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Optimization of composite structures

Structural optimization is introduced and examples which illustrate potential problems associated with optimized structures are presented. Optimized structures may have very low load carrying ability for an off design condition. They tend to have multiple modes of failure occurring simultaneously and can, therefore, be sensitive to imperfections. Because composite materials provide more design variables than do metals, they allow for more refined tailoring and more extensive optimization. As a result, optimized composite structures can be especially susceptible to these problems. Previously announced in STAR as N83-10447

Stroud, W. J.

Optimizing Grain Boundary Structures with LAMMPS Using Evolutionary Algorithms

Grain boundary structure optimization is an important part of materials modeling. Current methods for grain boundary structure optimization involve inefficient, time-consuming processes that do not fully explore the interface parameter space. Evolutionary algorithms have recently been demonstrated to be effective at determining both stable and metastable grain boundary interface structures. In this work, we demonstrate the use of GBOpt, a grain boundary structure optimization software designed to use the Large-scale Atomic/Molecular Massively Parallel Simulation (LAMMPS) software to efficiently determine grain boundary structures. We demonstrate that a only a few manipulations, namely atom insertion, atom removal, and relative grain displacement, are sufficient to explore much of the grain boundary structure parameter space. The efficacy of this approach is demonstrated on an FCC Ni system, and a BCC Fe system. The computational cost is compared against the gamma-surface sampling approach to demonstrate performance improvement.

Evolutionary algorithms

Integrated structure-control optimization of space structures

In the past few years there has been substantial interest in the integrated design of large space structures and their vibration control systems. This paper overviews two aspects of integrated control-structure design. The first is the calculation of derivatives of control system stability margins with respect to structural parameters, and the effect of modal truncation on the accuracy of these derivatives. The second aspect is the various formulations used to define an integrated design optimization problem.

Haftka, Raphael T.

Deterministic Design Optimization of Structures in OpenMDAO Framework

Nonlinear programming algorithms play an important role in structural design optimization. Several such algorithms have been implemented in OpenMDAO framework developed at NASA Glenn Research Center (GRC). OpenMDAO is an open source engineering analysis framework, written in Python, for analyzing and solving Multi-Disciplinary Analysis and Optimization (MDAO) problems. It provides a number of solvers and optimizers, referred to as components and drivers, which users can leverage to build new tools and processes quickly and efficiently. Users may download, use, modify, and distribute the OpenMDAO software at no cost. This paper summarizes the process involved in analyzing and optimizing structural components by utilizing the framework s structural solvers and several gradient based optimizers along with a multi-objective genetic algorithm. For comparison purposes, the same structural components were analyzed and optimized using CometBoards, a NASA GRC developed code. The reliability and efficiency of the OpenMDAO framework was compared and reported in this report.

Coroneos, Rula M.

Deterministic Design Optimization of Structures in OpenMDAO Framework

Nonlinear programming algorithms play an important role in structural design optimization. Several such algorithms have been implemented in OpenMDAO framework developed at NASA Glenn Research Center (GRC). OpenMDAO is an open source engineering analysis framework, written in Python, for analyzing and solving Multi-Disciplinary Analysis and Optimization (MDAO) problems. It provides a number of solvers and optimizers, referred to as components and drivers, which users can leverage to build new tools and processes quickly and efficiently. Users may download, use, modify, and distribute the OpenMDAO software at no cost. This paper summarizes the process involved in analyzing and optimizing structural components by utilizing the framework s structural solvers and several gradient based optimizers along with a multi-objective genetic algorithm. For comparison purposes, the same structural components were analyzed and optimized using CometBoards, a NASA GRC developed code. The reliability and efficiency of the OpenMDAO framework was compared and reported in this report.

Coroneos, Rula M.

Dual structural-control optimization of large space structures

A new approach is proposed for solving dual structural-control optimization problems for high-order flexible space structures where reduced-order structural models are employed. For a given initial structural dessign, a quadratic control cost is minimized subject to a constant-mass constraint. The sensitivity of the optimal control cost with respect to the stuctural design variables is then determined and used to obtain successive structural redesigns using a contrained gradient optimization algorithm. This process is repeated until the constrained control cost sensitivity becomes negligible. A numerical example is presented which demonstrates that this new approach effectively addresses the problem of dual optimization for potentially very high-order structures.

Messac, A.

Design and testing of thermal-expansion-molded graphite-epoxy hat-stiffened sandwich panels

Minimum weight configurations for two types of graphite-epoxy hat-stiffened compression-loaded panels fabricated by the thermal-expansion-molding (TEM) manufacturing process were evaluated analytically and experimentally for designs with load index Nx/L values ranging from 100 to 800. The two types of panels contain graphite-epoxy face sheets with a foam core and hat stiffeners which are either open or filled with foam. Constraints on the extensional and shear stiffnesses are imposed on the design so that the panels will satisfy typical constraints for aircraft wing structures. Optimal structurally efficient TEM panels are compared to commercially available aluminum aircraft structures. Predicted load-strain relationships agree well with experimental results. Significant impact damage to the unstiffened face sheet and foam core does not noticeably reduce the load carrying ability of the panels, but damage to the stiffened face sheet reduces the failure load by 20 percent compared to unimpacted panels.

Jegley, Dawn C.

TPSAS-NF1676L-32708-DND

Proposed Effort under Advanced Air Transport Technology (AATT): - Select advanced Al alloy with formability and additive manufacturability, high combined strength and toughness - Fabricate single-piece Integrally Stiffened Cylinders (~10 ft. dia. x 10 ft. long) with longitudinal stiffeners - Demonstrate joining technology for assembly of two cylinders into 20-ft. long fuselage structure - Optimize structural design incorporating tailored, selective reinforcement for durability and damage tolerance - Build-up window, door and circumferential ring frames with large-scale additive manufacturing - Structural test to validate manufacturing demonstration, structural models and analysis

Taminger, Karen M

Implementation of efficient sensitivity analysis for optimization of large structures

The paper presents the theoretical bases and implementation techniques of sensitivity analyses for efficient structural optimization of large structures, based on finite element static and dynamic analysis methods. The sensitivity analyses have been implemented in conjunction with two methods for optimization, namely, the Mathematical Programming and Optimality Criteria methods. The paper discusses the implementation of the sensitivity analysis method into our in-house software package, AutoDesign.

Umaretiya, J. R.

Continuation methods in multiobjective optimization for combined structure control design

A homotopy approach involving multiobjective functions is developed to outline the methods that have evolved for the combined control-structure optimization of physical systems encountered in the technology of large space structures. A method to effect a timely consideration of the control performance prior to the finalization of the structural design involves integrating the control and structural design processes into a unified design methodology that combines the two optimization problems into a single formulation. This study uses the combined optimization problem as a family of weighted structural and control costs. Connections with vector optimizations are described; an analysis of the zero-set of required conditions is made, and a numerical example is given.

Milman, M.

Shape optimization and CAD

Structural optimization has attracted the attention since the days of Galileo. Olhoff and Taylor have produced an excellent overview of the classical research within this field. However, the interest in structural optimization has increased greatly during the last decade due to the advent of reliable general numerical analysis methods and the computer power necessary to use them efficiently. This has created the possibility of developing general numerical systems for shape optimization. Several authors, eg., Esping; Braibant & Fleury; Bennet & Botkin; Botkin, Yang, and Bennet; and Stanton have published practical and successful applications of general optimization systems. Ding and Homlein have produced extensive overviews of available systems. Furthermore, a number of commercial optimization systems based on well-established finite element codes have been introduced. Systems like ANSYS, IDEAS, OASIS, and NISAOPT are widely known examples. In parallel to this development, the technology of computer aided design (CAD) has gained a large influence on the design process of mechanical engineering. The CAD technology has already lived through a rapid development driven by the drastically growing capabilities of digital computers. However, the systems of today are still considered as being only the first generation of a long row of computer integrated manufacturing (CIM) systems. These systems to come will offer an integrated environment for design, analysis, and fabrication of products of almost any character. Thus, the CAD system could be regarded as simply a database for geometrical information equipped with a number of tools with the purpose of helping the user in the design process. Among these tools are facilities for structural analysis and optimization as well as present standard CAD features like drawing, modeling, and visualization tools. The state of the art of structural optimization is that a large amount of mathematical and mechanical techniques are available for the solution of single problems. By implementing collections of the available techniques into general software systems, operational environments for structural optimization have been created. The forthcoming years must bring solutions to the problem of integrating such systems into more general design environments. The result of this work should be CAD systems for rational design in which structural optimization is one important design tool among many others.

Rasmussen, John

Imparting Desired Attributes by Optimization in Structural Design

Commonly available optimization methods typically produce a single optimal design as a Constrained minimum of a particular objective function. However, in engineering design practice it is quite often important to explore as much of the design space as possible with respect to many attributes to find out what behaviors are possible and not possible within the initially adopted design concept. The paper shows that the very simple method of the sum of objectives is useful for such exploration. By geometrical argument it is demonstrated that if every weighting coefficient is allowed to change its magnitude and its sign then the method returns a set of designs that are all feasible, diverse in their attributes, and include the Pareto and non-Pareto solutions, at least for convex cases. Numerical examples in the paper include a case of an aircraft wing structural box with thousands of degrees of freedom and constraints, and over 100 design variables, whose attributes are structural mass, volume, displacement, and frequency. The method is inherently suitable for parallel, coarse-grained implementation that enables exploration of the design space in the elapsed time of a single structural optimization.

Sobieszczanski-Sobieski, Jaroslaw

On the optimization of discrete structures with aeroelastic constraints

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Mcintosh, S. C., Jr.

Application of artificial neural networks to the design optimization of aerospace structural components

The application of artificial neural networks to capture structural design expertise is demonstrated. The principal advantage of a trained neural network is that it requires trivial computational effort to produce an acceptable new design. For the class of problems addressed, the development of a conventional expert system would be extremely difficult. In the present effort, a structural optimization code with multiple nonlinear programming algorithms and an artificial neural network code NETS were used. A set of optimum designs for a ring and two aircraft wings for static and dynamic constraints were generated by using the optimization codes. The optimum design data were processed to obtain input and output pairs, which were used to develop a trained artificial neural network with the code NETS. Optimum designs for new design conditions were predicted by using the trained network. Neural net prediction of optimum designs was found to be satisfactory for most of the output design parameters. However, results from the present study indicate that caution must be exercised to ensure that all design variables are within selected error bounds.

Berke, Laszlo

Application of a two-point exponential approximation method in optimizing rotorcraft airframe structures

The Fadel (1990) two-point exponential approximation technique for rotorcraft airframe structural optimization is presently examined by comparing its results with the well established linear and hybrid first-order methods. Attention is given to both the elastic-line and FEM models of an AH-1G airframe. The Direct Matrix Abstraction Programming Language is used to compute sensitivity derivatives and motivate the CONMIN optimizer to produce the design change.

Sareen, Ashish K.

Variable Complexity Optimization of Composite Structures

The use of several levels of modeling in design has been dubbed variable complexity modeling. The work under the grant focused on developing variable complexity modeling strategies with emphasis on response surface techniques. Applications included design of plates with discontinuities subject to uncertainty in material properties and geometry, design of stiffened composite plates for improved damage tolerance, and the use of response surfaces for fitting weights obtained by structural optimization.

Haftka, Raphael T.