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Anisotropy and shape optimal design of shells by the polar-isogeometric approach. (English) Zbl 1439.49031
This paper is concerned with the optimal design of composite structures, in particular, of shells. The objective is to maximise the shell stiffness by optimising over both the shape, i.e., a domain \(\Omega \subset \mathbb{R}^3\), and the elastic anisotropic properties that may vary pointwise on \(\Omega\), i.e., an elastic tensor field \(\mathbb{E}:\Omega \to \bigotimes^4\mathbb{R}^3\).
The model adopted in this paper is Naghdi’s shell model, and the (static) state equation is given via a variational formulation, namely the “virtual work principle”. This principle states that the virtual work of applied loads is equal to the strain energy. An optimisation problem is formulated to find the argmin of an objective function constructed based on the strain energy, subject to various constraints arising from the geometry of the problem.
One of the main features of this paper, apart from the aforementioned formulation of the optimal control problem, is the combination of the isogeometric approach for determining basis functions and the polar formalism for representing the components of elastic tensors. Several interesting numerical examples are studied thoroughly, and various open questions are discussed towards the end of the paper.
Reviewer: Siran Li (Houston)
49J53 Set-valued and variational analysis
49K99 Optimality conditions
74K25 Shells
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
Full Text: DOI
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