Topic
Minimum weight
About: Minimum weight is a research topic. Over the lifetime, 2002 publications have been published within this topic receiving 28244 citations.
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TL;DR: The problem under consideration, even in simple cases, is shown to be equivalent to a large number of other problems that are notorious for their computational intractability, which justifies the development of methods that approximately solve the problem.
30 citations
TL;DR: A simple method for achieving a discrete optimum design from a segmental optimum design is described, avoiding the combinatorial nature of discrete optimization by introducing the concept of segmental members.
Abstract: A simple method based upon linear programming is described for the design of minimum weight structures under the restrictions that member sizes and/or material properties may be chosen only from discrete sets. The types of structures considered are those composed of axial force bars, membrane plates and shear panels. The method avoids the combinatorial nature of discrete optimization by introducing the concept of segmental members. The segmental optimum design is found by linear programming. Its weight is a lower bound to the weight of the discrete optimum design. A simple method for achieving a discrete optimum design from a segmental optimum design is described. Several examples of discrete optimum truss designs are presented.
30 citations
TL;DR: In this article, a power-series method developed for plane-strain slip-line field theory is applied to the construction of minimum-weight Michell frameworks, and the relationship between the space and force diagrams is defined as a basis for weight calculations.
Abstract: A power-series method developed for plane-strain slip-line field theory is applied to the construction of minimum-weight Michell frameworks. The relationship between the space and force diagrams is defined as a basis for weight calculations. Analytical solutions obtained by the method are shown to agree with known solutions that were obtained through virtual displacement calculations. Framework boundary conditions are investigated, and matrix operators used in slip-line field theory are shown to apply to the force-free straight framework boundary-value problem. The matrix operator method is used to illustrate the transition from circular arc-based to cycloid-based Michell solutions. Finally, an example is given in the use of the method for evaluation of support boundary conditions.
29 citations
29 citations
31 May 2014
TL;DR: In this article, a fixed parameter tractable algorithm for minimum bisection with running time O(2O(k3) n3 log3 n) was given, where n is the number of vertices in the graph.
Abstract: In the classic Minimum Bisection problem we are given as input a graph G and an integer k. The task is to determine whether there is a partition of V (G) into two parts A and B such that ||A| -- |B|| ≤ 1 and there are at most k edges with one endpoint in A and the other in B. In this paper we give an algorithm for Minimum Bisection with running time O(2O(k3) n3 log3 n). This is the first fixed parameter tractable algorithm for Minimum Bisection. At the core of our algorithm lies a new decomposition theorem that states that every graph G can be decomposed by small separators into parts where each part is "highly connected" in the following sense: any cut of bounded size can separate only a limited number of vertices from each part of the decomposition. Our techniques generalize to the weighted setting, where we seek for a bisection of minimum weight among solutions that contain at most k edges.
29 citations