J. Sladek¹, V. Sladek¹, S.N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.3, pp. 309-318, 2004, DOI:10.3970/cmes.2004.006.309

Abstract Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equations which are given in the Laplace transform domain. The analyzed domain is covered by small subdomains with a simple geometry. To eliminate the number of unknowns on artificial boundaries of subdomains the modified fundamental solution and/or the parametrix with a convenient cut-off… More >

Q. Li¹, S. Shen¹, Z. D. Han¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.5, pp. 571-586, 2003, DOI:10.3970/cmes.2003.004.571

Abstract In this paper, a truly meshless method, the Meshless Local Petrov-Galerkin (MLPG) Method, is developed for three-dimensional elasto-statics. The two simplest members of MLPG family of methods, the MLPG type 5 and MLPG type 2, are combined, in order to reduce the computational requirements and to obtain high efficiency. The MLPG5 method is applied at the nodes inside the 3-D domain, so that any domain integration is eliminated altogether, if no body forces are involved. The MLPG 2 method is applied at the nodes that are on the boundaries, and on the interfaces of material discontinuities, so that the boundary… More >

D. Zupan¹, M. Saje¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 301-318, 2003, DOI:10.3970/cmes.2003.004.301

Abstract A new finite element formulation of the `kinematically exact finite-strain beam theory' is presented. The finite element formulation employs the generalized virtual work in which the main role is played by the pseudo-curvature vector. The solution of the governing equations is found by using a combined Galerkin-collocation algorithm. More >

R. Vignjevic, T. De Vuyst, M. Gourma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 319-336, 2001, DOI:10.3970/cmes.2001.002.319

Abstract The work presented provides an overview of different types of kernel interpolation used in the SPH method: conventional SPH, normalised SPH (NSPH), corrected kernel SPH (CSPH) and normalised corrected kernel SPH (NCSPH). These four methods are considered in a fully mesh-free form (using no background mesh). To illustrate the effect of using different interpolation methods two problems were simulated: a 1D symmetric elastic impact problem, and a shock-tube. An overview of the simulation results for the two problems is given. Shortcomings for the interpolation schemes tested were identified and discussed. It is concluded that NCSPH provides the best results. To… 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 motion with an inertial term.… More >

Guojing Wu¹, Chao Zhang^1,*, Pingzeng Liu¹, Wanming Ren², Yong Zheng², Feng Guo¹, Xiaowei Chen³, Russell Higgs⁴

CMC-Computers, Materials & Continua, Vol.58, No.1, pp. 183-195, 2019, DOI:10.32604/cmc.2019.03792

Abstract In order to solve the hidden regional relationship among garlic prices, this paper carries out spatial quantitative analysis of garlic price data based on ArcGIS technology. The specific analysis process is to collect prices of garlic market from 2015 to 2017 in different regions of Shandong Province, using the Moran's Index to obtain monthly Moran indicators are positive, so as to analyze the overall positive relationship between garlic prices; then using the geostatistical analysis tool in ArcGIS to draw a spatial distribution Grid diagram, it was found that the price of garlic has a significant geographical agglomeration phenomenon and showed… More >

Xiaorui Zhang^1,2,3,*, Pengpai Wang¹, Wei Sun², Norman I. Badler³

CMC-Computers, Materials & Continua, Vol.55, No.2, pp. 297-319, 2018, DOI:10.3970/cmc.2018.01764

Abstract Real-time performance and accuracy are two most challenging requirements in virtual surgery training. These difficulties limit the promotion of advanced models in virtual surgery, including many geometric and physical models. This paper proposes a physical model of virtual soft tissue, which is a twist model based on the Kriging interpolation and membrane analogy. The proposed model can quickly locate spatial position through Kriging interpolation method and accurately compute the force change on the soft tissue through membrane analogy method. The virtual surgery simulation system is built with a PHANTOM OMNI haptic interaction device to simulate the torsion of virtual stomach… More >