Chih-Wen Chang¹, Jiang-Ren Chang¹, Chein-Shan Liu²

CMC-Computers, Materials & Continua, Vol.7, No.3, pp. 139-154, 2008, DOI:10.3970/cmc.2008.007.139

Abstract In this paper, we propose a Lie-group shooting method to deal with the classical Blasius flat-plate problem and to find unknown initial conditions. The pivotal point is based on the erection of a one-step Lie group element$\mathbf G(T) and the formation of a generalized mid-point Lie group element$\mathbf G(r). Then, by imposing G(T) = G(r) we can derive some algebraic equations to recover the missing initial conditions. It is the first time that we can apply the Lie-group shooting method to solve the classical Blasius flat-plate problem. Numerical examples are worked out to persuade that the novel approach has better… More >

C. Nikhare¹, K. Narasimhan²

CMC-Computers, Materials & Continua, Vol.7, No.3, pp. 129-138, 2008, DOI:10.3970/cmc.2008.007.129

Abstract The tube hydroforming process is a relatively complex manufacturing process; the performance of this process depends on various factors and requires proper combination of part design, material selection and boundary conditions. In manufacturing of automotive parts, such as engine cradles, frames rails, sub-frames, cross members, and other parts from circular tubes, pre-bending and per-forming operations are often required prior to the subsequent tubular hydroforming process to fit the tubular blank in the complex die shape. Due to these pre-- hydroforming operations, some of the strains are already developed before going to the actual hydroforming process. Such developed strains before hydroforming… More >

L.M. Xu¹, H. Fan^2,3, X M Xie³, C. Li³

CMC-Computers, Materials & Continua, Vol.7, No.3, pp. 119-128, 2008, DOI:10.3970/cmc.2008.007.119

Abstract In the present study we performed finite element simulation for bi-continuous heterogeneous solids via a random distribution of materials to predict effective elastic properties. With a random distributing scheme, a statistical analysis via finite element becomes feasible for the multi-phase heterogeneous solids. Using a two-phase bi-continuous material as example, the numerical prediction of the effective properties is obtained in terms of a mean value and standard deviation with a sample size of 30 for each of given volume fraction. The finite element simulation results fall within the analytical bounds proposed by Hashin and Shtrikman (1963) based on the principle of… More >

S.X. Li¹, L. Zhao¹, Y.W. Liu²

CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 109-118, 2008, DOI:10.3970/cmc.2008.007.109

Abstract Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4~0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The… More >

Chein-Shan Liu¹, Jiang-Ren Chang², Kai-Huey Chang², Yung-Wei Chen²

CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 97-108, 2008, DOI:10.3970/cmc.2008.007.097

Abstract For the inverse vibration problem a mathematical method is required to determine unknown parameters from the measurement of vibration data. When both damping and stiffness functions are identified, it is a rather difficult problem. In this paper we will propose a feasible method to simultaneously estimate both the time-dependent damping and stiffness coefficients through three mathematical transformations. First, the second-order equation of motion is transformed into a self-adjoint first-order system by using the concept of integrating factor. Then, we transform these two ODEs into two hyperbolic type PDEs. Finally, we apply a one-step group preserving scheme for the semi-discretizations of… More >

Chein-Shan Liu^1,2

CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 81-96, 2008, DOI:10.3970/cmc.2008.007.081

Abstract We consider an inverse problem for estimating an unknown heat conductivity parameter α(t) in a heat conduction equation T_t(x,t) = α(t)T_xx(x,t) with the aid of an extra measurement of temperature gradient on boundary. Basing on an establishment of the one-step Lie-group elements G(r) and G(l) for the semi-discretization of heat conduction equation in time domain, we can derive algebraic equations from G(r) = G(l). The new method, namely the Lie-group estimation method (LGEM), is examined through numerical examples to convince that it is highly accurate and efficient; the maximum estimation error is smaller than 10^-5 for smooth parameter and for… More >

E. Ferretti¹, A. Di Leo¹

CMC-Computers, Materials & Continua, Vol.7, No.2, pp. 59-80, 2008, DOI:10.3970/cmc.2008.007.059

Abstract The main assumption on the basis of the identifying model of the effective law, developed by the Author, is the impossibility of considering the specimen as a continuum, when an identifying procedure from load-displacement to stress-strain in uniaxial compression is attempted. Actually, a failure mechanism with propagation of a macro-crack was found to activate from the very beginning of the uniaxial compression test forth. This leads to considering the acquired displacements as composed by two quotes: one constitutive, due to the material strain, and one of crack opening. Since the ratio between these two quotes is not constant during the… More >

K.Y. Liu^1,2,3, S.Y. Long^1,2,4, G.Y. Li¹

CMC-Computers, Materials & Continua, Vol.7, No.1, pp. 43-58, 2008, DOI:10.3970/cmc.2008.007.043

Abstract A meshless local Petrov-Galerkin method (MLPG) [[Atluri and Zhu (1998)] for the analysis of cracks in isotropic functionally graded materials is presented. The meshless method uses the moving least squares (MLS) to approximate the field unknowns. The shape function has not the Kronecker Delta properties for the trial-function-interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular integrals to generate the global effective stiffness matrix if body force is ignored; it only involves a regular boundary integral. The material properties are smooth functions of spatial coordinates and… More >

Xiuqing Qian¹, Yanping Cao², Jianyu Zhang¹, Dierk Raabe², Zhenhan Yao³, Binjun Fei¹

CMC-Computers, Materials & Continua, Vol.7, No.1, pp. 33-42, 2008, DOI:10.3970/cmc.2008.007.033

Abstract In this work, an inverse approach based on depth-sensing instrumented indentation tests is proposed to determine the Young's modulus, yield strength and strain hardening exponent of the materials for which the elastoplastic part of the stress-strain curve can be described using a power function. Numerical verifications performed on typical engineering metals demonstrate the effectiveness of the new method. The sensitivity of the method to data noise and some experimental uncertainties are also discussed, which may provide useful information for the application of the method in practice. More >

Ren Jiusheng¹

CMC-Computers, Materials & Continua, Vol.7, No.1, pp. 25-32, 2008, DOI:10.3970/cmc.2008.007.025

Abstract Elastic instability for the inflation and deflation of a thin-walled spherical rubber balloon is examined within the framework of finite pseudo-elasticity. When a spherical rubber balloon is inflated, it is subject to a complex deformation after a pressure maximum has been obtained. One part of the balloon is lightly stretched while the remainder becomes highly stretched. So an aspherical deformation is observed after the initial spherical inflation. A pseudo-elastic strain energy function including a damage variable which may model the loading, unloading and reloading of rubber is used. The balloon is idealized as an elastic membrane and the inflation, deflation… More >