This paper presents a new method, called Mesh Matching, for handling non-conforming hexahedral-to-hexahedral interfaces for finite element analysis. Mesh Matching modifies the hexahedral element topology on one or both sides of the interface until there is a one-to-one pairing of finite element nodes, edges and quadrilaterals on the interface surfaces, allowing mesh entities to be merged into a single conforming mesh. Element topology is modified using hexahedral dual operations, including pillowing, sheet extraction, dicing and column collapsing. The primary motivation for this research is to simplify the generation of unstructured all-hexahedral finite element meshes. Mesh Matching relaxes global constraint propagation which currently hinders hexahedral meshing of large assemblies, and limits its extension to parallel processing. As a secondary benefit, by providing conforming mesh interfaces, Mesh Matching provides an alternative to artificial constraints such as tied contacts and multi-point constraints. The quality of the resultant conforming hexahedral mesh is high and the increase in number of elements is moderate. Copyright © 2009 John Wiley & Sons, Ltd.
viernes, 4 de diciembre de 2009
Hexahedral Mesh Matching: Converting non-conforming hexahedral-to-hexahedral interfaces into conforming interfaces
This paper presents a new method, called Mesh Matching, for handling non-conforming hexahedral-to-hexahedral interfaces for finite element analysis. Mesh Matching modifies the hexahedral element topology on one or both sides of the interface until there is a one-to-one pairing of finite element nodes, edges and quadrilaterals on the interface surfaces, allowing mesh entities to be merged into a single conforming mesh. Element topology is modified using hexahedral dual operations, including pillowing, sheet extraction, dicing and column collapsing. The primary motivation for this research is to simplify the generation of unstructured all-hexahedral finite element meshes. Mesh Matching relaxes global constraint propagation which currently hinders hexahedral meshing of large assemblies, and limits its extension to parallel processing. As a secondary benefit, by providing conforming mesh interfaces, Mesh Matching provides an alternative to artificial constraints such as tied contacts and multi-point constraints. The quality of the resultant conforming hexahedral mesh is high and the increase in number of elements is moderate. Copyright © 2009 John Wiley & Sons, Ltd.
Polygonal finite elements for topology optimization: A unifying paradigm
In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian-type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one-node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh-dependent sub-optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. Copyright © 2009 John Wiley & Sons, Ltd.
An edge-based smoothed finite element method for primal-dual shakedown analysis of structures
An edge-based smoothed finite element method (ES-FEM) using three-node linear triangular elements was recently proposed to significantly improve the accuracy and convergence rate of the standard finite element formulation for static, free and forced vibration analyses of solids. In this paper, ES-FEM is further extended for limit and shakedown analyses of structures. A primal-dual algorithm based upon the von Mises yield criterion and a non-linear optimization procedure is used to compute both the upper and lower bounds of the plastic collapse limit and the shakedown limit. In the ES-FEM, compatible strains are smoothed over the smoothing domains associated with edges of elements. Using constant smoothing function, only one Gaussian point is required for each smoothing domain ensuring that the total number of variables in the resulting optimization problem is kept to a minimum compared with standard finite element formulation. Three benchmark problems are presented to show the stability and accuracy of solutions obtained by the present method. Copyright © 2009 John Wiley & Sons, Ltd.
Analogue filter group delay optimization using a stochastic approach
An analogue filter group delay response is optimized using an all-pass network connected in the cascade of the filter. This contribution introduces an original method of all-pass network correction designing of using a random-based approach. The main objective of the method is the calculation of an optimal all-pass network order and optimal coefficients of its transfer function. To realize this objective it is necessary to find minima of so-called optimization spaces. The spaces definition provides an important generalization of the optimization task. The original stochastic approach is used to find the mentioned minima of the spaces. The minima can be detected using several probability densities. The method combines advantages of a numerical approach with rigorous analytical pre-processing. Compared to current optimization methods, the described approach provides very good convergence, velocity and especially independence from the initial estimation of the all-pass network transfer function coefficients. The original objective function ensures absolutely stable convergence in the multidimensional optimization spaces. This objective function was developed with regard to properties of the analogue filters. The designed method is illustrated by a few practical optimizations. A well-known circuit simulator, Micro-Cap, is used as a comparative system because of its relatively good optimization algorithm. All the presented original algorithms and functions are debugged in the MATLAB® environment. Copyright © 2009 John Wiley & Sons, Ltd.
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