H. Okada ¹, T. Kamibeppu ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.3, pp. 229-238, 2005, DOI:10.3970/cmes.2005.010.229

Abstract In this paper, a three-dimensional VCCM (Virtual Crack Closure-Integral Method) for evaluating the energy release rate and the stress intensity factor is presented. Many engineers and researchers believe that hexahedral finite elements should be used to perform three-dimensional fracture analyses. Previous VCCM formulations assume the use of hexahedral finite elements. In present study, the authors have been developing a VCCM that works with tetrahedral finite elements. In the field of large-scale computation, the use of tetrahedral finite elements has becoming very popular as high performance mesh generation programs became available. Therefore, building a large and More >

V.V. Mykhas’kiv¹, O.I. Stepanyuk²

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 45-64, 2005, DOI:10.3970/cmes.2005.010.045

Abstract The 3D elastostatic problem for an infinite remotely loaded matrix containing a finite number of arbitrarily located rigid disk-inclusions and plane cracks is solved by the boundary integral equation (BIE) method. Its boundary integral formulation is achieved by the superposition principle with the subsequent integral representations of superposition terms through surface integrals, which should satisfy the displacement linearity conditions in the inclusion domains and load-free conditions in the crack domains. The subtraction technique in the conjunction with mapping technique under taking into account the structure of the solution at the edges of inhomogeneities is applied More >

C.-W. Chang¹, C.-S. Liu², J.-R. Chang^1,3

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 13-38, 2005, DOI:10.3970/cmes.2005.010.013

Abstract In this paper, the inverse heat conduction problem governed by sideways heat equation is investigated numerically. The problem is ill-posed because the solution, if it exists, does not depend continuously on the data. To begin with, this ill-posed problem is analyzed by considering the stability of the semi-discretization numerical schemes. Then the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group preserving scheme, and the stable range of the index r = 1/2ν Δt is investigated. When the numerical results are compared with exact solutions, it More >

Z. D. Han¹, A. M. Rajendran², S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.10, No.1, pp. 1-12, 2005, DOI:10.3970/cmes.2005.010.001

Abstract A nonlinear formulation of the Meshless Local Petrov-Galerkin (MLPG) finite-volume mixed method is developed for the large deformation analysis of static and dynamic problems. In the present MLPG large deformation formulation, the velocity gradients are interpolated independently, to avoid the time consuming differentiations of the shape functions at all integration points. The nodal values of velocity gradients are expressed in terms of the independently interpolated nodal values of displacements (or velocities), by enforcing the compatibility conditions directly at the nodal points. For validating the present large deformation MLPG formulation, two example problems are considered: 1)… More >

M. Mosaad², A. Ben-Nakhi², M. H. Al-Hajeri²

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.4, pp. 301-314, 2005, DOI:10.3970/fdmp.2005.001.301

Abstract This work deals with the problem of thermal interaction between two fluid media at two different bulk temperatures and separated by a vertical plate. The problem is analyzed by taking into account the heat conduction across the separating plate. The flow configuration considered is one in which the two vertical boundary layers of free and forced convection developed on plate sides are in parallel flow. The dimensionless parameters governing the thermal interaction mechanisms are analytically deduced. The obtained results are presented in graphs to demonstrate the heat transfer characteristics of investigated phenomenon. The work reports More >

Marcello Lappa¹

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.3, pp. 213-234, 2005, DOI:10.3970/fdmp.2005.001.213

Abstract The physical properties of many emulsions and metal alloys strongly depend on the multiphase morphology which is controlled to a great degree by particle-particle interaction during the related processing. In the present article significant effort is devoted to illustrate the philosophy of modeling for these phenomena and some insights into the physics. Within such a context working numerical techniques that have enjoyed a widespread use over recent years are presented and/or reviewed. Finally a focused and critical comparison of these possible approaches is reported illustrating advantages and disadvantages, strengths and weaknesses, past history and future More >

Marcello Lappa¹

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.3, pp. 201-212, 2005, DOI:10.3970/fdmp.2005.001.201

Abstract The manuscript deals with a presentation of the most reliable theories introduced over the years to model particle coalescence and non-coalescence phenomena at both macroscopic and microscopic length scales (including historical developments and very recent contributions) and moves through other macrophysical mechanisms that can cause spatial separation of the fluid phases (liquid-liquid or liquid-gas) in multi-material problems, while providing a rigorous theoretical framework for deeper understanding of how drop (or bubble) migration due to gravity and/or Marangoni effects can interact cooperatively with coalescence to significantly affect the multiphase pattern formation, its evolutionary progress as well More >

B. Šarler¹, R.Vertnik, J. Perko¹

CMC-Computers, Materials & Continua, Vol.2, No.1, pp. 77-84, 2005, DOI:10.3970/cmc.2005.002.077

Abstract The steady-state convective-diffusive solid-liquid phase change problem associated with temperature fields in direct-chill, semi-continuously cast billets and slabs from aluminum alloys has been solved by the Diffuse Approximate Method (DAM). The solution is based on formulation, which incorporates the mixture continuum physical model, nine-noded support, second order polynomial trial functions, and Gaussian window weighting functions. Realistic boundary conditions and temperature variation of material properties are included. Two-dimensional test case solution is shown, verified by comparison with the Finite Volume Method (FVM) results for coarse and fine grid arrangement. More >

Huajian Gao^1,1, Baohua Ji^1,1, Markus J. Buehler^1,1, Haimin Yao^1,1

Molecular & Cellular Biomechanics, Vol.1, No.1, pp. 37-52, 2004, DOI:10.3970/mcb.2004.001.037

Abstract Bone-like biological materials have achieved superior mechanical properties through hierarchical composite structures of mineral and protein. Gecko and many insects have evolved hierarchical surface structures to achieve extraordinary adhesion capabilities. We show that the nanometer scale plays a key role in allowing these biological systems to achieve their superior properties. We suggest that the principle of flaw tolerance may have had an overarching influence on the evolution of the bulk nanostructure of bone-like materials and the surface nanostructure of gecko-like animal species. We demonstrate that the nanoscale sizes allow the mineral nanoparticles in bone to More >

Z.Y. Qian¹, Z.D. Han¹, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.6, pp. 541-562, 2004, DOI:10.3970/cmes.2004.005.541

Abstract Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r⁻²) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity potential, are used in this derivation. Several basic identities governing the fundamental solution to the Helmholtz differential equation for velocity potential, are also derived. Using these basic identities, the strongly singular integral equations for the potential and its gradients [denoted here as φ-BIE, and… More >