J. Sladek¹, V. Sladek², P. Solek¹, S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.3, pp. 273-300, 2008, DOI:10.3970/cmes.2008.034.273

Abstract A meshless method based on the local Petrov-Galerkin approach is proposed, to solve boundary and initial value problems of piezoelectric and magneto-electric-elastic solids with continuously varying material properties. Stationary and transient dynamic 2-D problems are considered in this paper. The mechanical fields are described by the equations of motion with an inertial term. To eliminate the time-dependence in the governing partial differential equations the Laplace-transform technique is applied to the governing equations, which are satisfied in the Laplace-transformed domain in a weak-form on small subdomains. Nodal points are spread on the analyzed domain, and each More >

J. P. Xu¹, Y. Q. Liu^1,2, S. Q. Li³, S. C. Wu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.3, pp. 201-216, 2008, DOI:10.3970/cmes.2008.038.201

Abstract For the first time, a special-purpose finite element simulation system CoinForm is developed to analyze the embossing process of commemorative coin, in which one-point reduced integration approach is used in solid element finite element dynamic explicit program. Viscous damping hourglass control algorithm can effectively suppress the spurious modes activated by reduced integration and the computational effort is saved about 93% compared with other method that evaluate anti-hourglass force using stabilization matrix. The embossing process of commemorative coin is then simulated and compared with results from the DEFORM 3D software, which verify the excellent performance of More >

Briti Sundar Deb¹, Srinivasan Natesan²

CMES-Computer Modeling in Engineering & Sciences, Vol.38, No.2, pp. 179-200, 2008, DOI:10.3970/cmes.2008.038.179

Abstract This paper presents an almost second--order uniformly convergent Richardson extrapolation method for convection- dominated coupled system of boundary value problems. First, we solve the system by using the classical finite difference scheme on the layer resolving Shishkin mesh, and then we construct the Richardson approximation solution using the solutions obtained on N and 2N mesh intervals. Second-order parameter--uniform error estimate is derived. The proposed method is applied to a test example for verification of the theoretical results for the case ε ≤ N⁻¹. More >

Vikas Namdeo^1,2, C S Manohar^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.3, pp. 123-160, 2008, DOI:10.3970/cmes.2008.032.123

Abstract The problem of identification of nonlinear system parameters from measured time histories of response under known excitations is considered. Solutions to this problem are obtained by using the force state mapping technique with two alternative functional representation schemes. These schemes are based on the application of reproducing kernel particle method (RKPM) and kriging techniques to fit the force state map. The RKPM has the capability to reproduce exactly polynomials of specified order at any point in a given domain. The kriging based methods represent the function under study as a random field and the parameters… More >

G.A. Gravvanis, K.M. Giannoutakis¹

CMES-Computer Modeling in Engineering & Sciences, Vol.32, No.1, pp. 35-44, 2008, DOI:10.3970/cmes.2008.032.035

Abstract A new parallel normalized optimized approximate inverse algorithm, based on the concept of the ``fish bone'' computational approach with cyclic distribution of the processors satisfying an antidiagonal data dependency, for computing classes of explicit approximate inverses, is introduced for symmetric multiprocessor systems. The parallel normalized explicit approximate inverses are used in conjunction with parallel normalized explicit preconditioned conjugate gradient square schemes, for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new proposed algorithms are discussed and the parallel performance is presented, using OpenMP. More >

Chein-Shan Liu¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 71-84, 2008, DOI:10.3970/cmes.2008.031.071

Abstract Iterative algorithms for solving a nonlinear system of algebraic equations of the type: F_i(x_j) = 0, i,j = 1,…,n date back to the seminal work of Issac Newton. Nowadays a Newton-like algorithm is still the most popular one due to its easy numerical implementation. However, this type of algorithm is sensitive to the initial guess of the solution and is expensive in the computations of the Jacobian matrix ∂ F_i/ ∂ x_j and its inverse at each iterative step. In a time-integration of a system of nonlinear Ordinary Differential Equations (ODEs) of the type B_ijx_j + F_i = 0… More >

A. Takei¹, S. Yoshimura¹, H. Kanayama²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.1, pp. 13-24, 2008, DOI:10.3970/cmes.2008.031.013

Abstract This paper presents large-scale finite element analyses of high frequency electromagnetic fields in commuter trains. The ADVENTURE_Magnetic is one of the main modules of the ADVENTURE system, which is an open source parallel finite element analyses system, and is able to solve eddy current and magnetostatic problems using the hierarchical domain decomposition method (HDDM) with an iterative linear algebraic solver. In this paper, we improve the module so as to solve a high frequency electromagnetic field of 500-1000 M[Hz]. A stationary Helmholtz equation for electromagnetic wave problems is solved taking an electric field as an More >

B Radhika¹, S S P,a¹, C S Manohar^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 79-110, 2008, DOI:10.3970/cmes.2008.027.079

Abstract Reliability of nonlinear vibrating systems under stochastic excitations is investigated using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis tests, and the next stage involves More >

Jyoti Ranjan Majhi, Ranjan Ganguli¹

CMES-Computer Modeling in Engineering & Sciences, Vol.27, No.1&2, pp. 25-36, 2008, DOI:10.3970/cmes.2008.027.025

Abstract The flapping equation for a rotating rigid helicopter blade is typically derived by considering 1) small flap angle, 2) small induced angle of attack and 3) linear aerodynamics. However, the use of nonlinear aerodynamics can make the assumptions of small angles suspect. A general equation describing helicopter blade flap dynamics for large flap angle and large induced inflow angle of attack is derived in this paper with nonlinear aerodynamics . Numerical simulations are performed by solving the nonlinear flapping ordinary differential equation for steady state conditions and the validity of the small angle approximations are More >

Nagalinga Rajan, Soumyendu Raha¹

CMES-Computer Modeling in Engineering & Sciences, Vol.23, No.2, pp. 91-116, 2008, DOI:10.3970/cmes.2008.023.091

Abstract The article describes a numerical method for time domain integration of noisy dynamical systems originating from engineering applications. The models are second order stochastic differential equations (SDE). The stochastic process forcing the dynamics is treated mainly as multiplicative noise involving a Wiener Process in the Itô sense. The developed numerical integration method is a drift implicit strong order 2.0 method. The method has user-selectable numerical dissipation properties that can be useful in dealing with both multiplicative noise and stiffness in a computationally efficient way. A generalized analysis of the method including the multiplicative noise is More >