Keywords: deterministic solution, laminated cylinders, composites, optimization.

In this study different types of cost functionals leading to optimal prestresses of a typical plate laminated composite structure are treated. The generalized plane strain is used as a pseudo-spatial numerical model for solving the problem. The aim of this paper is to prove the meaning of selected cost functionals for their use in shape optimization of various, more general, laminated structures. In order to show the application of one of the cost functionals envisaged a cylindrical laminated hollow composite structure is discussed at the end of the paper. In this application the stresses in hoop direction are preferred and selected as the design parameters of the shape optimization problem, because their values prevail over the rest of the components of stress tensor. The radial stresses and eigenstrains are always negligible. In References [1,2] the axial stress is taken into account during the optimization. Reference [3] uses the cost functional discussed in the sixth section of this paper.

Here attention is drawn to introducing eigenparameters [3], but the procedure can easily be extended to more complex problems, such as optimization with respect to a change of thickness of particular laminas and in spatial problems of optimal lay-ups of fibers (filaments). To all these problems the approach put forward this paper can be applied and serves as a promising tool for determining appropriate cost functionals.

The above said laminates can be used as a template in wide spectrum of structures in civil engineering, aerospace structures, in assessment of submersibles, in design of cooling towers, tunnel linings, etc. Classical examples for applying eigenparameters to underground structures appears to be optimal freezing of soil or rock, in order to attain optimal economic and bearing properties of the intended underground structure. A natural application is not only to classical composites, but also it plays important role in functionally graded materials.

1

G.J. Dvorak, P.P. Prochazka, "Thin-walled composite cylinders with optimal fiber prestress", Composites B, 27B, 643-649, 1996. doi:10.1016/S1359-8368(96)00001-7

2

G.J. Dvorak, P.P. Prochazka, M.V. Srinivas, "Design and fabrication of submerged cylindrical laminates", International Journal of Solids and Structures, 4(36), 3917-3943, 1999. doi:10.1016/S0020-7683(98)00181-4

3

P.P. Prochazka, V. Dolezel, T.S. Lok, "Optimal shape design for minimum Lagrangian", Engineering Analysis with Boundary Elements, 33, 447-455, 2009. doi:10.1016/j.enganabound.2008.09.003

4

G.J. Dvorak, "Transformation field analysis of inelastic composite materials", Proceedings of Royal Society London, A 437, 311-327, 1992. doi:10.1098/rspa.1992.0063

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