C.-S. Liu¹, C.-W. Chang², J.-R. Chang²

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 67-82, 2006, DOI:10.3970/cmes.2006.012.067

Abstract In this paper we are concerned with the backward problems governed by differential equations. It is a first time that we can construct a backward time dynamics on the past cone, such that an augmented dynamical system of the Lie type X^˙ = B(X,t)X with t ∈ R⁻, X ∈ Mⁿ⁺¹ lying on the past cone and B ∈ so(n,1), was derived for the backward differential equations system x^· =f(x,t), t ∈ R⁻, x ∈ Rⁿ. These two differential equations systems are mathematically equivalent. Then we apply the backward group preserving scheme (BGPS), which is an explicit single-step algorithm… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 55-66, 2006, DOI:10.3970/cmes.2006.012.055

Abstract In this paper we are concerned with the numerical integration of Burgers equation backward in time. We construct a one-step backward group preserving scheme (BGPS) for the semi-discretization of Burgers equation. The one-step BGPS is very effectively to calculate the solution at an initial time t = 0 from a given final data at t = T, which with a time stepsize equal to T and with a suitable grid length produces a highly accurate solution never seen before. Under noisy final data the BGPS is also robust to against the disturbance. When the solution appears steep gradient, More >

A. P. S. Selvadurai¹, Wenjun Dong

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 41-54, 2006, DOI:10.3970/cmes.2006.012.041

Abstract A Fourier analysis conducted on both the spatial and the temporal discretizations of the governing partial differential equation shows that the Courant number as well as the time marching scheme have significant influences on the numerical behaviour of a Modified Least Squares (MLS) method for the solution of the advection equation. The variations of the amplification factor and the relative phase velocity with the Courant number and the dimensionless wave number indicate that when Courant number is equal to unity, the MLS method with the specified time-weighting and upwind function gives accurate results. This conclusion… More >

S.Yu. Reutskiy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 27-40, 2006, DOI:10.3970/cmes.2006.012.027

Abstract In this paper a new boundary method for eigenproblems with the Helmholtz equation in simply and multiply connected domains is presented. The solution of an eigenvalue problem is reduced to a sequence of inhomogeneous problems with the differential operator studied. The method shows a high precision in simply and multiply connected domains and does not generate spurious eigenvalues. The results of the numerical experiments justifying the method are presented. More >

A. Dimitrov¹, F.-G. Buchholz², E. Schnack³

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 1-26, 2006, DOI:10.3970/cmes.2006.012.001

Abstract Crack propagation in 3D-structures cannot be reduced (in general) to a series of plane problems along the crack front edge, due to the existence of some "corners'' on the crack front, where the elastic fields are of a real three-dimensional nature. The most important example for such a corner ist the point, where the crack front intersects a free surface of the body. According to the concept of weak and strong singularities, it is possible to obtain the asymptotics for the stress intensity factor (SIF) as well as the strain energy release rate (SERR) in… More >

T. Hasebe¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 145-156, 2006, DOI:10.3970/cmes.2006.011.145

Abstract This paper presents recent achievements in field theoretical approach toward substantial linkage among key hieratical scales dominating polycrystalline plasticity of metals and alloys. Major ingredients of the theory are briefly shown first, which is followed by several overwhelming results and some implications including key factors for dislocation cell structure evolution, key features of polycrystalline plasticity and their rational modeling in crystal plasticity-based constitutive equation. More >

S. Masuda¹, H. Noguchi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 131-144, 2006, DOI:10.3970/cmes.2006.011.131

Abstract This paper presents a novel and accurate technique for modeling discontinuous derivatives in meshfree methods, which will be used in the analysis of structures with material interfaces. The novelty lies in the formulation of the Moving Least Squares Approximation (MLSA) scheme where an introduced discontinuous derivative basis function replaces the conventional linear basis function. Furthermore, it is easy to implement this novelty into existing meshfree methods, such as the Element Free Galerkin (EFG) method, which are based on the MLSA scheme. The successful analyses of one and two-dimensional structures with material interfaces demonstrate the potential More >

T. Ishizawa¹, M. Iura¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 121-130, 2006, DOI:10.3970/cmes.2006.011.121

Abstract A one-dimensional model is proposed for numerical analysis of partially concrete-filled steel tubular (PCFST) columns subjected to cyclic loadings. The present formulation does not require experimental results nor shell analysis to obtain the constitutive equation of the model. The material properties and dimensions of PCFST columns are required for numerical analysis of the present model. The PCFST columns are assumed to consist of elastic beam and base plastic-hinge region in which steel local buckling is observed. Two parameters are introduced in order to express hardening phenomena of PCFST columns subjected to cyclic loading. Resisting forces More >

H. Kawai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 111-120, 2006, DOI:10.3970/cmes.2006.011.111

Abstract ADVENTURE AutoGL (pronounced as ‘Ote- ga-lu’) is a graphics and GUI library, dedicated for simulation-based research and development. It is designed for the simulation users to develop their own data viewers and editors. Currently, the library is used among many researchers and simulation users, mainly in universities and national research centers. Its functionalities and supported platforms are explained. AutoGL applications of various kinds of simulation methods are demonstrated also. More >

Y. Suetake¹

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.3, pp. 103-110, 2006, DOI:10.3970/cmes.2006.011.103

Abstract Since Reissner and Mindlin proposed their classical thick plate theories, many authors have presented refined theories including transverse shear deformation. Most of those plate theories have tended to use higher order power series for displacements and stresses along the thickness in order to achieve the higher accuracy. However, they have not carefully noticed lateral load effect. In this paper, we pay attention to constitution of the lateral loads: a body force and upper and lower surface tractions. Especially we formulate a modified theory for plate bending, in which the effect of a body force is More >