Wenyuan Chen¹, Tao Zhang², Yantao Yang^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.3, pp. 1-1, 2023, DOI:10.32604/icces.2023.09754

Abstract Based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary. For boundary with simple geometry, we theoretically analyze the error between the desired volume force at boundary and the actual force applied by the original method. The ratio between the two forces is very close to a constant and exhibits a very narrow distribution. A spatially uniform coefficient is then introduced to correct the force and can be fixed by the least-square method over all boundary markers. Such method is explicit and non-iterative, and is easy… More >

Mohd Ahmed^1,*, Devender Singh², Saeed Al Qadhi¹, Nguyen Viet Thanh³

CMES-Computer Modeling in Engineering & Sciences, Vol.129, No.1, pp. 167-189, 2021, DOI:10.32604/cmes.2021.014672

Abstract The performance of a-posteriori error methodology based on moving least squares (MLS) interpolation is explored in this paper by varying the finite element error recovery parameters, namely recovery points and field variable derivatives recovery. The MLS interpolation based recovery technique uses the weighted least squares method on top of the finite element method's field variable derivatives solution to build a continuous field variable derivatives approximation. The boundary of the node support (mesh free patch of influenced nodes within a determined distance) is taken as circular, i.e., circular support domain constructed using radial weights is considered. The field variable derivatives (stress… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.6, pp. 665-678, 2003, DOI:10.3970/cmes.2003.004.665

Abstract The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weak-forms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numerical solution of the non-hyper-singular displacement and traction BIEs [given in Han, and Atluri (2003)], which are simply derived by using the gradients of the displacements of the fundamental solutions [Okada, Rajiyah, and Atluri (1989a,b)]. By employing the various types of test functions,… More >

Jin Yeon Cho¹, Jae Mo An², You Me Song¹, Seungsoo Lee¹, Dong Whan Choi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.1, pp. 1-18, 2005, DOI:10.3970/cmes.2005.009.001

Abstract A displacement welding technique is proposed to carry out coupled analysis of the integrated whole model which consists of independently modeled finite element substructures. In the proposed method, the incompatible displacement fields in the interfaces of independently modeled substructures are directly welded together through a blended function that is newly defined in the transient region of mismatching interface. To construct the blended function, the moving least squares function, which does not require well-defined nodal connectivity, is utilized along with the original finite element shape function. The meshless character of the moving least squares function makes it possible to efficiently handle… More >

S. N. Atluri¹, Shengping Shen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.3, pp. 241-268, 2005, DOI:10.3970/cmes.2005.007.241

Abstract Various MLPG methods, with the MLS approximation for the trial function, in the solution of a 4$^{th}$ order ordinary differential equation are illustrated. Both the primal MLPG methods and the mixed MLPG methods are used. All the possible local weak forms for a 4$^{th}$ order ordinary differential equation are presented. In the first kind of mixed MLPG methods, both the displacement and its second derivative are interpolated independently through the MLS interpolation scheme. In the second kind of mixed MLPG methods, the displacement, its first derivative, second derivative and third derivative are interpolated independently through the MLS interpolation scheme. The… More >

S. N. Atluri¹, Z. D. Han¹, A. M. Rajendran²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 491-514, 2004, DOI:10.3970/cmes.2004.006.491

Abstract The Meshless Finite Volume Method (MFVM) is developed for solving elasto-static problems, through a new Meshless Local Petrov-Galerkin (MLPG) ``Mixed'' approach. In this MLPG mixed approach, both the strains as well as displacements are interpolated, at randomly distributed points in the domain, through local meshless interpolation schemes such as the moving least squares(MLS) or radial basis functions(RBF). The nodal values of strains are expressed in terms of the independently interpolated nodal values of displacements, by simply enforcing the strain-displacement relationships directly by collocation at the nodal points. The MLPG local weak form is then written for the equilibrium equations over… More >

J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 477-490, 2004, DOI:10.3970/cmes.2004.006.477

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for solution of static and elastodynamic problems in a homogeneous anisotropic medium. The Heaviside step function is used as the test functions in the local weak form. It is leading to derive local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace transfor technique is applied and the LBIEs are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry such as circles in 2-d problems. The final form of local integral equations has a pure contour character only in… More >

Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 169-188, 2004, DOI:10.3970/cmes.2004.006.169

Abstract Three different truly Meshless Local Petrov-Galerkin (MLPG) methods are developed for solving 3D elasto-static problems. Using the general MLPG concept, these methods are derived through the local weak forms of the equilibrium equations, by using different test functions, namely, the Heaviside function, the Dirac delta function, and the fundamental solutions. The one with the use of the fundamental solutions is based on the local unsymmetric weak form (LUSWF), which is equivalent to the local boundary integral equations (LBIE) of the elasto-statics. Simple formulations are derived for the LBIEs in which only weakly-singular integrals are included for a simple numerical implementation.… More >

Z. D. Han¹, S. N. Atluri²

CMC-Computers, Materials & Continua, Vol.1, No.2, pp. 129-140, 2004, DOI:10.3970/cmc.2004.001.129

Abstract A Meshless Local Petrov-Galerkin (MLPG) method has been developed for solving 3D elasto-dynamic problems. It is derived from the local weak form of the equilibrium equations by using the general MLPG concept. By incorporating the moving least squares (MLS) approximations for trial and test functions, the local weak form is discretized, and is integrated over the local sub-domain for the transient structural analysis. The present numerical technique imposes a correction to the accelerations, to enforce the kinematic boundary conditions in the MLS approximation, while using an explicit time-integration algorithm. Numerical examples for solving the transient response of the elastic structures… More >

Q. Wang¹, Y. Miao^1,2, H.P. Zhu¹, C. Zhang³

CMC-Computers, Materials & Continua, Vol.28, No.1, pp. 1-26, 2012, DOI:10.3970/cmc.2012.028.001

Abstract The Hybrid boundary node method (Hybrid BNM) is a boundary type meshless method which based on the modified variational principle and the Moving Least Squares (MLS) approximation. Like the boundary element method (BEM), it has a dense and unsymmetrical system matrix and needs to be speeded up while solving large scale problems. This paper combines the fast multipole method (FMM) with Hybrid BNM for solving 3D elasticity problems. The formulations of the fast multipole Hybrid boundary node method (FM-HBNM) which based on spherical harmonic series are given. The computational cost is estimated and an O(N) algorithm is obtained. The algorithm… More >