scholarly journals A Branch and Bound Approach for Truss Topology Design Problems with Valid Inequalities

2010 ◽  
Author(s):  
Adelaide Cerveira ◽  
Agostinho Agra ◽  
Fernando Bastos ◽  
Humberto Varum ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Branch And Bound ◽  
Valid Inequalities ◽  
Topology Design ◽  
Design Problems ◽  
Truss Topology ◽  
Truss Topology Design

A new Branch and Bound method for a discrete truss topology design problem

2012 ◽  
Vol 54 (1) ◽  
pp. 163-187 ◽  
Author(s):  
Adelaide Cerveira ◽  
Agostinho Agra ◽  
Fernando Bastos ◽  
Joaquim Gromicho
Keyword(s):  
Branch And Bound ◽  
Design Problem ◽  
Topology Design ◽  
Branch And Bound Method ◽  
Truss Topology ◽  
Truss Topology Design

A New Method for Optimal Truss Topology Design

1993 ◽  
Vol 3 (2) ◽  
pp. 322-358 ◽  
Author(s):  
Aharon Ben-Tal ◽  
Martin P. Bendsøe
Keyword(s):  
Topology Design ◽  
New Method ◽  
Truss Topology ◽  
Truss Topology Design

Robust Truss Topology Design with Beam Elements via Mixed Integer Nonlinear Semidefinite Programming

2015 ◽  
Vol 807 ◽  
pp. 229-238 ◽  
Author(s):  
Tristan Gally ◽  
Christopher M. Gehb ◽  
Philip Kolvenbach ◽  
Anja Kuttich ◽  
Marc E. Pfetsch ◽  
...  
Keyword(s):  
Stiffness Matrix ◽  
Optimal Choice ◽  
Topology Design ◽  
Mixed Integer ◽  
Semidefinite Program ◽  
Cross Sectional ◽  
Beam Elements ◽  
Truss Topology ◽  
Truss Topology Design ◽  
General Method

In this article, we propose a nonlinear semidefinite program (SDP) for the robust trusstopology design (TTD) problem with beam elements. Starting from the semidefinite formulation ofthe robust TTD problem we derive a stiffness matrix that can model rigid connections between beams.Since the stiffness matrix depends nonlinearly on the cross-sectional areas of the beams, this leads toa nonlinear SDP. We present numerical results using a sequential SDP approach and compare them toresults obtained via a general method for robust PDE-constrained optimization applied to the equationsof linear elasticity. Furthermore, we present two mixed integer semidefinite programs (MISDP), onefor the optimal choice of connecting elements, which is nonlinear, and one for the correspondingproblem with discrete cross-sectional areas.

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