Dual methods for optimizing finite element flexural systems

Modern numerical methods for the optimization of large discretized systems are now well developed and highly efficient in the case of thin walled elastic structures modeled by finite elements. However, this is not yet true for structures whose components are subject simultaneously to bending and extension loads. In this paper, the idea of Generalized Optimality Criterion (GOC), set forth in previous papers for bar, membrane, and pure bending elements, is extended to deal with general beam and flat shell elements. The modifications brought to the GOC result in explicit approximations for the behavior constraints that are correct up to the first order, but that exhibit a more complex algebraic form. Indeed these explicit expressions are no longer merely linear in the reciprocal design variables. However, they continue to be additively separable, and therefore dual methods remain fully applicable, just as in the original statement of the GOC approach. Numerical examples will be offered to demonstrate the efficiency of the method presented.