Mathematical Sciences: Direct Relaxation of Optimal Layout Problems

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9305840 Lurie This research will develop a direct approach to the relaxation of nonselfadjoint problems of optimal design. The associated min-max problems are investigated applying the notion of quasi-saddle behavior of integrand as the necessary and sufficient condition for the existence of min-max. We also develop an alternative approach to the problem reducing it to a standard minimization after the Legendre transform is applied to the adjoint field. %%% The goal of the research is to develop a methodology for the determination of optimal structural characteristics of elastic bodies designed for work in a variety of external conditions (load, static and dynamic response, loss of stability,) or under the action of combined physical fields (stresses and temperature, electric and magnetic fields, etc.) The analytic results will be implemented in a new numerical technique to compute optimal designs using advanced composites. This technique will give truly optimal designs as compared to existing methods. ***