摘要 :
Nonconforming point interpolation method (NPIM) is a meshless method that has been applied to problems in mechanics in the last years. In this paper, we investigate NPIM in electromagnetism. We present its formulation and shape fu...
展开
Nonconforming point interpolation method (NPIM) is a meshless method that has been applied to problems in mechanics in the last years. In this paper, we investigate NPIM in electromagnetism. We present its formulation and shape functions, which are generated by the radial point interpolation method with polynomial terms. The numerical results are compared to the ones obtained by the finite flement method (FEM) and the element-free Galerkin method (EFG).
收起
摘要 :
In this work a computational model based on a meshless method, the Element Free Galerkin Method (EFG), is applied in the simulation of forging processes. Contact and friction are handled by blending finite elements with the EFG in...
展开
In this work a computational model based on a meshless method, the Element Free Galerkin Method (EFG), is applied in the simulation of forging processes. Contact and friction are handled by blending finite elements with the EFG in order to overcome the difficulty of meshless methods in dealing with essential boundary conditions. Special interface finite elements are established between the tools and the workpiece, allowing to impose directly those conditions. An application example in forging is analyzed and the numerical solution of the proposed model is compared with experimental results as well as with a traditional finite element solution.
收起
摘要 :
This paper demonstrates that the element-free Galerkin 9EFG) method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2D elasticity. The continuum-based variational equations for ...
展开
This paper demonstrates that the element-free Galerkin 9EFG) method can be successfully used in shape design sensitivity analysis and shape optimization for problems in 2D elasticity. The continuum-based variational equations for displacement sensitivities are derived and are subsequently discretized.
收起
摘要 :
Meshless methods have shown increased accuracy and better convergence rates compared to other well-known simulation methods in a variety of computational mechanics problems. Their computational cost is relatively higher especially...
展开
Meshless methods have shown increased accuracy and better convergence rates compared to other well-known simulation methods in a variety of computational mechanics problems. Their computational cost is relatively higher especially in adaptivity analysis, when new nodes are inserted at each step, where the construction of updated shape functions requires a significant amount of computational effort. In this paper, two hierarchical formulations are proposed in the context of an h-type refinement scheme. The addition of new nodes and subsequently the re-calculation of the influenced moment matrices, that are necessary for obtaining the shape functions and their derivatives and subsequently for the construction of the stiffness matrix, are properly addressed. Both hierarchical schemes do not need the recalculation of the initial stiffness matrix but only the additional node contributions to each shape function field, while the second scheme produces purely hierarchically refined stiffness matrices leaving the initial stiffness matrix unmodified.
收起
摘要 :
Chloride-induced corrosion is a key factor in the premature corrosion of concrete structures exposed to a marine environment. Fick's second law of diffusion is the dominant equation to model diffusion of chloride ions. This equati...
展开
Chloride-induced corrosion is a key factor in the premature corrosion of concrete structures exposed to a marine environment. Fick's second law of diffusion is the dominant equation to model diffusion of chloride ions. This equation is traditionally solved by Finite Element Method (FEM) and Finite Difference Method (FDM). Although these methods are robust and efficient, they may face some numerical issues due to discretization process. This study solves the Fick's equation using the Element-Free Galerkin (EFG) method as well as traditional FEM and FDM. The results of these numerical methods are compared together, and validated with the analytical solution in special cases. The results show that the EFG method predicts the service life of the concrete structures, more accurately than the other methods, and exhibits the lowest displacement error and energy error for a constant diffusion coefficient problem. FDM can be performed very efficiently for simple models, and the displacement errors produced by this method do not differ considerably from the EFG results. Therefore, FDM could compete with the EFG method in simple geometries. FEM can be used with a sufficient number of elements while the convergence of the results should be controlled. However, in complicated models, FEM and especially the EFG method are much more flexible than FDM.
收起
摘要 :
In this paper, an error estimator for element-free Galerkin (EFG) method has been proposed. Since meshfree methods do not require a structured mesh or a sense of nodal belongingness, the methods offer the advantage of insertion, d...
展开
In this paper, an error estimator for element-free Galerkin (EFG) method has been proposed. Since meshfree methods do not require a structured mesh or a sense of nodal belongingness, the methods offer the advantage of insertion, deletion, and redistribution of nodes adaptively in the problem domain. The trial function of the field variable is constructed entirely in terms of consistent basis functions and its associated coefficient. The proposed error estimator is based on the nodal coefficient-vector of the basis functions that are used to construct the trial function. After obtaining the nodal coefficient-vector from EFG solution, an attempt is made to recover the best nodal coefficient-vector based on the reduced domain of influence [Chung and Belytschko (1998)], which is sufficient enough to maintain the regularity of the EFG moment matrix and also ensuring that sufficient influencing nodes are present in all the four quadrants defined at the sample node. The vertices of the Voronoi polygon of the critical error nodes are considered as potential neighborhood and new nodes are inserted at the vertices. Numerical studies have been carried out to illustrate the performance of the proposed methodology of error estimator and adaptivity.
收起
摘要 :
This paper presents a formulation for shape optimization in thermoelasticity using a meshless method, namely the element-free Galerkin method. Two examples are treated in detail and comparisons with previously published finite ele...
展开
This paper presents a formulation for shape optimization in thermoelasticity using a meshless method, namely the element-free Galerkin method. Two examples are treated in detail and comparisons with previously published finite element analysis results demonstrate the excellent opportunities the EFG offers for solving these types of problems. Smoother stresses, no remeshing, and better accuracy than finite element solutions, permit answers to shape optimization problems in thermoelasticity that are practically unattainable with the classical FEM without remeshing. For the thermal fin example, the EFG finds finger shapes that are missed by the FEM analysis, and the objective value is greatly improved compared to the FEM solution. A study of the influence of the number of design parameters is performed and it is observed that the EFG can give better results with a smaller number of design parameters than is possible with traditional methods.
收起
摘要 :
In this article, the element free Galerkin (EFG) method is applied to carry out the topology optimization of the geometrically non-linear continuum structures. In EFG method, the moving least squares shape function is used to appr...
展开
In this article, the element free Galerkin (EFG) method is applied to carry out the topology optimization of the geometrically non-linear continuum structures. In EFG method, the moving least squares shape function is used to approximate the displacements. The 2D geometrically non-linear formulation is presented based on the EFG method. The penalty method is explored to enforce the essential boundary conditions. Considering the relative density of nodes as design variables, the minimization of compliance as an objective function, the mathematical formulation of the topology optimization is developed using the solid isotropic microstructures with penalization interpolation scheme. Sensitivity of the objective function is derived based on the adjoint method. Numerical examples show that the proposed approach is feasible and effective for the topology optimization of the geometrically non-linear continuum structures.
收起
摘要 :
In this article, the element free Galerkin (EFG) method is applied to carry out the topology optimization of the geometrically non-linear continuum structures. In EFG method, the moving least squares shape function is used to appr...
展开
In this article, the element free Galerkin (EFG) method is applied to carry out the topology optimization of the geometrically non-linear continuum structures. In EFG method, the moving least squares shape function is used to approximate the displacements. The 2D geometrically non-linear formulation is presented based on the EFG method. The penalty method is explored to enforce the essential boundary conditions. Considering the relative density of nodes as design variables, the minimization of compliance as an objective function, the mathematical formulation of the topology optimization is developed using the solid isotropic microstructures with penalization interpolation scheme. Sensitivity of the objective function is derived based on the adjoint method. Numerical examples show that the proposed approach is feasible and effective for the topology optimization of the geometrically non-linear continuum structures.
收起
摘要 :
This paper presents a signal inversion technique in nondestructive evaluation (NDE) application for defect profile reconstruction using the element-free galerkin (EFG) method and state space search. The advantage of EFG method is...
展开
This paper presents a signal inversion technique in nondestructive evaluation (NDE) application for defect profile reconstruction using the element-free galerkin (EFG) method and state space search. The advantage of EFG method is that it relies only on a set of nodes, instead of a complex mesh to discretize the solution domain. In the inversion procedure, remeshing is avoided to increase the efficiency and accuracy of the solution, which is a major advantage over the traditional finite-element method (FEM). The iterative state space search method using the tree structure is developed for implementing the defect updating scheme. Preliminary results are presented for validation. The robustness of the technique has been shown on noisy signals.
收起
原文获取