M.F. Liu¹

CMC-Computers, Materials & Continua, Vol.22, No.2, pp. 97-128, 2011, DOI:10.3970/cmc.2011.022.097

Abstract A new invented Orthogonal Tapered Beam Functions (OTBFs) have been introduced in this paper and used in accordance with the Rayleigh-Ritz method to determine the natural frequencies and mode shapes of the non-uniform rectangular isotropic plates with varying thickness in one or two directions. The generation of the OTBFs is based on the static solution of a one-dimensional beam problem subjected to constant applied load, and then extends to an orthogonal or orthonomal infinite set of admissible functions by performing the three-term recurrence scheme. A wide range of non-uniform rectangular plate whose domain is referenced by a so-called truncation factor… More >

V.G.Yakhno¹

CMC-Computers, Materials & Continua, Vol.21, No.1, pp. 1-16, 2011, DOI:10.3970/cmc.2011.021.001

Abstract Homogeneous non-dispersive anisotropic materials, characterized by a positive constant permeability and a symmetric positive definite conductivity tensor, are considered in the paper. In these anisotropic materials, the electric and magnetic dyadic Green's functions are defined as electric and magnetic fields arising from impulsive current dipoles and satisfying the time-dependent Maxwell's equations in quasi-static approximation. A new method of deriving these dyadic Green's functions is suggested in the paper. This method consists of several steps: equations for electric and magnetic dyadic Green's functions are written in terms of the Fourier modes; explicit formulae for the Fourier modes of dyadic Green's functions… More >

Hrvoje Gotovac¹, Vedrana Kozulić², Blaž Gotovac¹

CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 173-198, 2010, DOI:10.3970/cmc.2010.015.173

Abstract The space-time Adaptive Fup Collocation Method (AFCM) for solving boundary-initial value problems is presented. To solve the one-dimensional initial boundary value problem, we convert the problem into a two-dimensional boundary value problem. This quasi-boundary value problem is then solved simultaneously in the space-time domain with a collocation technique and by using atomic Fup basis functions. The proposed method is a generally meshless methodology because it requires only the addition of collocation points and basis functions over the domain, instead of the classical domain discretization and numerical integration. The grid is adapted progressively by setting the threshold as a direct measure… More >

TakehikoNakama¹

CMC-Computers, Materials & Continua, Vol.14, No.1, pp. 35-60, 2009, DOI:10.3970/cmc.2009.014.035

Abstract Random noise perturbs objective functions in practical optimization problems, and genetic algorithms (GAs) have been proposed as an effective optimization tool for dealing with noisy objective functions. In this paper, we investigate GAs in a variety of noisy environments where fitness perturbation can occur in any form-for example, fitness evaluations can be concurrently disturbed by additive and multiplicative noise. We reveal the convergence properties of GAs by constructing and analyzing a Markov chain that explicitly models the evolution of the algorithms in noisy environments. We compute the one-step transition probabilities of the Markov chain and show that the chain has… More >

Wen Chen^1,2, Zhuo-Jia Fu^1,3, Qing-Hua Qin³

CMC-Computers, Materials & Continua, Vol.13, No.3, pp. 201-218, 2009, DOI:10.3970/cmc.2009.013.201

Abstract This paper presents high-order Trefftz functions for some commonly used differential operators. These Trefftz functions are then used to construct boundary particle method for solving inhomogeneous problems with the boundary discretization only, i.e., no inner nodes and mesh are required in forming the final linear equation system. It should be mentioned that the presented Trefftz functions are nonsingular and avoids the singularity occurred in the fundamental solution and, in particular, have no problem-dependent parameter. Numerical experiments demonstrate the efficiency and accuracy of the present scheme in the solution of inhomogeneous problems. More >

Y. C. Hon¹, L. Ling², K. M. Liew³

CMC-Computers, Materials & Continua, Vol.2, No.1, pp. 39-50, 2005, DOI:10.3970/cmc.2005.002.039

Abstract In this paper we investigate a thermal driven Micro-Electrical-Mechanical system which was originally designed for inkjet printer to precisely deliver small ink droplets onto paper. In the model, a tiny free-ended beam of metal bends and projects ink onto paper. The model is solved by using the recently developed radial basis functions method. We establish the accuracy of the proposed approach by comparing the numerical results with reported experimental data. Numerical simulations indicate that a light (low composite mass) beam is more stable as it does not oscillate much. A soft (low rigidity) beam results in a higher rate of… More >