L. Gao¹, K. Liu^1,2, Y. Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 181-196, 2006, DOI:10.3970/cmes.2006.012.181

Abstract A new numerical algorithm based on the Meshless Local Petrov-Galerkin approach is presented for analyzing the dynamic fracture problems in elastic media. To simplify the treatment of essential boundary condition, a novel modified Moving Least Square (MLS) procedure is proposed by introducing Lagrange multiplier into MLS procedure, which can perform both MLS approximation and interpolation in one approximation domain. The compact spline function is used as the test function in the local form of elasto-dynamic equations. For the feature of stress wave propagation, the coupled second-order ODEs respect to the time are solved by the… More >

R. Ahrem¹, A. Beckert², H. Wendland³

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.2, pp. 121-136, 2006, DOI:10.3970/cmes.2006.012.121

Abstract We present a new efficient scheme for loose coupling in fluid-structure-interaction problems as they typically appear in the context of aircraft design. This coupling scheme is based upon a multivariate scattered data interpolation approach, based on radial basis functions and partition of unity methods. It allows us to couple arbitrary meshes on fluid and structure side. It conserves virtual work and forces. It is designed for large scale problems and allows the coupling of entire aircraft meshes. More >

S. Masuda¹, H. Noguchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 131-144, 2006, DOI:10.3970/cmes.2006.011.131

Abstract This paper presents a novel and accurate technique for modeling discontinuous derivatives in meshfree methods, which will be used in the analysis of structures with material interfaces. The novelty lies in the formulation of the Moving Least Squares Approximation (MLSA) scheme where an introduced discontinuous derivative basis function replaces the conventional linear basis function. Furthermore, it is easy to implement this novelty into existing meshfree methods, such as the Element Free Galerkin (EFG) method, which are based on the MLSA scheme. The successful analyses of one and two-dimensional structures with material interfaces demonstrate the potential More >

Vladimir Sladek¹, Jan Sladek¹, Chuanzeng Zhang²

CMC-Computers, Materials & Continua, Vol.4, No.3, pp. 177-188, 2006, DOI:10.3970/cmc.2006.004.177

Abstract This paper concerns the stability, convergence of accuracy and cost efficiency of four various formulations for solution of boundary value problems in non-homogeneous elastic solids with functionally graded Young's modulus. The meshless point interpolation method is employed with using various basis functions. The interaction among the elastic continuum constituents is considered in the discretized formulation either by collocation of the governing equations or by integral satisfaction of the force equilibrium on local sub-domains. The exact benchmark solutions are used in numerical tests. More >

J. Sladek¹, V. Sladek¹, Ch. Zhang², F. Garcia-Sanche³, M. Wünsche²

CMC-Computers, Materials & Continua, Vol.4, No.2, pp. 109-118, 2006, DOI:10.3970/cmc.2006.004.109

Abstract Piezoelectric materials have wide range engineering applications in smart structures and devices. They have usually anisotropic properties. Except this complication electric and mechanical fields are coupled each other and the governing equations are much more complex than that in the classical elasticity. Thus, efficient computational methods to solve the boundary or the initial-boundary value problems for piezoelectric solids are required. In this paper, the Meshless local Petrov-Galerkin (MLPG) method with a Heaviside step function as the test functions is applied to solve two-dimensional (2-D) piezoelectric problems. The mechanical fields are described by the equations of… More >

H. T. Liu¹, Z. D. Han¹, A. M. Rajendran², S. N. Atluri³

CMC-Computers, Materials & Continua, Vol.4, No.1, pp. 43-54, 2006, DOI:10.3970/cmc.2006.004.043

Abstract The Rajendran-Grove (RG) ceramic damage model is a three-dimensional internal variable based constitutive model for ceramic materials, with the considerations of micro-crack extension and void collapse. In the present paper, the RG ceramic model is implemented into the newly developed computational framework based on the Meshless Local Petrov-Galerkin (MLPG) method, for solving high-speed impact and penetration problems. The ability of the RG model to describe the internal damage evolution and the effective material response is investigated. Several numerical examples are presented, including the rod-on-rod impact, plate-on-plate impact, and ballistic penetration. The computational results are compared More >

L.S. Miers¹, J.C.F. Telles²

Structural Durability & Health Monitoring, Vol.1, No.3, pp. 225-232, 2005, DOI:10.3970/sdhm.2005.001.225

Abstract The present paper aims at introducing the concept of Green's function type fundamental solutions (i.e., unit source fundamental solutions satisfying particular boundary conditions) into the context of meshless approaches, particularly dealing with the local boundary integral equation method (LBIE) derived from the classic boundary integral equation procedure. The Green's functions discussed here are mainly the so-called half-plane solution, corresponding to a unit source within a semi-plane bounded by a flux-free straight line and an infinite plane containing internal lines of potential discontinuity. The latter is here introduced in numerical fashion, as an extension of the More >

J. Sladek¹, V. Sladek, Ch.Zhang²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 131-144, 2005, DOI:10.3970/sdhm.2005.001.131

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-d), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test function in the local weak-form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is More >

G. Dhondt¹

Structural Durability & Health Monitoring, Vol.1, No.1, pp. 21-34, 2005, DOI:10.3970/sdhm.2005.001.021

Abstract An algorithm is described which allows for the automatic calculation of crack propagation due to cyclic loading under mixed-mode conditions. The core of the procedure deals with the insertion of an arbitrarily formed crack into a virgin 20-node brick element mesh, thereby generating new quadratic bricks. One especially difficult aspect is the extension of the triangulation of the crack surface up to the boundary of the crack front elements. In the present article the technique is applied to linear elastic calculations using the stress intensity factor concept and a Paris-type law. However, other crack propagation More >

E. Ferretti¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.1, pp. 19-48, 2005, DOI:10.3970/cmes.2005.009.019

Abstract In this study nonlocality is discussed with regard to the differential and discrete formulations. Here, nonlocality is found to be a concept attaining not to the description of the material, but to the governing equations. This has made it possible to discuss the opportunity of introducing nonlocality in the constitutive equations, in order to give respectability to strain-softening damage models. When using the differential formulation, a length scale must be introduced into the material description of a strain-softening modeling, particularly when the size-effect is involved. In the opinion of the Author, this need lies in… More >