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… 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 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 >

R. Sedaghati, A. Suleman¹, S. Dost, B. Tabarrok²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 259-272, 2001, DOI:10.3970/cmes.2001.002.259

Abstract A structural analysis and optimization method is developed to find the optimal topology of adaptive determinate truss structures under various impact loading conditions. The objective function is based on the maximization of the structural strength subject to geometric constraints. The dynamic structural analysis is based on the integrated finite element force method and the optimization procedure is based on the Sequential Quadratic Programming (SQP) method. The equilibrium matrix is generated automatically through the finite element analysis and the compatibility matrix is obtained directly using the displacement-deformation relations and the Single Value Decomposition (SVD) technique. By More >

Enzo TONTI¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 237-258, 2001, DOI:10.3970/cmes.2001.002.237

Abstract We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiffness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one More >

S.-P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 227-236, 2001, DOI:10.3970/cmes.2001.002.227

Abstract Problems defined on infinite domains must be treated on a finite computational domain. The treatment of the artificially placed boundaries (usually referred to as open boundaries) of such domain truncations can be quite subtle; an over truncation would normally result in large, undesirable reflection of signals back to the computational domain whereas an under truncation would imply an injudicious use of computational resources. In particular, problems occur when strongly nonlinear free surface waves generated in a numerical wave tank are passing through such an open boundary.
In this paper, some recent numerical test results of… More >

Chyou-Chi Chien, Tong-Yue Wu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 213-226, 2001, DOI:10.3970/cmes.2001.002.213

Abstract This study presents a novel computational method for implementing the time finite element formulation for the equations of linear structural dynamics. The proposed method adopts the time-discontinuous Galerkin method, in which both the displacement and velocity variables are represented independently by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can effectively obtain the solutions for the resulting system of coupled equations. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical results are compared with exact and accepted solutions from More >

S. Rugonyi, K. J. Bathe¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 195-212, 2001, DOI:10.3970/cmes.2001.002.195

Abstract The solution of fluid flows, modeled using the Navier-Stokes or Euler equations, fully coupled with structures/solids is considered. Simultaneous and partitioned solution procedures, used in the solution of the coupled equations, are briefly discussed, and advantages and disadvantages of their use are mentioned. In addition, a simplified stability analysis of the interface equations is presented, and unconditional stability for certain choices of time integration schemes is shown. Furthermore, the long-term dynamic stability of fluid-structure interaction systems is assessed by the use of Lyapunov characteristic exponents, which allow differentiating between a chaotic and a regular system More >

M.Ganesh¹, D. Sheen²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 183-194, 2001, DOI:10.3970/cmes.2001.002.183

Abstract A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in Sheen, Sloan, and Thomée (2000) for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows one to compute solutions in a wide range of time. Instead of using a standard time-marching method, which is not easily parallelizable, we take the Laplace transform in time of the parabolic problems. The resulting elliptic problems can be solved in parallel. Solutions are then computed by More >

S.T. Lie¹, Guoyou Yu, Z. Zhao²

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 171-182, 2001, DOI:10.3970/cmes.2001.002.171

Abstract The BEM/FEM coupling procedure is applied to 2-D time domain structural-acoustic interaction problems. The acoustic domain for fluid or air is modeled by BEM scheme that is suitable for both finite and infinite domains, while the structure is modeled by FEM scheme. The input impact, which can be either plane waves or non-plane waves, can either be forces acting directly on the structural-acoustic system or be explosion sources. The far field or near field explosion sources which are difficult to be simulated by finite element modeling, can be simulated exactly by boundary element modeling as More >