Chunglun Kuo*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 173-173, 2019, DOI:10.32604/icces.2019.05272

Abstract In this article, a directional method of particular solution (DMPS) is derived to solve the 3D Poisson equation in an arbitrary domain. The proposed DMPS for the 3D problems are based on the 2D particular solution. Together with the directional technique we can construct the 3D particular solution easily by introducing a series of planar directors into the 2D particular solution. The intensities of the basis functions are determined by imposing the boundary condition on the boundary collocation points. Besides, the inverse Cauchy problems are also addressed in this article. The inverse problems are highly ill-posed in nature. In order… More >

Ming-Hsiao Lee^1,2, Wen-Hwa Chen^1,3

The International Conference on Computational & Experimental Engineering and Sciences, Vol.14, No.4, pp. 115-124, 2010, DOI:10.3970/icces.2010.014.115

Abstract The meshless method has a distinct advantage that it needs only nodes without an element mesh which usually induces time-consuming work and inaccuracy when the elements are distorted during the analysis process. However, the element mesh provides the geometric information for numerical simulation without the need to judge if the nodes or integration points are inside the analysis domain as in the meshless method, such as the boundary of the analysis domain which is defined by the element's edges or faces and that the integration points are intrinsically inside the elements. Because the analysis model with only nodes in the… More >

Yanan Liu¹, Yinghua liu¹, Zhangzhi Cen¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.3, pp. 139-144, 2007, DOI:10.3970/icces.2007.003.139

Abstract In this paper, a Daubechies(DB) wavelet-based meshless method is proposed to analyze 2-D elastoplasticity problems. Using DB wavelet scaling functions and wavelet functions as basis functions to approximate the unknown field functions, there is no need to construct the shape functions costly as done in FEM and conventional meshless methods. Incremental formulations are established for solution of 2-D elastoplasticity problems. In addition, the property of DB wavelet is used to make the method concise in formulations, flexible in applications and easy to realize. Due to the lack of Kroneker delta properties in scaling functions and wavelet functions, the penalty method… More >

R. Vignjevic¹, T. De Vuyst², J.C. Campbell¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 107-112, 2007, DOI:10.3970/icces.2007.003.107

Abstract An approach to the treatment of contact problems involving frictionless sliding and separation under large deformations in meshless methods is proposed. The method is specially suited for non-structured spatial discretisation. The contact conditions are imposed using a contact potential for particles in contact. Inter-penetration is checked as a part of the neighbourhood search. In the case of conventional SPH contact conditions are enforced on the boundary layer 2h thick while in the case of the normalized SPH contact conditions are enforced for the particles lying on the contact surface. The implementation of the penalty based contact algorithm for the central… More >

Chein-Shan Liu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.2, pp. 57-68, 2007, DOI:10.3970/icces.2007.003.057

Abstract A new method is developed to solve the interior and exterior Dirichlet problems for the two-dimensional Laplace equation, namely the meshless regularized integral equation method (MRIEM), which consists of three parts: Fourier series expansion, the second kind Fredholm integral equation and an analytically regularized solution of the unknown boundary condition on an artificial circle. We find that the new method is powerful even for the problem with very complex boundary shape and with boundary noise. 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 >

Wen-Hwa Chen¹, Cheng-Hung Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 177-190, 2005, DOI:10.3970/cmes.2005.008.177

Abstract An enriched meshless method, using meshless interpolations and a global Galerkin approach, is developed for the analysis of three-dimensional fracture problems. The displacement field which accounts for the stress singularity nearby the crack front and the boundary layer effect at the intersection between the crack front and the free surface of the structure is adopted to enrich the trial functions. The three-dimensional stress intensity factors can thus be treated as independent unknown parameters and calculated with the nodal displacements directly. To estimate the accuracy of the method developed, several representative three-dimensional cracks are analyzed. These include single-edge crack, embedded elliptical… More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 149-172, 2005, DOI:10.3970/cmes.2005.007.149

Abstract The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some example problems are solved by… More >

E. J. Sellountos¹, V. Vavourakis², D. Polyzos³

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.1, pp. 35-48, 2005, DOI:10.3970/cmes.2005.007.035

Abstract A new meshless local Petrov-Galerkin (MLPG) type method based on local boundary integral equation (LBIE) considerations is proposed for the solution of elastostatic problems. It is called singular/hypersingular MLPG (LBIE) method since the representation of the displacement field at the internal points of the considered structure is accomplished with the aid of the displacement local boundary integral equation, while for the boundary nodes both the displacement and the corresponding traction local boundary integral equations are employed. Nodal points spread over the analyzed domain are considered and the moving least squares (MLS) interpolation scheme for the approximation of the interior and… 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 >