Abstract
The design of mechanical structures may be posed as an optimization problem where some performance measure, such as structural weight, is optimized subject to constraints on stresses, deformations, buckling load, and other response characteristics. Design variables are usually chosen to be design parameters such as thicknesses and other cross-sectional dimensions of structural members, the shape of the structural boundary, and similar properties. The response of the structure is almost always determined using a finite element approximation to the partial differential equations governing the response of the structure.
The paper describes how different optimization strategies may be necessary to solve the many possible structural design problems that arise in applications. A particular issue to be considered is whether or not the state variables, typically the deformations in the finite element model, should be eliminated using the equilibrium equations. A nonlinear structural model may require that the state variables are kept as independent variables although the most common approach in structural optimization is to eliminate the state variables.
This work was financially supported by the Swedish Research Council for Engineering Sciences (TFR).
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Ringertz, U.T. (1997). Large-Scale Structural Design Optimization. In: Biegler, L.T., Coleman, T.F., Conn, A.R., Santosa, F.N. (eds) Large-Scale Optimization with Applications. The IMA Volumes in Mathematics and its Applications, vol 93. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1960-6_10
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