Journal ArticleDOI
Equivalent displacement based formulations for maximum strength Truss topology design
Reads0
Chats0
TLDR
A number of equivalent formulations in the displacements only are presented, taking full advantage of the structure of the optimization problem, and reducing in some cases even to linear programming problems.Abstract:
Maximum strength elastic truss structural design is conveniently formulated in terms of displacements and bar volumes. The resulting problem is nonconvex, and for topology design very large, as one seeks the optimal topology as a subset of a large number of potential bars connecting all nodal points of an initially chosen set. In this paper we present a number of equivalent formulations in the displacements only, taking full advantage of the structure of the optimization problem. The equivalent formulations are of min-max type or are quadratic programming problems in the displacements, reducing in some cases even to linear programming problems.read more
Citations
More filters
Journal ArticleDOI
Applications of second-order cone programming
TL;DR: In this paper, an efficient primal-dual interior-point method for solving second-order cone programs (SOCP) is presented. But it is not a generalization of interior point methods for convex problems.
Book ChapterDOI
Disciplined Convex Programming
TL;DR: A new methodology for constructing convex optimization models called disciplined convex programming is introduced, which enforces a set of conventions upon the models constructed, in turn allowing much of the work required to analyze and solve the models to be automated.
BookDOI
Handbook of Semidefinite Programming
TL;DR: Conditions and an accurate semidefinite programming solver are described in The Journal of the SDPA family for solving large-scale SDPs and in Handbook on Semidefinitely Programming.
Journal ArticleDOI
Robust Truss Topology Design via Semidefinite Programming
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: A new model of the truss topology design problem is presented, where the rigidity of the resulting truss with respect both to given loading scenarios and small "occasional" loads is optimized.
Journal ArticleDOI
Optimization Methods for Truss Geometry and Topology Design
TL;DR: In this article, a number of equivalent potential or complementary energy problem formulations in terms of member forces, displacements and bar areas were derived using duality principles and non-smooth analysis and discussed the implications these formulations have for the construction and implementation of efficient algorithms for large scale truss topology design.
References
More filters
Book
Introduction to Numerical Analysis
Josef Stoer,Roland Bulirsch +1 more
TL;DR: This well written book is enlarged by the following topics: B-splines and their computation, elimination methods for large sparse systems of linear equations, Lanczos algorithm for eigenvalue problems, implicit shift techniques for theLR and QR algorithm, implicit differential equations, differential algebraic systems, new methods for stiff differential equations and preconditioning techniques.
Journal ArticleDOI
Generating optimal topologies in structural design using a homogenization method
Martin P. Bendsøe,Noboru Kikuchi +1 more
TL;DR: In this article, the authors present a methodology for optimal shape design based on homogenization, which is related to modern production techniques and consists of computing the optimal distribution in space of an anisotropic material that is constructed by introducing an infimum of periodically distributed small holes in a given homogeneous, i.i.