G.P.Nikishkov², J.H.Park³, S.N.Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 401-422, 2001, DOI:10.3970/cmes.2001.002.401

Abstract An efficient and highly accurate, Symmetric Galerkin Boundary Element Method - Finite Element Method - based alternating method, for the analysis of three-dimensional non-planar cracks, and their growth, in structural components of complicated geometries, is proposed. The crack is modeled by the symmetric Galerkin boundary element method, as a distribution of displacement discontinuities, as if in an infinite medium. The finite element method is used to perform the stress analysis for the uncracked body only. The solution for the structural component, containing the crack, is obtained in an iteration procedure, which alternates between FEM solution for the uncracked body, and… More >

K.Yu. Volokh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 389-400, 2001, DOI:10.3970/cmes.2001.002.389

Abstract A computational framework is described for modeling pin-jointed structures comprising unilateral cable members and slender struts. The deep postbuckling behavior of struts is considered by means of 'elastica' analytical approximation. Prestressing is allowed. The proposed approach is incorporated into equilibrium path following procedures and illustrated in numerical examples. 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 one investigated experimentally by Abdul-Latif… More >

F. Cosmi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 365-372, 2001, DOI:10.3970/cmes.2001.002.365

Abstract The aim of this paper is to present a methodology for solving the plane elasticity problem using the Cell Method. It is shown that with the use of a parabolic interpolation in a vectorial problem, a convergence rate of 3.5 is obtained. Such a convergence rate compares with, or is even better than, the one obtained with FEM with the same interpolation – depending on the integration technique used by the FEM application. The accuracy of the solution is also comparable or better. More >

KwangsooHo¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 351-364, 2001, DOI:10.3970/cmes.2001.002.351

Abstract Negative, zero or positive rate sensitivity of the flow stress can be observed in metals and alloys over a certain range of strain, strain rate and temperature. It is believed that negative rate sensitivity is an essential feature of dynamic strain aging, of which the Portevin-Le Chatelier effect is one other manifestation. The viscoplasticity theory based on overstress (VBO), one of the unified state variable theories, is generalized to model zero (rate independence) and negative as well as positive rate sensitivity in a consistent way. The present model does not have the stress rate term in the evolution law for… More >

Xiaolin Chen, Yijun Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 337-350, 2001, DOI:10.3970/cmes.2001.002.337

Abstract An advanced boundary element method (BEM) is developed in this paper for analyzing thin layered structures, such as thin films and coatings, under the thermal loading. The boundary integral equation (BIE) formulation for steady-state thermoelasticity is reviewed and a special case, that is, the BIE for a uniform distribution of the temperature change, is presented. The new nearly-singular integrals arising from the applications of the BIE/BEM to thin layered structures under thermal loading are treated in the same way as developed earlier for thin structures under the mechanical loading. Three 2-D test problems involving layered thin films and coatings on… More >

R. Vignjevic, T. De Vuyst, M. Gourma¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 319-336, 2001, DOI:10.3970/cmes.2001.002.319

Abstract The work presented provides an overview of different types of kernel interpolation used in the SPH method: conventional SPH, normalised SPH (NSPH), corrected kernel SPH (CSPH) and normalised corrected kernel SPH (NCSPH). These four methods are considered in a fully mesh-free form (using no background mesh). To illustrate the effect of using different interpolation methods two problems were simulated: a 1D symmetric elastic impact problem, and a shock-tube. An overview of the simulation results for the two problems is given. Shortcomings for the interpolation schemes tested were identified and discussed. It is concluded that NCSPH provides the best results. To… More >

Jianming Zhang, Zhenhan Yao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.3, pp. 307-318, 2001, DOI:10.3970/cmes.2001.002.307

Abstract The Meshless Local Boundary Integral Equation (MLBIE) method is a truly meshless one as it does not need a 'finite element or boundary element mesh', either for variable interpolation or for 'energy' integration. The Boundary Node Method (BNM) further reduces the dimensionality of the problem by one, i.e. it only requires nodes constructed on the surface. However, the BNM is not truly meshless, as a background mesh is needed for boundary integration; and the MLBIE does not have the advantage of reduced dimensionality as the BNM. A new Regular Hybrid Boundary Node method based on a modified functional and the… More >

Yu.A. Melnikov, M.Yu. Melnikov¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 291-306, 2001, DOI:10.3970/cmes.2001.002.291

Abstract The use of potential (integral) representations is studied when computing Green's functions for boundary value problems stated for Laplace and biharmonic equations over regions of complex configuration in two dimensions. The emphasis is on the non-traditional potentials, whose observation and source points occupy different sets. Such potentials reduce the original boundary value problems to functional (integral) equations with smooth kernels. Special integral representations are studied, the ones whose kernels are built not of the fundamental solutions of governing differential equations but of the Green's functions for simply shaped regions, which are associated with boundary value problems under consideration. Such integral… 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 three problems, the stress intensity… More >