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

A Genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint Approximations

This paper describes a new approach for reducing the number of the fitness and constraint 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, and multivariate approximation of the individual functions' responses in terms of several continuous design variables. The approximation is demonstrated for the minimum weight design of a composite cylindrical shell with grid stiffeners

Acoustic scattering of broadband echolocation signals from prey of Blainville's beaked whales : modeling and analysis

Submitted in partial fulfillment of the requirements for the degree of Master of Science at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2006Blainville's beaked whales (Mesoplodon densirostris) use broadband, ultrasonic echolocation signals (27 to 57 kHz) to search for, localize, and approach prey that generally consist of mid-water and deep-water fishes and squid. Although it is well known that the spectral characteristics of broadband echoes from marine organisms are a strong function of size, shape, orientation and anatomical group, little is known as to whether or not these or other toothed whales use spectral cues in discriminating between prey and non-prey. In order to study the prey-classification process, a stereo acoustic tag was mounted on a Blainville's beaked whale so that emitted clicks and corresponding echoes from prey could be recorded. A comparison of echoes from prey selected by the whale and those from randomly chosen scatterers suggests that the whale may have, indeed, discriminated between echoes using spectral features and target strengths. Specifically, the whale appears to have favored prey with one or more deep nulls in the echo spectra as well as ones with higher target strength. A three-dimensional, acoustic scattering model is also developed to simulate broadband scattering from squid, a likely prey of the beaked whale. This model applies the distorted wave Born approximation (DWBA) to a weakly-scattering, inhomogeneous body using a combined ray trace and volume integration approach. Scatterer features are represented with volume elements that are small (less than 1/12th of the wavelength) for the frequency range of interest (0 to 120 kHz). Ranges of validity with respect to material properties and numerical considerations are explored using benchmark computations with simpler geometries such as fluid-filled spherical and cylindrical fluid shells. Modeling predictions are compared with published data from live, freely swimming squid. These results, as well as previously published studies, are used in the analysis of the echo spectra of the whale's ensonified targets

Efficient Design Optimization Methodology for Manufacturable Variable Stiffness Laminated Composite Structures

Because of their superior mechanical and environmental properties compared to traditional metals, fiber-reinforced composite materials have earned a widespread acceptance for different structural applications. The tailoring potential of composites to achieve high specific stiffness and strength has promoted them as promising candidates for constructing lightweight structures. From that aspect, designers have tackled the problem of designing composite laminates, which is inherently challenging due to the presence of non-linear, non-convex, and multi-dimensional optimization problems with discrete and continuous design variables. However, despite their increased usage, the possible improvements that can be achieved by composite laminates have not been fully exploited. With the introduction of new manufacturing technologies such as advanced fiber placement, engineers now have the capability to harness the full potential of nonconventional variable stiffness composite laminates using in-plane fiber steering. This can be a blessing as well as a curse for the designer, where the additional improvements can be attained at the expense of an increased complexity of the design problem. To circumvent this difficulty, this research aims to develop appropriate design tools to help unlock the advancements achieved by nonconventional variable stiffness laminates. The purpose is to adopt an efficient design optimization methodology to abandon the traditional usage of straight fiber composite laminates in the favor of exploring the structural improvements that can be achieved by steered laminated composite structures, subject to manufacturing constraints and industry design guidelines. This represents a remarkable step in the development of energy-efficient light-weight structures and in their certification. The complexity of the optimization problem imposes the need for an efficient multi-level optimization approach to achieve a global optimum design. In this work, the importance of including a design-manufacturing mesh is demonstrated in each optimization step of the multi-level optimization framework. In the first step (Stiffness Optimization), a theoretical optimum stiffness distribution parameterized in terms of lamination parameters is achieved that accounts for optimum structural performance while maintaining smoothness and robustness. The design-manufacturing mesh allows the spatial stiffness distribution to be expressed as a B-spline or NURBS surface defined by the control points of the design-manufacturing mesh. The fiber angle distribution is then obtained in the second optimization step (Stacking Sequence Retrieval) to match the optimum stiffness properties from the first optimization step while accounting for the maximum steering constraint and laminate design guidelines to attain manufacturability and feasibility. A bilinear sine angle variation is presented to obtain smooth fiber angle distributions, and the maximum steering constraint is derived to guarantee a certain degree of manufacturability at the second optimization step. Using the design-manufacturing mesh, a constant curvature arc solution is developed in the third optimization step (Fiber Path Construction) to generate manufacturable fiber paths with piecewise constant curvature arcs that match the optimal fiber orientation angles from the second optimization step while locally satisfying the maximum curvature constraint. To minimize gaps and overlaps obtained due to fiber steering, a design-for-manufacturing tool is developed to generate tow-by-tow descriptions of the steered plies in the form of manufacturing boundaries for the AFP machine with optimized cut and restart positions. The design of cylindrical shells under bending with a specified cutout is chosen as an aerospace application to demonstrate the effectiveness of using nonconventional variable stiffness laminates compared to traditional conventional laminates. The presence of the cutout in the cylindrical shell imposes severe stress concentrations yielding a need to use variable stiffness laminates that have continuously varying fiber orientation angles to redistribute the stresses and obtain a structurally optimal design. A design-manufacturing mesh was introduced to perform the buckling load optimization, where both circumferential and longitudinal stiffness variations were considered to physically understand the importance of the stiffness tailoring mechanism in efficient load redistribution and local reinforcements around the regions of the cutouts. The multi-level optimization framework is utilized to obtain a manufacturable fiber-steered laminate that improves the buckling load significantly. The design-for-manufacturing tool developed then generates the tow-level information in the form of exported AFP boundaries. The designed cylindrical shell is imported into CATIA V5® for composite design programming to demonstrate the applicability of the design-for-manufacturing tool developed

Structural optimization of thin shells using finite element method

The objective of the present work was the structural optimization of thin shell structures that are subjected to stress and displacement constraints. In order to accomplish this, the structural optimization computer program DESAP1 was modified and improved. In the static analysis part of the DESAP1 computer program the torsional spring elements, which are used to analyze thin, shallow shell structures, were eliminated by modifying the membrane stiffness matrix of the triangular elements in the local coordinate system and adding a fictitious rotational stiffness matrix. This simplified the DESAP1 program input, improved the accuracy of the analysis, and saved computation time. In the optimization part of the DESAP1 program the stress ratio formula, which redesigns the thickness of each finite element of the structure, was solved by an analytical method. This scheme replaced the iterative solution that was previously used in the DESAP1 program, thus increasing the accuracy and speed of the design. The modified program was used to design a thin, cylindrical shell structure with optimum weight, and the results are reported in this paper

The Number of Cylindrical Shells

Given a set P of n points in three dimensions, a cylindrical shell or zone cylinder is formed by two cylindrical cylinders with the same axis such that all points of P are between the two cylinders. We prove that the number of cylindrical shells enclosing P passing through combinatorially different subsets of P has size Omega(n^3) and O(n^4) (previous known bound was O(n^5) )