Hanjiang Chang^1,2,*, Qiang Tian¹, Haiyan Hu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 825-860, 2023, DOI:10.32604/cmes.2023.022774

Abstract To model a multibody system composed of shell components, a geometrically exact Kirchhoff-Love triangular shell element is proposed. The middle surface of the shell element is described by using the DMS-splines, which can exactly represent arbitrary topology piecewise polynomial triangular surfaces. The proposed shell element employs only nodal displacement and can automatically maintain C¹ continuity properties at the element boundaries. A reproducing DMS-spline kernel skill is also introduced to improve computation stability and accuracy. The proposed triangular shell element based on reproducing kernel DMS-splines can achieve an almost optimal convergent rate. Finally, the proposed shell element is validated via three… More > Graphic Abstract

Hongfen Gao¹, Gaofeng Wei^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.3, pp. 1793-1814, 2022, DOI:10.32604/cmes.2022.019687

Abstract By introducing the radial basis functions (RBFs) into the reproducing kernel particle method (RKPM), the calculating accuracy and stability of the RKPM can be improved, and a novel meshfree method of the radial basis RKPM (meshfree RRKPM) is proposed. Meanwhile, the meshfree RRKPM is applied to transient heat conduction problems (THCP), and the corresponding equations of the meshfree RRKPM for the THCP are derived. The two-point time difference scheme is selected to discretize the time of the THCP. Finally, the numerical results illustrate the effectiveness of the meshfree RRKPM for the THCP. More >

Radwan Abu-Gdairi¹, Shatha Hasan², Shrideh Al-Omari^3,*, Mohammad Al-Smadi^2,4, Shaher Momani^4,5

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 299-313, 2022, DOI:10.32604/cmes.2022.017010

Abstract In this paper, an efficient multi-step scheme is presented based on reproducing kernel Hilbert space (RKHS) theory for solving ordinary stiff differential systems. The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform form for a rapidly convergent series in the posed Sobolev space. Using the Gram-Schmidt orthogonality process, complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction. Consequently, by applying the standard RKHS method to each subinterval, approximate solutions that converge uniformly to the exact solutions are obtained. For this purpose,… More >

Hossein M. Shodja^{1, 2, 3}, Alireza Hashemian^{2, 4}

The International Conference on Computational & Experimental Engineering and Sciences, Vol.13, No.3, pp. 57-58, 2009, DOI:10.3970/icces.2009.013.057

Abstract Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations (ODEs). Subsequently, Gear's method is… More >

Mani Khezri¹, Alireza Hashemian¹, Hossein M. Shodja^1,2,3

The International Conference on Computational & Experimental Engineering and Sciences, Vol.11, No.4, pp. 99-108, 2009, DOI:10.3970/icces.2009.011.099

Abstract Meshless methods using kernel approximation like reproducing kernel particle method (RKPM) and gradient RKPM (GRKPM) generally use a set of particles to discretize the subjected domain. One of the major steps in discretization procedure is determination of associated volumes particles. In a non-uniform or irregular configuration of particles, determination of these volumes comprises some difficulties. This paper presents a straightforward numerical method for determination of related volumes and conducts a survey on influence of different assumption about computing the volume for each particle. Stress intensity factor (SIF) as a major representing parameter in fracture of solids is calculated by employing… More >

M. J. Dai, S. Tanaka^*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.21, No.1, pp. 16-16, 2019, DOI:10.32604/icces.2019.05895

Abstract The J-integral evaluation are analyzed employing effective reproducing kernel method. Several numerical examples of cracked shell structure are carried out to investigate the mixed-mode stress resultant intensity factors (SRIFs). It is formulated by the first order shear deformation plate theory. Reproducing kernel (RK) is used to the meshfree interpolant. A diffraction method, visibility criterion and enriched basis are introduced to model the through crack. J-integral is evaluated based on the stress resultants and is decomposed into the symmetric and asymmetric parts for extracting the mixed-mode SRIFs. The stabilized conforming nodal integration (SCNI) and sub-domain stabilized conforming nodal integration (SSCI) are… More >

H. Rafieayan Zadeh¹, M. Mohammadi^1,2, E. Babolian¹

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.6, pp. 375-396, 2015, DOI:10.3970/cmes.2015.108.375

Abstract A local reproducing kernel method based on spatial trial space spanned by the Newton basis functions in the native Hilbert space of the reproducing kernel is proposed. It is a truly meshless approach which uses the local sub clusters of domain nodes for approximation of the arbitrary field. It leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs). An adaptive algorithm, so-called adaptive residual subsampling, is used to adjust nodes in order to remove oscillations which are caused by a sharp gradient. The method is applied for solving the Allen-Cahn and Burgers’ equations.… More >

Chih-Ping Wu^1,2, Ruei-Yong Jiang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.3, pp. 239-279, 2014, DOI:10.3970/cmes.2014.097.239

Abstract A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) buckling analysis of simply-supported, carbon nanotube-reinforced composite (CNTRC) circular hollow cylinders and laminated composite ones under axial compression. The single-walled carbon nanotubes (CNTs) and polymer are used as the reinforcements and matrix, respectively, to constitute the CNTRC cylinder. Three different distributions of CNTs varying in the thickness direction are considered (i.e., the uniform distribution and functionally graded rhombus-, and X-type ones), and the through-thickness distributions of effective material properties of the cylinder are determined using the rule of mixtures. The 3D linear buckling theory is used,… More >

M. Mohammadi¹, R. Mokhtari^2,3, R. Schaback⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.2, pp. 113-138, 2014, DOI:10.3970/cmes.2014.101.113

Abstract In this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by the method of lines. The proposed method is implemented as a meshless method based on spatial trial functions in the reproducing kernel Hilbert spaces. For efficiency and stability reasons, we use the Newton basis introduced recently by Müller and Schaback. The method is shown to work in all interesting situations described by Hopf bifurcations and Turing patterns. More >

Mohammad Mashayekhi¹, Hossein M. Shodja^1,2, Reza Namakian¹

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.1, pp. 19-60, 2011, DOI:10.3970/cmes.2011.076.019

Abstract A meshless method called reproducing kernel particle method (RKPM) is exploited to cope with elastic-plastic fracture mechanics (EPFM) problems. The idea of arithmetic progression is assumed to place particles within the refinement zone in the vicinity of the crack tip. A comparison between two conventional treatments, visibility and diffraction, to crack discontinuity is conducted. Also, a tracking to find the appropriate diffraction parameter is performed. To assess the suggestions made, two mode I numerical simulations, pure tension and pure bending tests, are executed. Results including J integral, crack mouth opening displacement (CMOD), and plastic zone size and shape are compared… More >