Angran Li¹, Xiaoqi Chai², Ge Yang^2,3, Yongjie Jessica Zhang^1,2,*

Molecular & Cellular Biomechanics, Vol.16, Suppl.2, pp. 66-66, 2019, DOI:10.32604/mcb.2019.07633

Abstract Neurons exhibit remarkably complex geometry in their neurite networks. So far, how materials are transported in the complex geometry for survival and function of neurons remains an unanswered question. Answering this question is fundamental to understanding the physiology and disease of neurons. Here, we have developed an isogeometric analysis (IGA) based platform for material transport simulation in neurite networks. We modeled the transport process by reaction-diffusion-transport equations and represented geometry of the networks using truncated hierarchical tricubic B-splines (THB-spline3D). We solved the Navier-Stokes equations to obtain the velocity field of material transport in the networks. We then solved the transport… More >

P.H. Wen¹, M.H. Aliabadi²

Structural Durability & Health Monitoring, Vol.3, No.2, pp. 107-120, 2007, DOI:10.3970/sdhm.2007.003.107

Abstract In the last decade, meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. Based on the variation of potential energy, the element-free Galerkin method is developed on the basis of finite element method by the use of radial basis function interpolation. An enriched radial basis function is formulated to capture the stress singularity at the crack tip. The usual advantages of finite element method are retained in this method but now significant improvement of accuracy. Neither the connectivity of mesh in the domain by the finite element method or integrations… More >

J. Sladek¹, V. Sladek, Ch.Zhang²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 131-144, 2005, DOI:10.3970/sdhm.2005.001.131

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2-d), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static and transient elastodynamic problems are considered. For time-dependent problems, the Laplace-transform technique is utilized. A unit step function is used as the test function in the local weak-form. It is leading to local boundary integral equations (LBIEs) involving only a domain-integral in the case of transient dynamic problems. The analyzed domain is divided into small subdomains with a circular shape. The moving least-squares (MLS) method is adopted for approximating the physical… More >

K. Wang, S.J. Zhou, Z.F. Nie

The International Conference on Computational & Experimental Engineering and Sciences, Vol.18, No.4, pp. 115-116, 2011, DOI:10.3970/icces.2011.018.115

Abstract The natural neighbour Galerkin method is tailored to solve boundary value problems of the couple-stress elasticity to model the size dependent behaviour of materials. This method is based on the displacement-based Galerkin approach, and the calculation of the global stiffness matrix is performed using gradient smoothing technique combined with the non-Sibsonian partition of unity approximation scheme. This method possesses the following properties: the complex C1-continuous approximation scheme is avoided without using either Lagrange multipliers or penalty parameters; no domain integrals involved in the assembly of the global stiffness matrix; and the imposition of essential boundary conditions is straightforward. The validity… More >

Ju Hye Park, Jeom Kee Paik, S.N. Atluri

The International Conference on Computational & Experimental Engineering and Sciences, Vol.19, No.3, pp. 69-70, 2011, DOI:10.3970/icces.2011.019.069

Abstract The aim of the present paper is to develop a semi-analytical method which and quickly and accurately compute the ultimate strength response of rectangular plates under combined loads and non-uniform lateral pressure. It is assumed that the plating is simply supported at four edges which are kept straight. A unique feature of developed method was found to give reasonably accurate results for practical design purpose in terms of the large deflection analysis of plates under non uniformed lateral pressure. The present paper treated by analytically solving the nonlinear governing differential equations of the elastic large deflection plate theory. It will… More >

K. Kakuda¹, Y. Maeda¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.14, No.1, pp. 37-42, 2010, DOI:10.3970/icces.2010.014.037

Abstract The applications of a finite element scheme to one-dimensional linear advection-diffusion equation, the incompressible Navier-Stokes equations, and compressible Euler system of equations are presented. The mesh-based scheme is the Petrov-Galerkin weak formulation with exponential weighting functions. Some numerical results demonstrate the workability and the validity of the present approach. More >

M.L. Xie¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.14, No.3, pp. 85-90, 2010, DOI:10.3970/icces.2010.014.085

Abstract Various basis function based on Fourier-Chebyshev Petrov-Galerkin spectral method is described for computation of temporal linear stability in a circular jet. Basis functions presented here are exponentially mapped Chebyshev functions. There is a linear dependence between the components of the vector field according to the perturbation continuum equation. Therefore, there are only two degrees of freedom. According to the principle of permutation and combination, the basis function has three basic forms, i.e., the radial, azimuthal or axial component is free. The results show that three eigenvalues for various cases are consistent, but the basis function in case I is preferable… More >

Xie Ming-Liang¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.14, No.2, pp. 57-62, 2010, DOI:10.3970/icces.2010.014.057

Abstract Various basis function based on Fourier-Chebyshev Petrov-Galerkin spectral method is described for computation of temporal linear stability in a circular jet. Basis functions presented here are exponentially mapped Chebyshev functions. There is a linear dependence between the components of the vector field according to the perturbation continuum equation. Therefore, there are only two degrees of freedom. According to the principle of permutation and combination, the basis function has three basic forms, i.e., the radial, azimuthal or axial component is free. The results show that three eigenvalues for various cases are consistent, but the basis function in case I is preferable… More >

Arif Amirov¹, Mustafa Yildiz¹, Zekeriya Ustaoglu¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.4, pp. 115-124, 2009, DOI:10.3970/icces.2009.012.115

Abstract In this work we deal with solvability and aproximation to the solution of the two dimensional integral geometry problem for a family of regular curves of given curvature. Solvability of the problem is proved by using the Galerkin method and an algorithm is developed to compute the approximate solution of the problem. More >

Mustafa Yildiz¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.12, No.3, pp. 103-110, 2009, DOI:10.3970/icces.2009.012.103

Abstract The solvability conditions of an inverse problem for the non-stationary kinetic equation is formulated and a new numerical method is developed to obtain the approximate solution of the problem. A comparison between the approximate solution and the exact solution of the problem is presented. More >