K.G. Vinod¹, S. Gopalakrishnan¹, R. Ganguli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 197-208, 2006, DOI:10.3970/cmes.2006.016.197

Abstract A spectral finite element formulation for a rotating beam subjected to small duration impact is presented in this paper. The spatial variation in centrifugal force is modeled in an average sense. Spectrum and dispersion plots are obtained as a function of rotating speed. It is shown that the flexural wave tends to behave non-dispersively at very high rotation speeds. The numerical results are simulated for two rotating waveguides of different dimensions. The results show that there is a steep increase in responses with the response peaks and the reflected signals almost vanishing at higher rotating More >

J. X. Zhou¹, T. Koziara¹, T. G. Davies¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 131-140, 2006, DOI:10.3970/cmes.2006.016.131

Abstract The classical BEM approach for elastodynamics can produce poor results when high gradients are generated by impulses. High gradient areas evolve over time and their locations are unknown a priori, so they usually can not be captured by uniform meshes. In this paper, we propose a novel method which interpolates both spatial and temporal domains. A direct space-time discretization scheme is used to capture the wave fronts accurately and to forestall generation of spurious oscillations there. Some numerical examples are given to demonstrate the power and scope of the method. More >

Fabian M. E. Duddeck¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 1-14, 2006, DOI:10.3970/cmes.2006.016.001

Abstract In general, the use of Boundary Element Methods (BEM) is restricted to physical cases for which a fundamental solution can be obtained. For simple differential operators (e.g. isotropic elasticity) these special solutions are known in their explicit form. Hence, the realization of the BEM is straight forward. For more complicated problems (e.g. anisotropic materials), we can only construct the fundamental solution numerically. This is normally done before the actual problem is tackled; the values of the fundamental solutions are stored in a table and all values needed later are interpolated from these entries. The drawbacks… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.3, pp. 179-196, 2006, DOI:10.3970/cmes.2006.015.179

Abstract This paper studies the numerical computations of the second-order singularly perturbed boundary value problems (SPBVPs). In order to depress the singularity we consider a coordinate transformation from the x-domain to the t-domain. The relation between singularity and stiffness is demonstrated, of which the coordinate transformation parameter λ plays a key role to balance these two tendencies. Then we construct a very effective Lie-group shooting method to search the missing initial condition through a weighting factor r ∈ (0,1) in the t-domain formulation. For stabilizing the new method we also introduce two new systems by a translation of More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.15, No.2, pp. 69-86, 2006, DOI:10.3970/cmes.2006.015.069

Abstract In this paper we will study the numerical integrations of second order boundary value problems under the imposed conditions at t=0 and t=T in a general setting. We can construct a compact space shooting method for finding the unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(u₀,u_T) and the establishment of a mid-point Lie group element G(r). Then, by imposing G(u₀,u_T) = G(r) we can search the missing initial conditions through an iterative solution of the weighting factor r ∈ (0,1). Numerical examples were examined to convince that the new More >

L.S. Miers¹, J.C.F. Telles²

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 161-170, 2006, DOI:10.3970/cmes.2006.014.161

Abstract This work aims at extending the concept of the Numerical Green's Function (NGF), well known from boundary element applications to fracture mechanics, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals over the crack boundary and is introduced only for source points whose support touches or contains the crack. The results obtained with the coupling of NGF-LBIE in previous potential discontinuity Laplace's equation problems and the authors' experience in NGF-BEM fracture mechanics were the motivation for this development. More >

L.A. de Lacerda¹, J. M. da Silva¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.3, pp. 153-160, 2006, DOI:10.3970/cmes.2006.014.153

Abstract A two-dimensional boundary element formulation is presented and coupled to a genetic algorithm to identify polarization curves of buried slender structures. The dual boundary element method is implemented to model the cathodic protection of the metallic body and the genetic algorithm is employed to deal with the inverse problem of determining the non-linear polarization curve, which describes the relation between current density and electrochemical potential at the soil metal interface. In this work, this non-linear relation resulting from anodic and cathodic reactions is represented by a classical seven parameters expression. Stratified soil resistivity is modeled More >

Z. D. Han¹, H. T. Liu¹, A. M. Rajendran², S. N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 119-128, 2006, DOI:10.3970/cmes.2006.014.119

Abstract This paper presents the implementation of a three-dimensional dynamic code, for contact, impact, and penetration mechanics, based on the Meshless Local Petrov-Galerkin (MLPG) approach. In the current implementation, both velocities and velocity-gradients are interpolated independently, and their compatibility is enforced only at nodal points. As a result, the time consuming differentiations of the shape functions at all integration points is avoided, and therefore, the numerical process becomes more stable and efficient. The ability of the MLPG code for solving high-speed contact, impact and penetration problems with large deformations and rotations is demonstrated through several computational More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.14, No.2, pp. 77-90, 2006, DOI:10.3970/cmes.2006.014.077

Abstract In this paper we derive the first-order and second-order one-step GPS applied to the estimation of thermophysical properties. Solving the resultant algebraic equations, which usually converges within ten iterations, it is not difficult to estimate the unknown temperature-dependent thermal conductivity and heat capacity simultaneously, if some supplemented data of measured temperature at a time T is provided. When the measured temperature in the conducting slab is contaminated by noise, our estimated results are also good. The new method does not require any prior information on the functional forms of thermal conductivity and heat capacity. Numerical examples More >

H. K. Ching^1,2, J. K. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.3, pp. 199-218, 2006, DOI:10.3970/cmes.2006.013.199

Abstract The Meshless Local Petrov-Galerkin (MLPG) method is a novel numerical approach similar to finite element methods, but it allows the construction of the shape function and domain discretization without defining elements. In this study, the MLPG analysis for transient thermomechanical response of a functionally graded composite heated by Gaussian laser beams is presented. The composite is modeled as a 2-D strip which consists of metal and ceramic phases with the volume fraction varying over the thickness. Two sets of the micromechanical models are employed for evaluating the effective material properties, respectively. Numerical results are presented More >