Engineering Computations

Analytical Trial Function Method for Development of New 8-node Plane Element Based on the Variational Principle Containing Airy Stress Function : Table of Contents

Dr. Xiang-Rong Fu, Dr. Song Cen, Dr. C.F. Li, Dr. Xiao-Ming Chen — Mon Mar 01 02:05:39 GMT 2010

Abstract:
Purpose - A novel and simple strategy for construction of hybrid-‘stress function’ plane element is proposed for the first time. Design/methodology/approach - Firstly, a complementary energy functional, in which the Airy stress function is taken as the functional variable, is established within an element for analysis of plane problems. Secondly, fifteen basic analytical solutions (in global Cartesian coordinates) of the stress function are taken as the trial functions for an 8-node element, and meanwhile, 15 unknown constants are then introduced. Thirdly, according to the principle of minimum complementary energy, the unknown constants can be expressed in terms of the displacements along element edges, which are interpolated by element nodal displacements. Finally, the whole system can be rewritten in terms of element nodal displacement vector,Findings - and thus, a new hybrid element stiffness matrix is obtained. The resulting 8-node plane element, denoted as ATF-Q8, possesses excellent performance in numerical examples. Furthermore, some numerical defects, such as direction dependence and interpolation failure, are not found in present model. Originality/value - This new strategy for developing finite element models exhibits advantages of both analytical and discrete method.

Suboptimal cycle bases of graphs using ant colony system algorithm : Table of Contents

Prof. A. Kaveh, Mrs. Maryam Daei — Mon Mar 01 02:05:39 GMT 2010

Abstract:
Purpose - Cycle bases of graphs have many applications in science and engineering. For an efficient force method of structural analysis, a special cycle basis corresponding to sparse cycle adjacency matrix is required.Design/methodology/approach - In this paper, an ant colony system algorithm is developed for the generation of a cycle basis, leading to suboptimal cycle basis corresponding to highly sparse flexibility matrices. Examples are included to illustrate the efficiency of the developed algorithm.Findings - A new approach is developed which uses the recently developed ant colony system algorithm for the optimization.Research limitations/implications - No limitation.Practical implications - Efficient analysis of rigid-jointed frames become feasible.Originality/value - Previously graph theoretical method had been used for the formation of suboptimal cycle bases. Here, optimization is performed using ant colony system algorithm for the first time.

Three dimensional ellipsoidal discrete element modeling of granular materials and its coupling with finite element facets : Table of Contents

Dr. Beichuan Yan, Prof. Richard Regueiro, Prof. Stein Sture — Mon Mar 01 02:05:39 GMT 2010

Abstract:
Purpose - To develop a discrete element (DE) and multiscale modelling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil-tool, tire, penetrometer, pile, etc., interfaces.Design/methodology/approach - A three-dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modelling of granular media.Findings - A closed-form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi-static oedometer, triaxial compression, and pile penetration. The DE-FE facet coupling demonstrates the potential to alleviate artificial boundary effects in the shear deformation region between DEM granular media and deformable solid bodies.Research limitations/implications - The research is being extended to couple more robustly the ellipsoidal DEM code and a higher order continuum FE code via overlapping bridging scale methods, in order to remove dependence of penetration/shear resistance on the boundary placement for DE simulation.Practical implications - When concurrent multiscale computational modelling of interface conditions between deformable solid bodies and granular materials reaches maturity, modellers will be able to simulate the mechanical behaviour accounting for physical particle sizes and flow in the interface region, and thus design their tool, tire, penetrometer, or pile accordingly.Originality/value - A closed-form solution for ellipsoidal particle contact was demonstrated, and the ability to couple DE to FE facets.

Remarks on symmetry conditions in computational homogenisation problems. : Table of Contents

Mr. Erick Saavedra, Dr. E A de Souza Neto — Mon Mar 01 02:05:39 GMT 2010

Abstract:
Purpose - To use symmetry conditions for the reduction of computing times in problems involving finite element-based multi-scale constitutive models of non-linear heterogeneous media.Design/methodology/approach - Two types of RVE symmetry often found in practice are considered: staggered-translational and point symmetry. These are analysed under three types RVE of kinematical constraints: periodic boundary fluctuations (typical of periodic media), linear boundary displacements (which gives an upper bound for the macroscopic stiffness) and the minimum kinematical constraint (corresponding to uniform boundary tractions and providing a lower bound for the macroscopic stiffness).Findings - Numerical examples show that substantial savings in computing times are achieved by taking advantage of such symmetries. These are particularly pronounced in fully coupled two-scale analyses, where the macroscopic equilibrium problem is solved simultaneously with a large number of microscopic equilibrium problems at Gauss-point level. Speed-up factors in excess of seven have been found in such cases, when both symmetry conditions considered are present at the same time.Originality/value - Extends the original considerations of Ohno et al. to account for other RVE kinematical constraints, namely, the linear boundary displacement and the minimum kinematical constraint (or uniform boundary traction model). Provides a more precise assessment of the impact of the use of such symmetries on computing times by means of numerical examples. In addition, for completeness, the direct enforcement of such constraints within a Newton-based finite element solution procedure for the RVE equilibrium problem is detailed in the paper.