CMES-Vol. 73, No. 4, 2011

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ARTICLE

A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis
N. Vu-Bac¹, H. Nguyen-Xuan², L. Chen³, S. Bordas⁴, P. Kerfriden⁴, R.N. Simpson⁴, G.R. Liu⁵, T. Rabczuk¹
CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 331-356, 2011, DOI:10.3970/cmes.2011.073.331
Abstract This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration… More >

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Improvement of Coarse-Grained Particle Method for Materials: Finite-Temperature and Inhomogeneity Effects
T. Nakamura¹, R. Kobyashi¹, S. Ogata¹
CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 357-386, 2011, DOI:10.3970/cmes.2011.073.357
Abstract The coarse-grained particle (CGP) method has been proposed to coarse-grain a crystalline system of atoms to meso-scale. In the method, virtual particles are distributed in the system, and the inter-particle interaction is calculated through the constrained statistical ensemble average of the atomic Hamiltonian at a given temperature. For simplicity, however, the harmonic approximation has been used for the inter-atomic interaction and hence anharmonicity at finite temperatures has been ignored. We improve the former CGP method to incorporate the anharmonicity of atomic system at finite temperatures into the inter-particle interaction. Also the divide-and-conquer strategy is applied to calculate the inter-particle interaction… More >

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Three-Dimensional Simulation of the Shear Properties of Steel-Concrete Composite Beams using an Interface Slip Model
Shiqin He¹, Pengfei Li¹, Feng Shang²
CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 387-394, 2011, DOI:10.3970/cmes.2011.073.387
Abstract A three-dimensional finite element (FE) and analytical approach for the simulation of the shear properties of steel-concrete composite beams are presented in this paper. To simulate the interfacial behavior between steel girders and concrete slabs, we apply an interface slip model in the simulation. This model has been used in analyzing the flexural properties of composite beams. Both simply supported beam and continuous composite beam experiments reported in literature are simulated. The load deflection and slip rule between steel girders and concrete slabs, as well as the crack pattern and contour at the ultimate load, are analyzed. The results obtained… More >

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An Iterative Algorithm for Solving a System of Nonlinear Algebraic Equations, F(x) = 0, Using the System of ODEs with an Optimum α in x^· = λ[αF + (1−α)B^TF]; B_ij = ∂F_i/∂x_j
Chein-Shan Liu¹, Satya N. Atluri²
CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 395-432, 2011, DOI:10.3970/cmes.2011.073.395
Abstract In this paper we solve a system of nonlinear algebraic equations (NAEs) of a vector-form: F(x) = 0. Based-on an invariant manifold defined in the space of (x,t) in terms of the residual-norm of the vector F(x), we derive a system of nonlinear ordinary differential equations (ODEs) with a fictitious time-like variable t as an independent variable: x^· = λ[αF + (1−α)B^TF], where λ and α are scalars and B_ij = ∂F_i/∂x_j. From this set of nonlinear ODEs, we derive a purely iterative algorithm for finding the solution vector x, without having to invert the Jacobian (tangent stiffness matrix)… More >

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