D. H. Pahr¹, H.J. Böhm¹

CMES-Computer Modeling in Engineering & Sciences, Vol.34, No.2, pp. 117-136, 2008, DOI:10.3970/cmes.2008.034.117

Abstract The combination of heterogeneous volume elements and numerical analysis schemes such as the Finite Element method provides a powerful and well proven tool for studying the mechanical behavior of composite materials. Periodicity boundary conditions (PBC), homogeneous displacement boundary conditions (KUBC) and homogeneous traction boundary conditions (SUBC) have been widely used in such studies. Recently Pahr and Zysset (2008) proposed a special set of mixed uniform boundary conditions (MUBC) for evaluating the macroscopic elasticity tensor of human trabecular bone. These boundary conditions are not restricted to periodic phase geometries, but were found to give the same… More >

Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

CMES-Computer Modeling in Engineering & Sciences, Vol.33, No.3, pp. 293-312, 2008, DOI:10.3970/cmes.2008.033.293

Abstract A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are More >

O. Buzzi¹, D. M. Pedroso², A. Giacomini¹

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.2, pp. 85-106, 2008, DOI:10.3970/cmes.2008.031.085

Abstract The material point method (MPM) is a numerical method for the solution of problems in continuum mechanics, including situations of large deformations. A generalization (GMPM) of this method was introduced by Bardenhagen and Kober (2004) in order to avoid some computational instabilities inherent to the original method (MPM). This generalization leads to a method more akin of the Petrov-Galerkin procedure. Although it is possible to find in the literature examples of the deduction and applications of the MPM/GMPM to specific problems, its detailed implementation is yet to be presented. Therefore, this paper attempts to describe… More >

Sen Yung Lee¹, Sheei Muh Lin², Chien Shien Lee³, Shin Yi Lu³, Yen Tse Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.1, pp. 27-36, 2008, DOI:10.3970/cmes.2008.030.027

Abstract An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with More >

Thi D. Dang¹, Bhavani V. Sankar²

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 169-188, 2008, DOI:10.3970/cmes.2008.026.169

Abstract In this paper the meshless local Petrov-Galerkin (MLPG) method is used in the micromechanical analysis of a unidirectional fiber composite. The methods have been extended to include shear loadings, thus permitting a more complete micromechanical analysis of the composite subjected to combined loading states. The MLPG formulation is presented for the analysis of the representative volume element (RVE) of the periodic composite containing material discontinuities. Periodic boundary conditions are imposed between opposite faces of the RVE. The treatment of periodic boundary conditions in the MLPG method is handled by using the multipoint constraint technique. Examples More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.1, pp. 53-66, 2007, DOI:10.3970/cmes.2007.021.053

Abstract A newly modified Trefftz method is developed to solve the exterior and interior Dirichlet problems for two-dimensional Laplace equation, which takes the characteristic length of problem domain into account. After introducing a circular artificial boundary which is uniquely determined by the physical problem domain, we can derive a Dirichlet to Dirichlet mapping equation, which is an exact boundary condition. By truncating the Fourier series expansion one can match the physical boundary condition as accurate as one desired. Then, we use the collocation method and the Galerkin method to derive linear equations system to determine the More >

K. Han ¹, Y. T. Feng ¹, D. R. J. Owen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.18, No.2, pp. 87-100, 2007, DOI:10.3970/cmes.2007.018.087

Abstract Numerical procedures are introduced for simulations of irregular particle transport in turbulent flows using the coupled lattice Boltzmann method (LBM) and the discrete element method (DEM). The fluid field is solved by the extended LBM with the incorporation of the Smagorinsky turbulence approach, while particle interaction is modeled by the DEM. The hydrodynamic interactions between fluid and particles are realised through an immersed boundary condition, which gives rise to a coupled solution strategy to model the fluid-particle system under consideration. Main computational aspects comprise the lattice Boltzmann formulation for the solution of fluid flows; the More >

A. J. C. Crespo¹, M. Gómez-Gesteira¹, R. A. Dalrymple²

CMC-Computers, Materials & Continua, Vol.5, No.3, pp. 173-184, 2007, DOI:10.3970/cmc.2007.005.173

Abstract Smoothed Particle Hydrodynamics is a purely Lagrangian method that can be applied to a wide variety of fields. The foundation and properties of the so called dynamic boundary particles (DBPs) are described in this paper. These boundary particles share the same equations of continuity and state as the moving particles placed inside the domain, although their positions and velocities remain unaltered in time or are externally prescribed. Theoretical and numerical calculations were carried out to study the collision between a moving particle and a boundary particle. The boundaries were observed to behave in an elastic More >

Jin Yeon Cho¹

CMC-Computers, Materials & Continua, Vol.5, No.2, pp. 99-116, 2007, DOI:10.3970/cmc.2007.005.099

Abstract A novel way is proposed to fulfill Kronecker delta condition in moving least squares (MLS) approximation along the essential boundary. In the proposed scheme, the original MLS weight is modified to boundary interpolatable (BI) weight based on the observation that the support of weight function is exactly the same as the support of MLS nodal shape function. The BI weight is zero along the boundary edges except the edges containing the nodal point associated with the concerned weight. In order to construct the BI weight from the original weight, concept of edge distance function is… More >

Zai You Yan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.13, No.2, pp. 81-90, 2006, DOI:10.3970/cmes.2006.013.081

Abstract Boundary element method in acoustics for Neumann boundary condition problems including sharp edges & corners is investigated. In previous acoustic boundary element method, acoustic pressure and normal velocity are the two variables at sharp edges & corners. However, the normal velocity at sharp edges & corners is discontinuous due to the indefinite normal vector. To avoid the indefinite normal vector and the discontinuous normal velocity at sharp edges & corners, normal vector of elemental node is defined and applied in the numerical implementation. Then the normal velocity is transformed to velocity which is unique even More >