K. Y. Liu^1,2, S. Y. Long^1,2,3, G. Y. Li¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.5, No.2, pp. 99-120, 2008, DOI:10.3970/icces.2008.005.099

Abstract A meshless local Petrov-Galerkin method (MLPG)^[1] for the analysis of cracks in isotropic functionally graded materials is presented. The meshless method uses the moving least squares (MLS) to approximate the field unknowns. The shape function has not the Kronecker Delta properties for the trial-function-interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular integrals to generate the global effective stiffness matrix if body force is ignored; it only involves a regular boundary integral. The material properties are smooth functions of spatial coordinates and two interaction integrals^[2,3] are… More >

S. Tanaka¹, H. Okada¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 217-224, 2007, DOI:10.3970/icces.2007.003.217

Abstract It has been recognized that the bottle-neck in solid/structural analyses using the finite element method is in their model generation phase. Methodologies that eliminate the needs for "elements" have been proposed by many researchers. They can be categorized into "meshless" and "virtually meshless" finite element methods. The "meshless" method may be represented by moving least square Ptrov-Galerkin (MLPG) method [1] and element free Galerkin Method (EFGM) [2]. The free-mesh method [3] and voxel finite element method [4], etc. are classified to be the "virtually meshless" approaches. The "meshless" methods eliminated needs for element connectivity information in their input data and… More >

S.S. Chen¹, Y.H. Liu¹, Z.Z. Cen¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 145-150, 2007, DOI:10.3970/icces.2007.003.145

Abstract A solution procedure for lower bound limit analysis is presented making use of the element free Galerkin (EFG) method rather than of the traditional numerical methods such as finite element method and boundary element method. A reduced basis technique is adopted to solve the mathematical programming iteratively in a sequence of reduced self-equilibrium stress subspaces with very low dimensions. Numerical example in this paper shows that it is feasible and efficient to solve the problems of limit analysis by using the EFG method. More >

Taku Itoh^1,*, Soichiro Ikuno²

The International Conference on Computational & Experimental Engineering and Sciences, Vol.21, No.2, pp. 44-44, 2019, DOI:10.32604/icces.2019.05521

Abstract The purpose of this study is to efficiently solve N by N linear systems Ax = b obtained by eXtended Element-free Galerkin method (X-EFG). X-EFG is one of the meshless methods for discretizing partial differential equations, and the linear systems have asymmetric saddle point structure. In this study, the block Krylov subspace methods have been applied for solving linear systems obtained by X-EFG. Note that the block Krylov subspace methods are usually employed for solving linear systems with multiple right hand sides, AX = B, where X = [x₁, x₂, …, x_L], B = [b₁, b₂, …, b_L], and L… More >

J. Sladek¹, V. Sladek¹, J. Krivacek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 259-270, 2005, DOI:10.3970/cmes.2005.008.259

Abstract A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary value problem into a 2-d… 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 >

Angran Li¹, Xiaoqi Chai², Ge Yang^2,3, Yongjie Jessica Zhang^1,2,*

Molecular & Cellular Biomechanics, Vol.16, No.2, pp. 123-140, 2019, DOI:10.32604/mcb.2019.06479

Abstract Neurons exhibit remarkably complex geometry in their neurite networks. So far, how materials are transported in the complex geometry for survival and function of neurons remains an unanswered question. Answering this question is fundamental to understanding the physiology and disease of neurons. Here, we have developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solved the Navier-Stokes equations to obtain the velocity field of material transport in the networks. We then solved the transport… More >

J. Sladek¹, V. Sladek¹, S. Krahulec¹, M. Wünsche², Ch. Zhang²

CMC-Computers, Materials & Continua, Vol.29, No.1, pp. 75-102, 2012, DOI:10.3970/cmc.2012.029.075

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve static and dynamic problems of two-layered magnetoelectroelastic composites with specific properties. One layer has pure piezoelectric properties and the second one is a pure piezomagnetic material. It is shown that the electric potential in the piezoelectric layer is induced by the magnetic potential in the piezomagnetic layer. The magnetoelectric effect is dependent on the ratio of the layer thicknesses. Functionally graded material properties of the piezoelectric layer and homogeneous properties of the piezomagnetic layer are considered too. The magnetoelectric composites are analyzed under a pure magnetic or… More >

A. Rezaei Mojdehi^1,2, A. Darvizeh³, A. Basti²

CMC-Computers, Materials & Continua, Vol.29, No.1, pp. 15-40, 2012, DOI:10.3970/cmc.2012.029.015

Abstract The meshless local Petrov-Galerkin approach is proposed for the nonlinear dynamic analysis of three-dimensional (3D) elasto-plastic problems. Galerkin weak-form formulation is applied to derive the discrete governing equations. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a unit test function and local weak-form formulation in three dimensional continua for the general dynamic problems is derived. Three dimensional Moving Least-Square (MLS) approximation is considered as shape function to approximate the field variable of scattered nodes in the problem domain. Normality hypothesis of plasticity is adopted to define the stress-strain… More >

V. Panchore¹, R. Ganguli², S. N. Omkar³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.4, pp. 215-237, 2015, DOI:10.3970/cmes.2015.108.215

Abstract A rotating Timoshenko beam free vibration problem is solved using the meshless local Petrov-Galerkin method. A locking-free shape function formulation is introduced with an improved radial basis function interpolation and the governing differential equations of the Timoshenko beam are used instead of the alternative formulation used by Cho and Atluri (2001). The locking-free approximation overcomes the problem of ill conditioning associated with the normal approximation. The radial basis functions satisfy the Kronercker delta property and make it easier to apply the essential boundary conditions. The mass matrix and the stiffness matrix are derived for the meshless local Petrov-Galerkin method. Results… More >