P.B. Béda¹

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.2, pp. 231-238, 2003, DOI:10.3970/cmes.2003.004.231

Abstract The paper studies the behavior of a spatial Euler-Bernoulli beam loaded by a terminal thrusting force and a couple. The classical Clebsch-Kirchhoff equilibrium equations are written by using appropriate angular coordinates describing the finite rotations of the local frames attached to each cross-sections of the beam with respect to a fixed system. When we have geometric boundary conditions at one end and dynamic boundary conditions (a force and a couple) at the other the set of equilibrium equations form and initial value probem which can easily be solved with standard Runge-Kutta method. More >

L. F. Qian^1,3, R. C. Batra², L. M. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.4, No.1, pp. 161-176, 2003, DOI:10.3970/cmes.2003.004.161

Abstract We use two meshless local Petrov-Galerkin formulations, namely, the MLPG1 and the MLPG5, to analyze infinitesimal deformations of a homogeneous and isotropic thick elastic plate with a higher-order shear and normal deformable plate theory. It is found that the two MLPG formulations give results very close to those obtained by other researchers and also by the three-dimensional analysis of the problem by the finite element method. More >

R. C. Batra¹, H.-K. Ching¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.6, pp. 717-730, 2002, DOI:10.3970/cmes.2002.003.717

Abstract The Meshless Local Petrov-Galerkin (MLPG) method is used to analyze transient deformations near either a crack or a notch tip in a linear elastic plate. The local weak formulation of equations governing elastodynamic deformations is derived. It results in a system of coupled ordinary differential equations which are integrated with respect to time by a Newmark family of methods. Essential boundary conditions are imposed by the penalty method. The accuracy of the MLPG solution is established by comparing computed results for one-dimensional wave propagation in a rod with the analytical solution of the problem. Results… More >

Robb Thomson, Retired¹, L. E. Levine¹, Y. Shim E. ², M. F. Savage¹, D. E. Kramer¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 245-254, 2002, DOI:10.3970/cmes.2002.003.245

Abstract A conceptual theoretical scheme for single crystal metal deformation is presented consisting of multi-scale models from dislocation dynamics to the continuum constitutive relations. The scheme rests on the fundamental observations that deformation is characterized by partially ordered internal dislocation wall structures, discontinuous strain bursts in time, and strain localization in a surface slip band structure. A percolation strain model corresponds to elementary slip line burst events, with percolation parameters to be supplied from experiments and dislocation dynamics studies of wall structures. A model for localization of the slip lines into bands is proposed (for suitable More >

K. Garikipati¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 175-184, 2002, DOI:10.3970/cmes.2002.003.175

Abstract The embedding of micromechanical models in the macromechanical formulation of continuum solid mechanics can be treated by a variational multiscale method. A scale separation is introduced on the displacement field into coarse and fine scale components. The fine scale displacement is governed by the desired micromechanical model. Working within the variational framework, the fine scale displacement field is eliminated by expressing it in terms of the coarse scale displacement and the remaining fields in the problem. The resulting macromechanical formulation is posed solely in terms of the coarse scale displacements, but is influenced by the More >

E. H. Glaessgen¹, W.T. Riddell², I. S. Raju¹

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 103-116, 2002, DOI:10.3970/cmes.2002.003.103

Abstract The effects of several critical assumptions and parameters on the computation of strain energy release rates for delamination and debond configurations modeled with plate elements have been quantified. The method of calculation is based on the virtual crack closure technique (VCCT), and models of the upper and lower surface of the delamination or debond that use two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler configurational modeling. Specific issues that are discussed include: constraint of translational degrees of More >

K. Nesnas¹, A. Abdul-Latif²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 373-388, 2001, DOI:10.3970/cmes.2001.002.373

Abstract Large plastic collapse of an identical pair of cylinders of various geometries having the same length and volume is studied under lateral compressive load. Superplastic material is employed as a representative material to simulate the classical engineering material behavior under high strain rate. The effects of the strain rate and the geometry of cylinders on the plastic collapse are taken into account. The experimental study is conducted using a structure in which one cylinder is superplastic and the other is steel (referred to as deformable and non-deformable situation "DND''). The actual structure (DND) and that More >

H.-K. Ching, R. C. Batra¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 273-290, 2001, DOI:10.3970/cmes.2001.002.273

Abstract It is shown that the MLPG method augmented with the enriched basis functions and either the visibility criterion or the diffraction criterion successfully predicts the singular stress fields near a crack tip. Results are presented for a single edge-cracked plate and a double edge-cracked plate with plate edges parallel to the crack axis loaded in tension, the single edge-cracked plate with one plate edge parallel to the crack axis clamped and the other loaded by tangential tractions, and for a double edge-notched plate with the side between the notches loaded in compression. For the first 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 >

M. Kailasam¹, N. Aravas², P. Ponte Castañeda³

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 105-118, 2000, DOI:10.3970/cmes.2000.001.265

Abstract A constitutive model for a porous metal subjected to general three-dimensional finite deformations is presented. The model takes into account the evolution of porosity and the development of anisotropy due to changes in the shape and the orientation of the voids during deformation. A methodology for the numerical integration of the elastoplastic constitutive model is developed. Finally, some sample applications to plane strain extrusion and compaction of a porous disk are considered using the finite element method. More >