Chih-Ping Wu^*, Ruei-Syuan Chang

CMES-Computer Modeling in Engineering & Sciences, Vol.141, No.1, pp. 917-949, 2024, DOI:10.32604/cmes.2024.052307 - 20 August 2024

Abstract This work develops a Hermitian C differential reproducing kernel interpolation meshless (DRKIM) method within the consistent couple stress theory (CCST) framework to study the three-dimensional (3D) microstructure-dependent static flexural behavior of a functionally graded (FG) microplate subjected to mechanical loads and placed under full simple supports. In the formulation, we select the transverse stress and displacement components and their first- and second-order derivatives as primary variables. Then, we set up the differential reproducing conditions (DRCs) to obtain the shape functions of the Hermitian C differential reproducing kernel (DRK) interpolant’s derivatives without using direct differentiation. The interpolant’s… More >

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 - 05 January 2023

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 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 - 19 April 2022

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 - 29 November 2021

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 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 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 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… 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 More >

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.3, pp. 249-284, 2010, DOI:10.3970/cmes.2010.066.249

Abstract We propose a family of 3D versions of a smooth finite element method (Sunilkumar and Roy 2010), wherein the globally smooth shape functions are derivable through the condition of polynomial reproduction with the tetrahedral B-splines (DMS-splines) or tensor-product forms of triangular B-splines and 1D NURBS bases acting as the kernel functions. While the domain decomposition is accomplished through tetrahedral or triangular prism elements, an additional requirement here is an appropriate generation of knotclouds around the element vertices or corners. The possibility of sensitive dependence of numerical solutions to the placements of knotclouds is largely arrested… More >