Annamaria Mazzia¹, Giorgio Pini¹, Flavio Sartoretto²

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 475-497, 2014, DOI:10.3970/cmes.2014.102.475

Abstract Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques for solving Partial Differential Equations. One of pure meshless methods main applications is for implementing Adaptive Discretization Techniques. In this paper, we describe our fresh node–wise refinement technique, based upon estimations of the “local” Total Variation of the approximating function. We numerically analyze the accuracy and efficiency of our MLPG–based refinement. Solutions to test Poisson problems are approximated, which undergo large variations inside small portions of the domain. We show that 2D problems can be accurately solved. The gain in accuracy with respect to uniform discretizations is shown to be… More >

Y.C. Shiah¹, C.L. Tan^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.6, pp. 425-447, 2014, DOI:10.3970/cmes.2014.102.425

Abstract Green’s functions, or fundamental solutions, are necessary items in the formulation of the boundary integral equation (BIE), the analytical basis of the boundary element method (BEM). In the formulation of the BEM for 3D general anisotropic elasticity, considerable attention has been devoted to developing efficient algorithms for computing these quantities over the years. The mathematical complexity of this Green’s function has also posed an obstacle in the development of this numerical method to treat problems of 3D anisotropic thermoelasticity. This is because thermal effects manifest themselves as an additional domain integral in the integral equation; this has implications for the… More >

R. Q. Rodríguez^1,2, C. L. Tan², P. Sollero¹, E. L. Albuquerque³

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 359-372, 2014, DOI:10.3970/cmes.2014.102.359

Abstract The efficient evaluation of the fundamental solution for 3D general anisotropic elasticity is a subject of great interest in the BEM community due to its mathematical complexity. Recently, Tan, Shiah, andWang (2013) have represented the algebraically explicit form of it developed by Ting and Lee (Ting and Lee, 1997; Lee, 2003) by a computational efficient double Fourier series. The Fourier coefficients are numerically evaluated only once for a specific material and are independent of the number of field points in the BEM analysis. This work deals with the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross… More >

V. Giusti ¹, B. Montagnini ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.3, pp. 229-255, 2014, DOI:10.3970/cmes.2014.102.229

Abstract An application of a 3D Boundary Element Method (BEM), coupled with the Response Matrix (RM) technique, to solve the neutron diffusion and transport equations for multi-region domains is presented. The discussion is here limited to steady state problems, in which the neutrons have a wide energy spectrum, which leads to systems of several diffusion or transport equations. Moreover, the number of regions with different physical constants can be very large. The boundary integral equations concerning each region are solved via a polynomial moment expansion and, taking advantage of suitable recurrence formulas, the multi-fold integrals there involved are reduced to single… More >

Csaba Gáspár¹

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.6, pp. 365-386, 2014, DOI:10.3970/cmes.2014.101.365

Abstract The Method of Fundamental Solutions (MFS) is investigated for 3D potential problem in the case when the source points are located along the boundary of the domain of the original problem and coincide with the collocation points. This generates singularities at the boundary collocation points, which are eliminated in different ways. The (weak) singularities due to the singularity of the fundamental solution at the origin are eliminated by using approximate but continuous fundamental solution instead of the original one (regularization). The (stronger) singularities due to the singularity of the normal derivatives of the fundamental solution are eliminated by solving special… More >

Tao Jiang^1,2, Yuan-Sheng Tang¹, Jin-Lian Ren^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.4, pp. 249-297, 2014, DOI:10.3970/cmes.2014.101.249

Abstract In this work, a corrected three-dimensional smoothed particle hydrodynamics (CSPH-3D) method is proposed to simulate the polymer free surface flows in the filling process based on the eXtended Pom-Pom (XPP) model, and some complex deformation phenomena are also numerically predicted. The proposed CSPH-3D method is mainly motivated by a coupled concept that an extended kernel-gradient-corrected SPH (KGC-SPH) method is used in the interior of fluid flow and the traditional SPH (TSPH) method is used near the boundary domain. The present 3D particle method has higher accuracy and better stability than the TSPH-3D method. Meanwhile, a density diffusive term is introduced… More >

Xuejuan Li^1,2, Jie Ouyang^2,3, Wen Zhou²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.6, pp. 379-407, 2013, DOI:10.3970/cmes.2013.096.379

Abstract The three-dimensional (3D) mathematical models for thermal residual stress and warpage are proposed in injection molding, in which the temperature model is rebuilt by considering the phase-change effect to improve the computational accuracy. The 3D thermal residual stress model is transformed into the incremental displacement model so that the boundary conditions can be imposed easily. A modified finite element neural network (FENN) method is used for solving 3D warpage model based on the advantages of finite element method and neural network. The influence of phase-change on temperature is discussed. The numerical simulations of thermal residual stress and warpage are realized,… More >

Y.C. Shiah¹, C.L. Tan², Y.H. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 243-257, 2013, DOI:10.3970/cmes.2013.096.243

Abstract The present authors have recently proposed an efficient, alternative approach to numerically evaluate the fundamental solution and its derivatives for 3D general anisotropic elasticity. It is based on a double Fourier series representation of the exact, explicit form of the Green’s function derived by Ting and Lee (1997). This paper reports on the successful implementation of the fundamental solution and its derivatives based on this Fourier series scheme in the boundary element method (BEM) for 3D general anisotropic elastostatics. Some numerical examples of stress concentration problems and a crack problem are presented to demonstrate the veracity of the implementation. The… More >

F.C. de Araújo^1,2, C. R. da Silva Jr.¹, M. J. Hillesheim¹

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.3, pp. 185-198, 2013, DOI:10.3970/cmes.2013.096.185

Abstract In this paper, the BE SBS (subregion-by-subregion) algorithm, a generic substructuring technique for the BEM, is applied to evaluate stresses at boundary and interfacial points of general 3D composites and solids. At inner points, regular boundary integration schemes may be employed. For boundary or interfacial points, the Hooke’s law along with global-to-local axis-rotation transformations is directly applied. In fact, in thin-walled domain parts, only boundary stresses are needed. As the SBS algorithm allows the consideration of a generic number of subregions, the technique applies to the stress analysis in any composite and solid, including the microstructural (grain-by-grain) modeling of materials.… More >

Martino Pani¹, Fulvia Taddei¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.4, pp. 279-300, 2013, DOI:10.3970/cmes.2013.094.279

Abstract The Cell Method (CM) is a numerical method to solve field equations starting from its direct algebraic formulation. For two-dimensional problems it has been demonstrated that using simplicial elements with an affine interpolation, the CM obtains the same fundamental equation of the Finite Element Method (FEM); using the quadratic interpolation functions, the fundamental equation differs depending on how the dual cell is defined. In spite of that, the CM can still provide the same convergence rate obtainable with the FEM. Particularly, adopting a uniform triangulation and basing the dual cells on the Gauss points of the primal edges, the CM… More >