A design algorithm for the optimization of laminated composite structures

Abstract

This paper is devoted to the optimal design of laminated composite structures. The goal of the study is to assess the quality and the performance of an algorithm based on the directional derivative method. Particular attention is paid to the one-dimensional search, a critical step of the process, performed by cubic splines approximation. The optimization problem is formulated as weight minimization, under constraints on the mechanical behavior of the structure. The assumed design variables are the ply thicknesses, treated as continuous design variables, constrained by technological requirements. The structural analysis is performed making use of quadrilateral four-node composite elements, based on the first order shear deformation theory. The algorithm is applied to the optimization of a rectangular laminated plate. The results obtained are compared with those obtained by other similar studies and show the effectiveness and accuracy of the proposed approach.

Optimization for Buckling of Composite Sandwich Plates

“…In our own design computer program, the users can choose their own trial functions M*/, ..., w y j [Eq. (12)] to suit their boundary conditions. After they input these functions, all of the mathematical operations, such as differentiation, will be done automatically by computers.…”

Optimum Design of Fibre Orientation in Composite Laminate Plates for Out-Plane Stresses

“…SF MS and SF TW are equal to the safety factors according to the maximum stress, and Tsai-Wu criteria, respectively, if they are greater than 1.0, otherwise these terms are equal to zero; w i are suitable coefficients [35]. This penalty function is the same as the one defined by Akbulut and Sonmez [35] in 2008 except the last term of (18). In their work, the ply angles are optimised for inplane plate and the effect of shear stress and as a result induced twist angle of the plate was neglected.…”

“…Latterly, many studies have been devoted to the optimum strength design of multidirectional laminate. Among these are the works by Park [12], Fukunaga and Chou [13], Miravete [14], Fukunaga and Vanderplaats [15], Gurdal et al [16,17], Spallino et al [18], Weaver [19], Chattopadhyay et al [20], Luersen and Riche. [21], and Ghiasi et al [22].…”

Optimum Design of Composite Structures: A Literature Survey (1969–2009)

“…Researchers used various theories and methods to analyze composite structures. As an analytical method, many used the classical laminated plate theory, besides, some of them used von Karman plate theory, 795 3D laminated media analysis, 534 the zig-zag plate theory, 640,960,900,961 shear deformation theories, 61,193,240,304,342,351,372,373,380,404,418,420,432,439,458,470,471,504,516,521,533,541,572,575,576,577,590,591,615,656,664,665,685,701,750,752,815,819,904,928,934–936,945,1005 Flügge shell theory, 23,573,663,849 beam theories, 1,3,76,87,111,345,…”

“…In order to avoid unacceptable configurations, constraints are imposed on the design variables during an optimization process; e.g. a minimum stiffness is ensured by imposing an upper limit for deflections, 1,3,12,18,25,28,34,38,42,47,49,59,84,122,123,127–129,131,143,145,146,156,165,200,222,225,227,238,240,256,258,261,265,269,272,282,283,293,315,344,351,360,403,410,412,413,419,422,423,437,469,470,476,498,500,503,520,530,552,563,565,568,…”