Heng Cheng Lin^1,2, Chieh Kung³, Rong Sheng Chen²

CMC-Computers, Materials & Continua, Vol.6, No.1, pp. 43-50, 2007, DOI:10.3970/cmc.2007.006.043

Abstract Presented herein are the evaluation results of the BGA solder ball shape using energy method, two types of solder, viz. Sn37Pb and Sn80Pb, are selected .The geometry of the solder bump is firstly estimated using free computer software, the Surface Evolver, an interactive program which is an energy-based approach for the study of liquid droplet surfaces shaped by surface tension and other energies. The solder bump is then numerically constructed in a finite element model that simulates a BGA package. The influences of both upper and bottom solder pad radii, the surface tension on the… More >

Cheng-Hung Huang¹, Hsin-Hsien Wu²

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 197-212, 2007, DOI:10.3970/cmc.2007.005.197

Abstract The conjugate gradient method (CGM) is applied in an inverse fin design problem in estimating the optimum shapes for the non-Fourier spine and longitudinal fins based on the desired fin efficiency and fin volume at the specified time. One of the advantages in using CGM in the inverse design problem lies in that it can handle problems having a huge number of design parameters easily and converges very fast.
The validity of using CGM in solving the present inverse design problem is justified by performing the numerical experiments. Several test cases involving different design fin efficiency, More >

Kanchi Venkatesulu Reddy¹, Ranjan Ganguli²

CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 79-98, 2007, DOI:10.3970/cmc.2007.005.079

Abstract This paper investigates the effect of damage on beams with fixed boundary conditions using Fourier analysis of the mode shapes in spatial domain. A finite element model is used to obtain the mode shapes of a damaged fixed-fixed beam. Then the damaged beams are studied using a spatial Fourier analysis. This approach contrasts with the typical time domain application of Fourier analysis for vibration problems. It is found that damage causes considerable change in the Fourier coefficients of the mode shapes. The Fourier coefficients, especially the higher harmonics, are found to be sensitive to both More >

A. H. Muhr¹

CMC-Computers, Materials & Continua, Vol.5, No.1, pp. 11-30, 2007, DOI:10.3970/cmc.2007.005.011

Abstract The mechanics of laminates of elastomer and shims of high modulus material are reviewed. Such structures are often built to provide engineering components with specified, and quite different, stiffnesses in different modes of deformation. The shims may either be rigid or flexible, flat or curved, but are usually close to inextensible, being made of a high modulus material such as steel. On the other hand, rubber has an exceptionally low shear modulus, about one thousandth of its bulk modulus, so that shear of the rubber layers and flexure of the high modulus layers (if thin)… More >

Wendong Shi^∗,†, Xi-Qiao Feng^*, Huajian Gao^†

Molecular & Cellular Biomechanics, Vol.3, No.3, pp. 121-126, 2006, DOI:10.3970/mcb.2006.003.121

Abstract When pulling a vesicle adhered on a substrate, both the force-displacement profile and the maximum force at pull-off are sensitively dependent upon the substrate shape. Here we consider the adhesion between a two-dimensional vesicle and a rigid substrate via long-range molecular interactions. For a given contact area, the theoretical pull-off force of the vesicle is obtained by multiplying the theoretical strength of adhesion and the contact area. It is shown that one may design an optimal substrate shape to achieve the theoretical pull-off force. More >

S.Y. Wang^1,2, M.Y. Wang³

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 119-148, 2006, DOI:10.3970/cmes.2006.013.119

Abstract In this paper, an implicit free boundary parametrization method is presented as an effective approach for simultaneous shape and topology optimization of structures. The moving free boundary of a structure is embedded as a zero level set of a higher dimensional implicit level set function. The radial basis functions (RBFs) are introduced to parametrize the implicit function with a high level of accuracy and smoothness. The motion of the free boundary is thus governed by a mathematically more convenient ordinary differential equation (ODE). Eigenvalue stability can be guaranteed due to the use of inverse multiquadric… More >

M. Kassemi¹, Y. Wang², S. Barsi^1,3, B.T.F. Chung²

FDMP-Fluid Dynamics & Materials Processing, Vol.2, No.1, pp. 27-46, 2006, DOI:10.3970/fdmp.2006.002.027

Abstract Microgravity experiments, especially materials processing experiments, have often been hampered by presence of unwanted bubbles. In this work, the effect of thermocapillary convection generated by a bubble on the Bridgman growth of a dilute binary alloy in microgravity is investigated numerically. The model is based on the quasi-steady Navier-Stokes equations for the fluid flow in the melt coupled with the conservation equations for transport of energy and species in the growth ampoule. Numerical results indicate three different growth regimes based on the distance between the bubble and the growth interface: a diffusion dominated regime that More >

Aimin Jiang^1,2, Haojiang Ding²

CMC-Computers, Materials & Continua, Vol.3, No.1, pp. 1-12, 2006, DOI:10.3970/cmc.2007.003.001

Abstract This paper presents a development of the boundary contour method (BCM) for magneto-electro-elastic media. Firstly, the divergence-free of the integrand of the magneto- electro-elastic boundary element is proved. Secondly, the boundary contour method formulations are obtained by introducing linear shape functions and Green's functions (Computers & Structures, 82(2004):1599-1607) for magneto-electro-elastic media and using the rigid body motion solution to regularize the BCM and avoid computation of the corner tensor. The BCM is applied to the problem of magneto-electro-elastic media. Finally, numerical solutions for illustrative examples are compared with exact ones and those of the conventional boundary element More >

B. Chandrasekhar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 243-254, 2005, DOI:10.3970/cmes.2005.009.243

Abstract In this work, a novel numerical technique is presented to calculate the acoustic fields scattered by three dimensional rigid bodies of arbitrary shape using the method of moment's solution procedure. A new set of basis functions, namely, Node based basis functions are developed to represent the source distribution on the surface of rigid body and the same functions are used as testing functions as well. Both single layer formulation and double layer formulations are numerically solved using the same basis functions. The surface of the body is modeled by triangular patch modeling. Numerical technique presented More >

B. Chrasekhar¹, S. M. Rao²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.2, pp. 105-118, 2005, DOI:10.3970/cmes.2005.008.105

Abstract In this work, a simple, robust, and an efficient numerical algorithm to calculate the scattered acoustic fields from complex shaped objects such as aircrafts and missiles, subjected to a plane wave incidence is presented. The work is based on the recently proposed method of moments (MoM) and the potential theory, unlike the standard Helmholtz integral equation (HIE) solution method. For the numerical solution, the scattering structure is approximated by planar triangular patches. For the MoM solution of complex bodies involving open/closed/intersecting surfaces, a unified set of basis functions to approximate the source distribution is defined. More >