Otimização de estruturas reticuladas planas com comportamento geometricamente não linear
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2006-10-20
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Universidade Federal de Goiás
Resumo
The aim of this work is to present a formulation and corresponding computational
implementation for sizing optimization of plane frames and cable-stayed columns considering
geometric non liner behavior.
The structural analysis is based on the finite element method using the updated
lagrangian approach for plane frame and cable elements, which are represented by plane truss
elements. The non linear system is solved by the Newton-Raphson method coupled to load
increment strategies such as the arch length method and the generalized displacement
parameter method, which allow the algorithm to transpose any critical point that happen to
appear along the equilibrium path.
In the optimization process the design variables are the heights of the crosssection
of the frame elements, the objective function represents the volume of the structure
and the constraints impose limits to displacements and critical load. Lateral constraints
impose limits to the design variables. The finite difference method is used in the sensitivity
analysis of the displacement and critical load constraints. The optimization process is carried
out using three different optimization strategies: the sequential quadratic programming
algorithm; the interior points algorithm; and the branch and bound method.
Some numerical experiments are carried out so as to test the analysis and the
sensitivity strategies. Numerical experiments are presented to show the validity of the
implementation presented in this dissertation.
Descrição
Palavras-chave
Otimização , programação quadrática seqüencial , algoritmo de pontos interiores , branch and bound , análise não linear geométrica , pórticos planos , colunas estaiadas , Optimization , sequential quadratic programming , interior points algorithm , branch and bound , non linear geometric analysis , plane frames , cable stayed columns , 1. Estruturas Otimização 2. Programação quadrática seqüencial
3. Algoritmo de pontos interiores 4. Análise não linear geométrica
5. Pórticos planos 6. Colunas estaiadas
Citação
ASSIS, Lilian Pureza de. Optimization of plane frame structures with behavior
geometrically nonlinear. 2006. 151 f. Dissertação (Mestrado em Engenharias) - Universidade Federal de Goiás, Goiânia, 2006.