Topic
Meshfree methods
About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.
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12 May 2006
TL;DR: The comparison between the RKPM and the FEM under identical conditions shows that the RkPM is more suitable for problems, where there exists extremely large strain such as in the case of slope sliding.
Abstract: Among meshfree methods to overcome the ineffectiveness in handling extreme material deformation, Reproducing Kernel Particle Method (RKPM) has demonstrated its great suitability for structural analysis. This paper presents applications of RKPM in elasto-plastic problems after a review of meshfree methods and an introduction to RKPM. Different from the graph-based partitioning methods such as Metis, which is quite popular for mesh-based analysis, a geometry-based partitioner is developed and used in parallel computing of the meshfree method. The effectiveness and performance with different partitions are then compared and a comparison of the meshfree method with finite element methods is presented. A slope stability problem in geotechnical engineering is analyzed as an illustrative case. The parallel simulations are conducted on an SGI Onyx3900 supercomputer and a Dawning TC4000L PC cluster, with MPI message passing statements used for all communications among processors for various partitions. The comparison between the RKPM and the FEM under identical conditions shows that the RKPM is more suitable for problems, where there exists extremely large strain such as in the case of slope sliding.
1 citations
Journal Article•
TL;DR: Concrete fracture mechanics models and mesh free methods are summarized in this paper, and meshfree methods are focused on concrete fracture mechanics methods.
Abstract: Concrete fracture mechanics models and meshfree methods are summarized in this paper,and meshfree methods are focused on.Author's opinions and suggestion on simulation of cracks in concrete structure are proposed and could give reference to simulation of cracks.
1 citations
01 Jan 2009
TL;DR: In this paper, a cellular automata (CA) approach is presented for the solution of heat conduction problem, where each cell considered as a fixed point in a regular grid lead to the solutions of a system of equations is substituted by discrete systems of equations with small dimensions.
Abstract: Many computational techniques were applied to solution of heat conduction problem. Those techniques were the finite difference (FD), finite element (FE) and recently meshless methods. FE is commonly used in solution of equation of heat conduction problem based on the summation of stiffness matrix of elements and the solution of the final system of equations. Because of summation process of finite element, convergence rate was decreased. Hence in the present paper Cellular Automata (CA) approach is presented for the solution of heat conduction problem. Each cell considered as a fixed point in a regular grid lead to the solution of a system of equations is substituted by discrete systems of equations with small dimensions. Results show that CA can be used for solution of heat conduction problem.
1 citations
TL;DR: In this paper, the local radial point interpolation method (LRPIM) is developed for the investigation of time dependent problems in solid mechanics, where integrands are approximated up to the second order of the Taylor series and the integrals are evaluated on some points, which are located inside the local quadrature domains, called integration points.
Abstract: In this paper, the local radial point interpolation method (LRPIM) is developed for the investigation of time dependent problems in solid mechanics. By a new integration scheme considered for the obtained meshless weak form, integrands are approximated up to the second order of the Taylor series and the integrals are evaluated on some points, which are located inside the local quadrature domains, called integration points. In order to show the efficiency of the suggested method, some time dependent mechanical problems are considered for the engineering structures such as beams and plates, which are subjected to dynamical loads, the deflections and stresses are evaluated. Finally, it has been shown that using the proposed method greatly reduces the number of integration points without affecting the accuracy of the results.
1 citations
TL;DR: In this article, a regularized local boundary integral equation (RLBIE) method is proposed to solve problems of elasticity with nonhomogeneous material properties, which is a pure meshless integral method.
Abstract: The local boundary integral equation (LBIE) method is a pure meshless integral method proposed by Atluri and co-workers. Since the fundamental solutions are used as the test functions, the sub-domain can be very small and the LBIE method is a promising method for solving problems of elasticity with nonhomogeneous material properties. In this paper, the subtraction technique is introduced to remove the strong singularity that results in a regularized local boundary integral equation (RLBIE) method. The formula is rather straightforward and more accurate than other treatment techniques. Compared with other meshless methods, more geometrical parameters need to be assigned in the method. If the parameters change a little bit, the solutions obtained from the method may fluctuate quickly and uncertainly. Therefore the effects of weight function, support domain, sub-domain, and monomial basis are investigated and how to select the parameters is discussed. The appropriate parameters can be determined and the meshless RLBIE method is an accurate and robust method.
1 citations