Author
Pauli Pedersen
Other affiliations: University of Copenhagen
Bio: Pauli Pedersen is an academic researcher from Technical University of Denmark. The author has contributed to research in topics: Finite element method & Optimal design. The author has an hindex of 29, co-authored 110 publications receiving 2889 citations. Previous affiliations of Pauli Pedersen include University of Copenhagen.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the optimal orientation of an anisotropic material with respect to the actual strain condition was investigated and complete analytical results were derived, including local as well as global maxima and minima.
Abstract: In order to use an anisotropic material effectively it should be oriented optimally with respect to the actual strain condition. Orientations with extreme energy density are obtained for orthotropic materials. It is found that the optimal orientation depends on one non-dimensional material parameter only, plus the ratio of the two principal strains. Complete analytical results are derived, including local as well as global maxima and minima.
330 citations
239 citations
TL;DR: In this paper, the stiffness design of laminated plates subjected to single and multiple loads is considered and the stiffness of the laminates is parametrized in terms of the so-called lamination parameters.
159 citations
TL;DR: In this paper, an indirect identification technique to predict the mechanical properties of composite plate specimens is presented, which makes use of experimental eigenfrequencies, the corresponding numerical eigenvalue evaluation, sensitivity analysis and optimization.
153 citations
TL;DR: In this paper, sensitivity analysis for strain energy with anisotropic elasticity is applied to thickness and orientational design of laminated membranes, and the first order gradients of the total elastic energy are primarily used in an optimality criteria based method.
Abstract: Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. The first order gradients of the total elastic energy are primarily used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To gain a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of thickness design only, orientational design only and combined thickness-orientational design are presented.
138 citations
Cited by
More filters
TL;DR: In this article, a new method for non-linear programming in general and structural optimization in particular is presented, in which a strictly convex approximating subproblem is generated and solved.
Abstract: A new method for non-linear programming in general and structural optimization in particular is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and solved. The generation of these subproblems is controlled by so called ‘moving asymptotes’, which may both stabilize and speed up the convergence of the general process.
4,218 citations
TL;DR: In this article, various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable are described. But none of these methods can be used for shape optimization in a general setting.
Abstract: Shape optimization in a general setting requires the determination of the optimal spatial material distribution for given loads and boundary conditions. Every point in space is thus a material point or a void and the optimization problem is a discrete variable one. This paper describes various ways of removing this discrete nature of the problem by the introduction of a density function that is a continuous design variable. Domains of high density then define the shape of the mechanical element. For intermediate densities, material parameters given by an artificial material law can be used. Alternatively, the density can arise naturally through the introduction of periodically distributed, microscopic voids, so that effective material parameters for intermediate density values can be computed through homogenization. Several examples in two-dimensional elasticity illustrate that these methods allow a determination of the topology of a mechanical element, as required for a boundary variations shape optimization technique.
3,434 citations
TL;DR: In this article, the authors analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials, and derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design.
Abstract: In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.
2,088 citations
TL;DR: An overview, comparison and critical review of the different approaches to topology optimization, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
Abstract: Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.
1,816 citations
TL;DR: The current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method are summarized and the methods with which they can be avoided are listed.
Abstract: In this paper we seek to summarize the current knowledge about numerical instabilities such as checkerboards, mesh-dependence and local minima occurring in applications of the topology optimization method. The checkerboard problem refers to the formation of regions of alternating solid and void elements ordered in a checkerboard-like fashion. The mesh-dependence problem refers to obtaining qualitatively different solutions for different mesh-sizes or discretizations. Local minima refers to the problem of obtaining different solutions to the same discretized problem when choosing different algorithmic parameters. We review the current knowledge on why and when these problems appear, and we list the methods with which they can be avoided and discuss their advantages and disadvantages.
1,796 citations