Zafer Gurdal

Improved Genetic Algorithm for the Design of Stiffened Composite Panels

The design of composite structures against buckling presents two major challenges to the designer. First, the problem of laminate stacking sequence design is discrete in nature, involving a small set of fiber orientations, which complicates the solution process. Therefore, the design of the stacking sequence is a combinatorial optimization problem which is suitable for genetic algorithms. Second, many local optima with comparable performance may be found. Most optimization algorithms find only a single optimum, while often a designer would want to obtain all the local optima with performance close to the global optimum. Genetic algorithms can easily find many near optimal solutions. However, they usually require very large computational costs. Previous work by the authors on the use of genetic algorithms for designing stiffened composite panels revealed both the above strength and weakness of the genetic algorithm. The present paper suggests several changes to the basic genetic algorithm developed previously, and demonstrates reduced computational cost and increased reliability of the algorithm due to these changes. Additionally, for a stiffened composite panel used in this study, designs lighter by about 4 percent compared to previous results were obtained.

Linear Shepard Interpolation for High Dimensional Piecewise Smooth Functions

Scattered data interpolation and approximation problems arise in a variety of applications including data mining, engineering, meteorology, computer graphics, and scientific visualization. The basic problem, referred to as the functional scattered data problem, is to find a surface that interpolates or approximates a finite set of points in an m-dimensional space R. If the scattered data obtained is noisy, approximation is desirable. If the data obtained is exact or fairly accurate, interpolation is desired. This paper concerns the functional scattered data interpolation problem in high dimensions. Solutions to the scattered data interpolation problem are varied. Popular choices include subdivision methods, radial basis function (RBF) methods, Shepard’s techniques, multivariate adaptive regression splines (MARS), and non-uniform rational B-splines (NURBS). In spite of a large number of techniques available for scattered data interpolation, there is a need for developing new techniques and better understanding of existing algorithms. This situation obtains because there are serious gaps and shortcomings in many existing techniques. For example, NURBS is a very successful technique for gridded data, but it does not work on scattered data. Radial basis function methods cannot

Flutter of Partially Rigid Cantilevered Plates in Axial Flow

The introduction of adaptive materials for active camber line shape change makes adaptive wings more susceptible to non conventional instability phenomena. Motivated by a new wing concept for micro aerial vehicle applications the aeroelastic stability of partially rigid cantilevered plates in an axial ∞ow is investigated. The plate is modeled as a beam having a rigid and a ∞exible part. The beam is modeled using classical Euler Bernoulli bending theory, the unsteady aerodynamic pressure is modeled using Theodorsen’s theory and the Rayleigh Ritz method is used to obtain a discrete model. Stability analysis is carried out in Laplace’s domain. The results indicate that a partially cantilevered plate in an axial ∞ow does not show static aeroelastic divergence but exhibits dynamic aeroelastic instability. The ∞utter velocity at which this occurs is dependent on the mass ratio and on the ratio of the ∞exible length to the total length of the plate. At certain mass ratios, jumps in the ∞utter speed occur due to changes in ∞utter mode. The ∞exible length fraction has a signiflcant efiect on the ∞utter speed and the jump phenomena.

A Genetic Algorithm with Memory for Mixed Discrete-Continuous Design Optimization

This paper describes a new approach for reducing the number of the fitness function evaluations required by a genetic algorithm (GA) for optimization problems with mixed continuous and discrete design variables. The proposed additions to the GA make the search more effective and rapidly improve the fitness value from generation to generation. The additions involve memory as a function of both discrete and continuous design variables, multivariate approximation of the fitness function in terms of several continuous design variables, and localized search based on the multivariate approximation. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners.

Optimal Design of Composite Wing Structures with Blended Laminates

In this paper we formulate the problem of wingbox design optimization using composite laminates with blending constraints. The use of composite laminates necessitates the inclusion of fiber orientation angle of the layers as design variables in the design optimization problem. The wingbox design problem is decomposed into several independent local panel design problems. In general such an approach results in a nonblended solution with no continuity of laminate lay ups across the panels, which may not only increase the lay up cost but may also be structurally unsafe. The need for a blended solution increases the complexity of the problem many fold. In this paper we impose the blending constraints globally by using a guide based design methodology within the genetic algorithm optimization scheme and compare the results with the published ones. PTIMAL design of a fiber reinforced composite wing structure poses several problems due to the large design space of primarily discrete design variables. Composite structures are manufactured by stacking layers of fibers with different orientations bonded together via a curing process. Thus, the use of laminated composites entails fiber orientation angles as well as the number of layers of the laminates as design variables. Due to manufacturing constraints, the fiber orientation angles are usually limited to 0, ±45, and 90 degrees, and the thickness of the layers is kept constant. The number of layers and the laminate stacking sequence (ply orientation of each layer) are discrete design variables, while the wing structure dimensions and some of the subcomponent dimensions are continuous design variables. Design optimization problems with mixed integer variables, especially when there are a large number of discrete variables, are computationally expensive requiring a large number of analyses. In the case of a wing structure many of the response functions used in the design optimization require a complete analysis of the structure under the specified design loads. Full scale analysis of the wing structure is often performed numerically using detailed finite element models with a large number of degrees of freedom and is very expensive. When such analysis models are coupled with an optimizer, which necessitates repetitive analysis, the computational cost of the design optimization can become prohibitively expensive. In order to reduce the computational effort

Design of Variable Stiffness Composite Laminates For Maximum Bending Stiffness

Benefits of directional properties of fiber reinforced composites could be fully utilized by proper placement of the fibers in their optimal spatial orientations. This paper investigates an application of a Cellular Automata (CA) based strategy for design of variable stiffness composite laminates for optimal bending stiffness. CA are iterative numerical techniques that use local rules to update both field and design variables to satisfy equilibrium and optimality conditions. In the present study, displacement update rules are derived using a cell level model governing the equilibrium of the CA neighborhood. Local fiber orientation angles are treated as continuous design variables, and their spatial distribution is determined based on an optimality criterion formulation for minimum compliance design. Numerical examples for simply supported and clamped square plates are used to demonstrate the improvement in bending stiffness.