Chih-Ping Wu^1,2, Kuan-Hao Chiu², Yung-Ming Wang²

CMES-Computer Modeling in Engineering & Sciences, Vol.35, No.3, pp. 181-214, 2008, DOI:10.3970/cmes.2008.035.181

Abstract A mesh-free collocation method based on differential reproducing kernel (DRK) approximations is developed for the three-dimensional (3D) analysis of simply-supported, doubly curved functionally graded (FG) magneto-electro-elastic shells under the mechanical load, electric displacement and magnetic flux. The material properties of FG shells are firstly regarded as heterogeneous through the thickness coordinate and then specified to obey an identical power-law distribution of the volume fractions of the constituents. The novelty of the present DRK-based collocation method is that the shape functions of derivatives of reproducing kernel (RK) approximants are determined using a set of differential reproducing… More >

X.Y. Cui^1,2, G. R. Liu^2,3, G. Y. Li^1,4, G. Zheng¹

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 217-230, 2008, DOI:10.3970/cmes.2008.038.217

Abstract In this paper, a gradient smoothed formulation is proposed to deal with a fourth-order differential equation of Bernoulli-Euler beam problems for static and dynamic analysis. Through the smoothing operation, the C¹ continuity requirement for fourth-order boundary value and initial value problems can be easily relaxed, and C⁰ interpolating function can be employed to solve C¹ problems. In present thin beam problems, linear shape functions are employed to approximate the displacement field, and smoothing domains are further formed for computing the smoothed curvature and bending moment field. Numerical examples indicate that very accurate results can be yielded when More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are More >

P.H. Wen¹, M.H. Aliabadi², Y.W. Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 133-148, 2008, DOI:10.3970/cmes.2008.030.133

Abstract Based on the variation of potential energy, the element-free Galerkin method (MFGM) has been investigated for structures with crack on the basis of radial base function interpolation. An enriched radial base function is introduced to capture the singularities of stress at the crack tips. The advantages of the finite element method are remained in this method and there is a significant improvement of accuracy, particularly for the crack problems of fracture mechanics. The applications of the element-free Galerkin method with enriched radial base function to two-dimensional fracture mechanics in functionally graded materials have been presented More >

Chih-Ping Wu¹, Kuan-Hao Chiu, Yun-Ming Wang

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.3, pp. 163-186, 2008, DOI:10.3970/cmes.2008.027.163

Abstract A differential reproducing kernel particle (DRKP) method is proposed and developed for the analysis of simply supported, multilayered elastic and piezoelectric plates by following up the consistent concepts of reproducing kernel particle (RKP) method. Unlike the RKP method in which the shape functions for derivatives of the reproducing kernel (RK) approximants are obtained by directly taking the differentiation with respect to the shape functions of the RK approximants, we construct a set of differential reproducing conditions to determine the shape functions for the derivatives of RK approximants. On the basis of the extended Hellinger-Reissner principle, More >

W. Brocks¹, I. Scheider¹

Structural Durability & Health Monitoring, Vol.3, No.2, pp. 69-80, 2007, DOI:10.3970/sdhm.2007.003.069

Abstract Cohesive models are used for numerical crack extension analyses in order to predict the mechanical behavior of structures in cases of crack path bifurcation. Possible applications range from the macroscopic to the microscopic scale. As an example of applications to macroscopic engineering structures, simulations of a stiffened cylindrical shell under internal pressure are presented, where a skin crack may penetrate the rib or deviate. On the micro-scale, unit-cell calculation for a fiber-reinforced material is performed, where the fiber may debond or break. More >

S. Tanaka¹, H. Okada¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.4, pp. 217-224, 2007, DOI:10.3970/icces.2007.003.217

Abstract It has been recognized that the bottle-neck in solid/structural analyses using the finite element method is in their model generation phase. Methodologies that eliminate the needs for "elements" have been proposed by many researchers. They can be categorized into "meshless" and "virtually meshless" finite element methods. The "meshless" method may be represented by moving least square Ptrov-Galerkin (MLPG) method [1] and element free Galerkin Method (EFGM) [2]. The free-mesh method [3] and voxel finite element method [4], etc. are classified to be the "virtually meshless" approaches. The "meshless" methods eliminated needs for element connectivity information… More >

Jie Wang¹, Tong-Yi Zhang¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.3, No.1, pp. 1-8, 2007, DOI:10.3970/icces.2007.003.001

Abstract Two-dimensional phase field simulations of stress-free ferroelectric nanoparticles with different long-range (LR) electrostatic interactions are conducted based on the time-dependent Ginzburg-Landau equation. Polarization patterns and the toroidal moment of polarization are found to be dependent on the LR electrostatic interaction and the size of the simulated nanoparticle. Phase field simulations exhibit vortex patterns with purely toroidal moments of polarization and negligible macroscopic polarization in the stress-free ferroelectric nanoparticles when the LR electrostatic interaction is fully taken into account. However, a single-domain structure without any toroidal moment of polarization is formed in small particles if the More >

Chany Lee¹, Chang-Hwan Im², Hyun-Kyo Jung³, Hong-Kyu Kim⁴, Do Wan Kim⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process More >

M. Heshmatzadeh, G. E. Bridges¹

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.1, pp. 45-58, 2007, DOI:10.3970/cmes.2007.018.045

Abstract Cell Method, a Finite Formulation technique, is compared in detail with the Finite Element Method (FEM), a differential-based numerical technique. In the finite formulation technique, Poisson's equation is described starting from a topological foundation. The final set of algebraic equations resulting from the two approaches are compared in matrix form. The equivalence of the coefficient matrices is proven for a Voronoi dual mesh and linear shape functions in the FEM. The difference between the source (charge) vectors in the two approaches is described. It is shown that the use of linear shape functions in the More >