3114 14850 1 PB Essay

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Mecánica Computacional Vol XXIX, págs. 1761-1781 (artículo completo)
Eduardo Dvorkin, Marcela Goldschmit, Mario Storti (Eds.)
Buenos Aires, Argentina, 15-18 Noviembre 2010

Rafael F. Silvaa; Iuri B. C. M. Rochaa, Evandro Parente Jr.a, Antônio M. C. Meloa and
Áurea S. Holandab a Departamento de Engenharia Estrutural e Construção Civil, Universidade Federal do Ceará
Campus do Pici, Bloco 710, 60455-760, Fortaleza, Ceará, Brasil b Departamento de Engenharia de Transportes, Universidade Federal do Ceará
Campus do Pici, Bloco 703, 60455-760, Fortaleza, Ceará, Brasil

Keywords: Composite materials, laminated tubes, optimization, Finite Element Method.
Abstract. This work presents a methodology for minimum weight design of laminated composite tubes. The design variables are the number of plies and the thickness and fiber orientation of each ply.
The formulation includes stress and stability constraints. Multiple loading cases can be considered. A highly efficient axi-symmetric finite element formulation was developed and implemented for structural analysis. The stresses in the material system are used to compute the safety factor of the laminate using an appropriate failure criterion. The design optimization is performed using a sequential quadratic programming (SQP) algorithm. The proposed methodology is successfully applied to the design optimization of laminated composite tubes subjected to internal and external pressure, axial load and torsion. Several application examples are presented.

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Fiber Reinforced Composites (FRC) research and use have been rising in the recent years, due to its high specific stiffness and specific strength. Also, it features good corrosion resistance, thermal insulation, good damping performance and long fatigue life. Such features have led many industries to fund researches on the area, particularly the oil drilling and aerospace industries. Particularly, development of lighter composite tubes for fluid transportation and pressure vessels for fluid storage are on the rise. Comparative studies between steel and composite tubes for oil drilling (risers) are showed in Beyle et al. (1997).
Among many types of FRC, the use of laminated composite structures is growing widely in the last few years. This is due to the possibility of a more optimized structural design, utilizing the great tailorability it offers, since the number, orientation and sequence of plies (or laminas) can be optimized to give the exact desired structural behavior (Azarafza et al., 2009).
Laminated composites consist of a series of laminae, each one consisting of unidirectional fibers embedded in a polymeric matrix, the latter transmitting the stresses between the former.
(Jones, 1999; Mendonça, 2005). Design of such structures shows many complexities, as many design choices have to be made, such as the number of lamina and the thickness and orientation angle of each laminae.
A traditional design methodology can be used through the trial-and-error process, which can be an arduous process if applied to fiber reinforced composites, due its many design variables. Therefore, design of such structures is better fit to the use of optimization techniques (Vanderplaats, 2001).
The design variables can be continuous, as in Park et al. (2005), or discrete, as in Topal
(2009). No unique optimum solution is usually obtained when minimum thickness is searched and the ply thicknesses are discrete variables, e.g. multiple of a basic layer thickness (Gurdal et al., 1999). In this case, it is often better to use a multi-objective optimization formulation
(Marler and Arora, 2004; Silva et al., 2009; Walker and Smith, 2003). Usually, the weight of the laminate and another performance parameter is considered (Almeida and