On a class of optimum problems in structural design

Stress constrained 𝐺 closure and relaxation of structural design problems

“…Both of these functions are continuous with respect to weak convergence in W12(tt, R3). However, the results given here arc not restricted to this situation and apply to multi-load design problems or any design criteria that is continuous with respect to G convergent sequences of designs [5]. The objective of the design problem is to optimize F(u) over the class of admissible configurations subject to constraints on the stress.…”

Relaxation Through Homogenization for Optimal Design Problems with Gradient Constraints

“…The results given here are not restricted to this situation and apply to any design criteria that is continuous with respect to G convergent sequences of designs (Ref. 3).…”

“…The next step in the relaxation procedure is the correct description of the gradient constraints (2)(3)(4)(5) in the extended design space. Given a sequence {C n (P , x)} ∞ n=1 that G converges to C ∞ (P , x) for every P in N (A) the local corrector function associated with the sequence {C n (A, x)} ∞ n=1 is introduced.…”

A problem in the optimal design of networks under transverse loading

“…Thus, the problem reduces to studying the minimization of a cost functional defined over a certain class of operators, as is customary in many other optimization problems [1][2][3][4][5][6][7][8][9][10][11][12]. The theory of (/-convergence (see, e.g., [13,14]) proves to be the natural setting to discuss the existence of solutions for these problems. At this point, however, because of the constancy of the pretractions along the fibers (cf.…”

“…□ The situation in Theorem 3.1 suggests cases where there is nonuniqueness. Jn from the monotonicity of the stored energy with respect to a (see, e.g., [14]). It follows that / lKWKdx ^ / ^AU'adx> J a J n which shows that crA is in fact optimal for the given load qA.…”