Minimização da energia de deformação de vigas de espessura variável sujeitas a carregamentos incertos / Compliance optimization of variable thickness beams subjected to uncertain loading conditions

AUTOR(ES)

Leandro Cardozo

DATA DE PUBLICAÇÃO

2005

RESUMO

Optimization plays a very important role in space applications since mass and structural flexibility are critical requirements for space missions. Generally, it is desired that the structure be as lightweight and stiff as possible. As a contribution in this area this work investigates compliance optimization of a structure under multiple load cases. The problem can be solved through a multi-criterion optimization where the load cases associated with each and every loading configuration are treated as components of multi-objective function vector. This approach leads naturally to the concept of Pareto sets. However, numerical evaluation is not an easy task because sometimes it involves a very high computer effort. Alternatively, the multi-objective optimization problem can be re-formulated by using a min-max strategy that does not require simultaneous consideration of all the load cases as components of the multi-objective function vector. Instead, this formulation shows that, for compliance optimization purposes, it is sufficient to consider only those loads which define the convex hull of the applicable load set, i.e., the selected set of loads which will effectively lead to the optimum design. Thereby, the number of load cases involved in the design procedure is drastically reduced. The optimum designs provided by this method are able to sustain not only a few load cases but also an entire convex set of them. The efficiency of the proposed technique is illustrated through examples of Euler-Bernoulli beams. The problem of strain energy was investigated using a variable thickness beam subjected to uncertain loadings. Technically, the beam thickness was distributed in order to obtain a stiffer structure with the same initial mass, characterizing a shape optimization problem.

ASSUNTO(S)

otimização de forma structural analysis shape optimization vigas de euler bernoulli minimax technique euler bernoulli beams análise estrutural space technology and engineering compliance técnica minimax flexibilidade engenharia e tecnologia espacial

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