Naslov
Optimality criteria method in 2D linearized elasticity problems

Autori
Burazin, Krešimir ; Crnjac, Ivana ; Vrdoljak, Marko

Izvornik
Applied numerical mathematics (0168-9274) 160 (2021); 192-204

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Linearized elasticity ; Optimal design ; Optimality criteria method

Sažetak
In optimal design problems the goal is to find an optimal distribution of materials in a fixed domain which optimizes a criterion, computed through the solution of a partial differential equation modelling the involved physics. We consider optimal design problems in the setting of linearized elasticity, and restrict ourselves to domains filled with two isotropic elastic phases. Since a classical solution usually does not exist, we use the homogenization method in order to get a proper relaxation of the original problem. Unfortunately, the related G-closure problem in linearized elasticity is not solved. However, in the compliance minimization problem, G-closure can be replaced by a smaller subset made of sequential laminates, which is explicitly known. Moreover, for the compliance minimization the necessary conditions of optimality are easily derived, which enables a development of optimality criteria method for the numerical solution. We explicitly calculate the lower Hashin-Shtrikman bound on the complementary energy in two space dimensions, and necessary conditions of optimality. We develop an optimality criteria method for the single state compliance minimization problems.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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