Finite Elements in Analysis and Design 

Abstract: A proposed standard set of test problems is described and applied to representative quadrilateral plate and solid brick finite elements. The problem set contains patch tests and beam, plate, and shell problems, some of which have become de facto standards for comparing the accuracy of finite elements. Although few in number, the tests are able to display most of the parameters which affect finite element accuracy.

Abstract: In this paper three-dimensional geometrical models for concrete are generated taking the random structure of aggregates at the mesoscopic level into consideration. The generation process is based upon Monte Carlo's simulation method wherein the aggregate particles are generated from a certain aggregate size distribution and then placed into the concrete specimen in such a way that there is no intersection between the particles. For high volume fractions of aggregates, new algorithms for generating realistic concrete models are proposed.The generated geometrical models are then meshed using the aligned approach in which the finite element boundaries are coincident with materials interfaces and therefore there are no material discontinuities within the elements.The finite element method (FEM) is used in the direct computation of the effective properties of concrete. The results obtained from the numerical simulations and the subsequent homogenisation are then compared with experimental data. Furthermore numerical simulations of the damage and fracture process of concrete are performed using an isotropic damage model to model the progressive degradation of concrete. Finally, a concrete block is investigated where numerical and experimental results are discussed.

Abstract: This paper presents an improved algorithm for the bi-directional evolutionary structural optimization (BESO) method for topology optimization problems. The elemental sensitivity numbers are calculated from finite element analysis and then converted to the nodal sensitivity numbers in the design domain. A mesh-independency filter using nodal variables is introduced to determine the addition of elements and eliminate unnecessary structural details below a certain length scale in the design. To further enhance the convergence of the optimization process, the accuracy of elemental sensitivity numbers is improved by its historical information. The new approach is demonstrated by solving several compliance minimization problems and compared with the solid isotropic material with penalization (SIMP) method. Results show the effectiveness of the new BESO method in obtaining convergent and mesh-independent solutions.

Abstract: We present an approximate analytical method to evaluate efficiently and accurately the call blocking probabilities in wavelength routing networks with multiple classes of calls. The model is fairly general and allows each source-destination pair to service calls of different classes, with each call occupying one wavelength per link. Our approximate analytical approach involves two steps. The arrival process of calls on some routes is first modified slightly to obtain an approximate multiclass network model. Next, all classes of calls on a particular route are aggregated to give an equivalent single-class model. Thus, path decomposition algorithms for single-class wavelength routing networks may be readilt extended to the multiclass case. This article is a first step towards understanding the issues arising in wavelength routing networks that serve multiple classes of customers.

Abstract: Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.