C.M. Müller-Karger¹, C.González², M.H.Aliabadi³, M.Cerrolaza⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.1, pp. 1-14, 2001, DOI:10.3970/cmes.2001.002.001

Abstract In this paper, a three-dimensional Boundary Element model of the proximal tibia of the human knee is described and stresses and displacements in the tibial plateau under static loading are computed. The geometry is generated via three-dimensional reconstruction of Computerized Tomographies and Magnetic Resonance Imaging. Various models of different lengths from the tibia plateau are calculated. The BEM results are compared with a Finite Element model having the same geometry and tibia FE models available in the literature. Also reported are investigations of some pathological situations, including fractures. The results of the comparisons show that More >

W.W. Liou¹, Y.C. Fang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 119-128, 2000, DOI:10.3970/cmes.2000.001.571

Abstract A simple implicit treatment for the low speed inflow and outflow boundary conditions for the direct simulation Monte Carlo (DSMC) of the flows in microelectromechanical systems (MEMS) is proposed. The local mean flow velocity, temperature, and number density near the subsonic boundaries were used to determine the number of molecules entering the computational domain and their corresponding velocities at every sample average step. The proposed boundary conditions were validated against micro-Poiseuille flows and micro-Couette flows. The results were compared with analytical solutions derived from the Navier-Stokes equations using first-order and second order slip-boundary conditions. The More >

John L. Junkins¹, Kamesh Subbarao², Ajay Verma³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 99-118, 2000, DOI:10.3970/cmes.2000.001.551

Abstract Model reference adaptive control formulations are presented that rigorously impose the dynamical structure of the state space descriptions of several distinct large classes of dynamical systems. Of particular interest, the formulations enable the imposition of exact kinematic differential equation constraints upon the adaptation process that compensates for model errors and disturbances at the acceleration level. Other adaptive control formulations are tailored for redundantly actuated and constrained dynamical systems. The utility of the resulting structured adaptive control formulations is studied by considering examples from nonlinear oscillations, aircraft control, spacecraft control, and cooperative robotic system control. The More >

Paulo Santos, Julieta António, António Tadeu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 79-98, 2000, DOI:10.3970/cmes.2000.001.531

Abstract This paper presents the three-dimensional scattering field obtained when 2D smooth topographical deformations are subjected to a dilatational point load placed at some point in the medium. The solution is formulated using boundary elements for a wide range of frequencies and spatially harmonic line loads, which are then used to obtain time series by means of (fast) inverse Fourier transforms into space-time. The topographical surface is modeled with a number of boundary elements, defined according to the excitation frequency of the harmonic source, and in such a way that the free surface can be discretized More >

Y. Wei, C.L. Chow¹, C.T. Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 71-78, 2000, DOI:10.3970/cmes.2000.001.523

Abstract The paper presents a numerical simulation for mixed mode crack initiation based on the concepts of damage mechanics. A model with two scalar damage variables is introduced for characterization of damage in a material element. Then a tangent modulus tensor is derived for damage-coupled constitutive equations. A failure criterion is developed with the concept of damage accumulation not only to identify the location of damaged element where the crack initiation angle but also to determine the critical load for mixed mode fracture. The damage model developed is incorporated in a general-purpose finite element program ABAQUA More >

Farid F. Abraham¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 63-70, 2000, DOI:10.3970/cmes.2000.001.515

Abstract A challenging paradigm in the computational sciences is the coupling of the continuum, the atomistic and the quantum descriptions of matter for a unified dynamic treatment of a single physical problem. We described the achievement of such a goal. We have spanned the length scales in a concerted simulation comprising the finite-element method, classical molecular dynamics, quantum tight-binding dynamics and seamless bridges between these different physical descriptions. We illustrate and validate the methodology for crack propagation in silicon. More >

Z. Chen¹, W. Hu¹, E.P. Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 57-62, 2000, DOI:10.3970/cmes.2000.001.509

Abstract To simulate the dynamic failure evolution without using nonlocal terms in the strain-stress space, a damage diffusion equation is formulated with the use of a combined damage/plasticity model that was primarily applied to the case of rock fragmentation. A vectorized model solver is developed for large-scale simulation. Two-dimensional sample problems are considered to illustrate the features of the proposed solution procedure. It appears that the proposed approach is effective in simulating the evolution of localization, with parallel computing, in a single computational domain involving different lower-order governing differential equations. More >

Changyu Hwang¹, Philippe H. Geubelle²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 45-56, 2000, DOI:10.3970/cmes.2000.001.497

Abstract This paper presents the formulation and numerical implementation of a spectral scheme specially developed to simulate dynamic fracture events in unidirectional and cross-ply fiber-reinforced composites. The formulation is based on the spectral representation of the transversely isotropic elastodynamic relations between the traction stresses along the fracture plane and the resulting displacements. Example problems involving stationary or dynamically propagating cracks in fiber-reinforced composites are investigated and compared with reference solutions available in the literature and/or experimental observations. More >

M. Kögl, L. Gaul²

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 27-44, 2000, DOI:10.3970/cmes.2000.001.479

Abstract A Boundary Element formulation is presented for the solution of three-dimensional problems of anisotropic elastodynamics. Due to the complexity of the dynamic fundamental solutions for anisotropic materials and the resulting high computational costs, the approach at hand uses the fundamental solution of the static operator. This leads to a domain integral in the representation formula which contains the inertia term. The domain integral can be transformed to the boundary using the Dual Reciprocity Method. This results in a system of ordinary differential equations in time with time-independent matrices. Several general questions concerning the anisotropic solutions, More >

L. Ma¹, A.S. Kobayashi², S. N. Atluri³, P.W. Tan⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.4, pp. 19-26, 2000, DOI:10.3970/cmes.2000.001.471

Abstract Experimentally determined T_ε^* and CTOA resistance curves were used to simulate numerically, stable crack growth and the ensuing crack linkup in 0.8 mm thick 2024-T3 aluminum tension specimen with multiple site damage (MSD) subjected to monotonically/cyclically increasing loading. The T_ε^* integral correctly predicted the crack growth and linkup history as well as the onset of rapid fracture in MSD specimens. The CTOA criterion also predicted the crack growth history but in its present form, could not predict crack linkup and rapid fracture. More >