Maio 2014 vol. 1 num. 1 - 10th World Congress on Computational Mechanics

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OPTIMIZATION OF EIGENFREQUENCIES OF PSEUDO 3D COMPOSITE

Prochazka, P. P. ;

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In this paper an optimization of laminated arches is solved under condition that generally anisotropic layers are considered and the design parameters of optimization are eigenparameters (intrinsic fields), either eigenstrains or eigenstresses. Mathematical apparatus is to be discussed and the formulas needed for programming on computers will be derived. The focus here is concentrated on problem of the response of harmonic load, which can be simulated by developing time coordinate into the Fourier series. The solution on separated coordinates of position is formulated for simply supported or clamped layered arch in cylindrical coordinates. The semi-analytic solution is used for simply supported arch in the position coordinates. The conditions being valid for clamped edges are taken from the well known Lechnitski’s book on Theory of plates. The procedure used in the book enables us to solve the simply supported arch and by virtue of unit impulses of a slope at the supports to derive the solution for fixed ends. The boundary conditions are fulfilled by selections of sine or cosine series applied to different directions of displacements and eigenparameters. Then, the static case is described in each lamina separately and the overall relations are provided with fulfillment of interfacial conditions being valid on the interfaces of the adjacent laminas. Since the influence of inertia forces appear to be quite simple, the problem is focused on the separated static case (in the position coordinates). The formulation leads to the solution of a simultaneous system of ordinary differential equations, which are defined in one generic lamina. In our case harmonic load is discussed, as eigenfrequencies are of the main interest to us. The pseudo 3D formulation is based on generalized plain strain, so that also axial direction can be taken into account in the optimization. Examples are presented starting with twodimensional case, which is based on plain strain formulation, simplifying the general case.

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Palavras-chave: Optimization of laminated arches, Eigenparameters, Eigenfrequencies, Stationary point of Hamiltonian.,

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DOI: 10.5151/meceng-wccm2012-19541

Referências bibliográficas
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Como citar:

Prochazka, P. P.; "OPTIMIZATION OF EIGENFREQUENCIES OF PSEUDO 3D COMPOSITE", p. 3728-3743 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-19541

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