation is used to construct the shape function and the Heaviside step function is chosen for representing the test function. In the construction of the well-performed shape function, the trial function of 2D problem is formed with a one-dimensional (1D) basis function, thus improving computational efficiency. The governing elastodynamic equations are transformed into a standard local weak formulation, and then it is discretized into a meshfree system of time-dependent equations, which are solved by the standard implicit Newmark time integration scheme. Numerical results obtained from the proposed CVMLPG method are compared with the exact solutions and those of the conventional MLPG method and excellent agreement is achieved.

A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.

A moving Kriging interpolation-based element-free Galerkin method for structural dynamic analysis

In this paper, a meshfree method based on the moving Kriging interpolation is further developed for free and forced vibration analyses of two-dimensional solids. The shape function and its derivatives are essentially established through the moving Kriging interpolation technique. Following this technique, by possessing the Kronecker delta property the method evidently makes it in a simple form and efficient in imposing the essential boundary conditions. The governing elastodynamic equations are transformed into a standard weak formulation. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard implicit Newmark time integration scheme. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details. As a consequence, it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods.

The Architecture of SAGE - A Meshfree System Based on RFM

. In a meshfree system, a geometric model of a domain neither conforms to, nor is restricted by a spatial discretization. Such systems for engineering analysis offer numerous advantages over the systems that are based on traditional mesh-based methods, but they also require radical approaches to enforcing boundary conditions and novel computational tools for differentiation, integration, and visualization of fields and solutions. We show that all of these challenges can be overcome, and describe SAGE (Semi-Analytic Geometry Engine) – a successful system specifically intended for meshfree engineering analysis. Our approach and individual modules are based on Rvachev’s Function Method (RFM) but the described techniques, algorithms, and software are applicable to all mesh-based and meshfree methods and have broad use beyond solutions of boundary value problems.