CMES-Vol. 30, No. 1, 2008

Open Access

ARTICLE

A Lie-Group Shooting Method for Post Buckling Calculations of Elastica
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 1-16, 2008, DOI:10.3970/cmes.2008.030.001
Abstract In this paper we propose a new numerical integration method of second-order boundary value problems (BVPs) resulting from the elastica of slender rods under different loading conditions and boundary conditions. We construct a compact space shooting method for finding unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(T) and the establishment of a generalized mid-point Lie group element G(r) by using the mean value theorem. Then, by imposing G(T) = G(r) we can search the missing initial condition through a closed-form solution in terms of the weighting factor r More >

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ARTICLE

An Efficient Model for Crack Propagation
S.S. Xu, Y. Dong, Y. Zhang
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 17-26, 2008, DOI:10.3970/cmes.2008.030.017
Abstract A meshless method for arbitrary crack growths is presented. The new method is based on a local partition of unity by introducing additional degrees of freedom that determine the opening of the crack. The crack is modeled with overlapping crack segments located at the nodes. The crack segments are rotated at directional changes of the principal tensile stress such that smearing of the crack is avoided. Such smearing occurs in fixed crack method probably because of inaccurate stress state around the crack tip when the crack propagates. The key feature of our method is that More >

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ARTICLE

Exact Large Deflection of Beams with Nonlinear Boundary Conditions
Sen Yung Lee¹, Sheei Muh Lin², Chien Shien Lee³, Shin Yi Lu³, Yen Tse Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 27-36, 2008, DOI:10.3970/cmes.2008.030.027
Abstract An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five 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 More >

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ARTICLE

The MLPG Mixed Collocation Method for Material Orientation and Topology Optimization of Anisotropic Solids and Structures
Shu Li¹, S. N. Atluri²
CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 37-56, 2008, DOI:10.3970/cmes.2008.030.037
Abstract In this paper, a method based on a combination of an optimization of directions of orthotropy, along with topology optimization, is applied to continuum orthotropic solids with the objective of minimizing their compliance. The spatial discretization algorithm is the so called Meshless Local Petrov-Galerkin (MLPG) "mixed collocation'' method for the design domain, and the material-orthotropy orientation angles and the nodal volume fractions are used as the design variables in material optimization and topology optimization, respectively. Filtering after each iteration diminishes the checkerboard effect in the topology optimization problem. The example results are provided to illustrate More >

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