CMES-Vol. 12, No. 3, 2006

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Computing Prager's Kinematic Hardening Mixed-Control Equations in a Pseudo-Riemann Manifold
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 161-180, 2006, DOI:10.3970/cmes.2006.012.161
Abstract Materials' internal spacetime may bear certain similarities with the external spacetime of special relativity theory. Previously, it is shown that material hardening and anisotropy may cause the internal spacetime curved. In this paper we announce the third mechanism of mixed-control to cause the curvedness of internal spacetime. To tackle the mixed-control problem for a Prager kinematic hardening material, we demonstrate two new formulations. By using two-integrating factors idea we can derive two Lie type systems in the product space of M^m+1⊗Mⁿ⁺¹. The Lie algebra is a direct sum of so(m,1)⊕so(n,1), and correspondingly the symmetry group is a direct product of… More >

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Applications of MLPG Method in Dynamic Fracture Problems
L. Gao¹, K. Liu^1,2, Y. Liu³
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 181-196, 2006, DOI:10.3970/cmes.2006.012.181
Abstract A new numerical algorithm based on the Meshless Local Petrov-Galerkin approach is presented for analyzing the dynamic fracture problems in elastic media. To simplify the treatment of essential boundary condition, a novel modified Moving Least Square (MLS) procedure is proposed by introducing Lagrange multiplier into MLS procedure, which can perform both MLS approximation and interpolation in one approximation domain. The compact spline function is used as the test function in the local form of elasto-dynamic equations. For the feature of stress wave propagation, the coupled second-order ODEs respect to the time are solved by the explicit central difference method with… More >

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A Group Preserving Scheme for Burgers Equation with Very Large Reynolds Number
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 197-212, 2006, DOI:10.3970/cmes.2006.012.197
Abstract In this paper we numerically solve the Burgers equation by semi-discretizing it at the n interior spatial grid points into a set of ordinary differential equations: u^· = f(u,t), u ∈ Rⁿ. Then, we take the dissipative behavior of Burgers equation into account by considering the magnitude ||u|| as another component; hence, an augmented quasilinear differential equations system X^˙ = AX with X := (u^T,||u||)^T ∈ Mⁿ⁺¹ is derived. According to a Lie algebra property of A∈so(n,1) we thus develop a new numerical scheme with the transformation matrix G∈SO_o(n,1) being an element of the proper orthochronous Lorentz group.… More >

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Structured Mesh Refinement in Generalized Interpolation Material Point (GIMP) Method for Simulation of Dynamic Problems
Jin Ma, Hongbing Lu, Ranga Komanduri¹
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 213-228, 2006, DOI:10.3970/cmes.2006.012.213
Abstract The generalized interpolation material point (GIMP) method, recently developed using a C¹ continuous weighting function, has solved the numerical noise problem associated with material points just crossing the cell borders, so that it is suitable for simulation of relatively large deformation problems. However, this method typically uses a uniform mesh in computation when one level of material points is used, thus limiting its effectiveness in dealing with structures involving areas of high stress gradients. In this paper, a spatial refinement scheme of the structured grid for GIMP is presented for simulations with highly localized stress gradients. A uniform structured background… More >

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Buckling of Honeycomb Sandwiches: Periodic Finite Element Considerations
D. H. Pahr¹, F.G. Rammerstorfer¹
CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.3, pp. 229-242, 2006, DOI:10.3970/cmes.2006.012.229
Abstract Sandwich structures are efficient lightweight materials. Due to there design they exhibit very special failure modes such as global buckling, shear crimping, facesheet wrinkling, facesheet dimpling, and face/core yielding. The core of the sandwich is usually made of foams or cellular materials, e.g., honeycombs. Especially in the case of honeycomb cores the correlation between analytical buckling predictions and experiments might be poor (Ley, Lin, and Uy (1999)). The reason for this lies in the fact that analytical formulae typically assume a homogeneous core (continuous support of the facesheets). This work highlights problems of honeycomb core sandwiches in a parameter regime,… More >

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