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NASA NTRS1972

Applications of the theory of optimal control of distributed-parameter systems to structural optimization

An extension of classical methods of optimal control theory for systems described by ordinary differential equations to distributed-parameter systems described by partial differential equations is presented. An application is given involving the minimum-mass design of a simply-supported shear plate with a fixed fundamental frequency of vibration. An optimal plate thickness distribution in analytical form is found. The case of a minimum-mass design of an elastic sandwich plate whose fundamental frequency of free vibration is fixed. Under the most general conditions, the optimization problem reduces to the solution of two simultaneous partial differential equations involving the optimal thickness distribution and the modal displacement. One equation is the uniform energy distribution expression which was found by Ashley and McIntosh for the optimal design of one-dimensional structures with frequency constraints, and by Prager and Taylor for various design criteria in one and two dimensions. The second equation requires dynamic equilibrium at the preassigned vibration frequency.

Armand, J. P.↗

NASA NTRS1990

Optimal placement of actuators and sensors in control augmented structural optimization

A control-augmented structural synthesis methodology is presented in which actuator and sensor placement is treated in terms of (0,1) variables. Structural member sizes and control variables are treated simultaneously as design variables. A multiobjective utopian approach is used to obtain a compromise solution for inherently conflicting objective functions such as strucutal mass control effort and number of actuators. Constraints are imposed on transient displacements, natural frequencies, actuator forces and dynamic stability as well as controllability and observability of the system. The combinatorial aspects of the mixed - (0,1) continuous variable design optimization problem are made tractable by combining approximation concepts with branch and bound techniques. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.

Sepulveda, A. E.↗

NASA NTRSDate not supplied

Aerostructural Weight Estimation for a Transonic Truss-Braced Wing using the Higher-fidelity Conceptual Design and Structural Optimization Tool

Continued development and enhancements of the Higher-fidelity Conceptual Design and structural optimization (HCDstruct) tool has been driven largely by advanced aircraft concepts of interest to NASA. While previous versions of HCDstruct were limited to hybrid wing body (HWB) and generalized tube and wing (TW) aircraft concepts, the latest version of HCDstruct supports the analysis of Truss-Braced Wing (TBW) aircraft concepts, where users can model both high and low wing configurations as well as strut and jury geometries parametrically. Additionally, new methods for modeling advanced composite materials within HCDstruct have been implemented. These recent tool enhancements were demonstrated for an independent assessment of the NASA/Boeing SUGAR Phase VI Mach 0.8 Transonic Truss-Braced Wing (TTBW) concept.

Zachary D. Windous↗

NASA NTRS1995

Structural Optimization Using the Newton Modified Barrier Method

The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program.

Khot, N. S.↗

NASA NTRS1987

Structural optimization of an alternate design for the space shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the shuttle solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in. diameter and 135 studs of 1 3/16 in. diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonliner displacement analysis. The minimum weight design has 135 studs of 1 3/16 in. diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, J.-F. M.↗

NASA NTRS1987

Structural optimization of an alternate design for the Space Shuttle solid rocket booster field joint

A structural optimization procedure is used to determine the shape of an alternate design for the Shuttle's solid rocket booster field joint. In contrast to the tang and clevis design of the existing joint, this alternate design consists of two flanges bolted together. Configurations with 150 studs of 1 1/8 in diameter and 135 studs of 1 3/16 in diameter are considered. Using a nonlinear programming procedure, the joint weight is minimized under constraints on either von Mises or maximum normal stresses, joint opening and geometry. The procedure solves the design problem by replacing it by a sequence of approximate (convex) subproblems; the pattern of contact between the joint halves is determined every few cycles by a nonlinear displacement analysis. The minimum weight design has 135 studs of 1 3/16 in diameter and is designed under constraints on normal stresses. It weighs 1144 lb per joint more than the current tang and clevis design.

Barthelemy, Jean-Francois M.↗

NASA NTRS1981

Distributing structural optimization software between a mainframe and a minicomputer

This paper describes a distributed software system for solving large-scale structural optimization problems. Distributing the software between a mainframe computer and a minicomputer takes advantage of some of the best features available on each computer. The described software system consists of a finite element structural analysis computer program, a general purpose optimizer program, and several small user-supplied problem dependent programs. Comparison with a similar system executing entirely on the mainframe computer reveals that the distributed system costs less, uses computer resources more efficiently and improves production through faster turnaround and improved user control. The system interfaces with interactive graphics software for generating models and displaying the intermediate and final results

Rogers, J. L., Jr.↗

NASA NTRS1993

Reliability-based structural optimization: A proposed analytical-experimental study

An analytical and experimental study for assessing the potential of reliability-based structural optimization is proposed and described. In the study, competing designs obtained by deterministic and reliability-based optimization are compared. The experimental portion of the study is practical because the structure selected is a modular, actively and passively controlled truss that consists of many identical members, and because the competing designs are compared in terms of their dynamic performance and are not destroyed if failure occurs. The analytical portion of this study is illustrated on a 10-bar truss example. In the illustrative example, it is shown that reliability-based optimization can yield a design that is superior to an alternative design obtained by deterministic optimization. These analytical results provide motivation for the proposed study, which is underway.

Stroud, W. Jefferson↗

NASA NTRS1986

New reflective symmetry design capability in the JPL-IDEAS Structure Optimization Program

The JPL-IDEAS antenna structure analysis and design optimization computer program was modified to process half structure models of symmetric structures subjected to arbitrary external static loads, synthesize the performance, and optimize the design of the full structure. Significant savings in computation time and cost (more than 50%) were achieved compared to the cost of full model computer runs. The addition of the new reflective symmetry analysis design capabilities to the IDEAS program allows processing of structure models whose size would otherwise prevent automated design optimization. The new program produced synthesized full model iterative design results identical to those of actual full model program executions at substantially reduced cost, time, and computer storage.

Strain, D.↗

NASA NTRS1990

Airframe structural optimization for maximum fatigue life

A methodology is outlined for optimization of airframe structures under dynamic constraints to maximize service life of specified fatigue-critical components. For practical airframe structures, this methodology describes the development of sensitivity analysis and computational procedures for constraints on the steady-state dynamic response displacements and stresses. Strain energy consideration is used for selection of structural members for modification. Development of a design model and its relation to an analysis model, as well as ways to reduce the dimensionality of the problem via approximation concepts, are described. This methodology is demonstrated using an elastic stick model for the MH-53J helicopter to show service life improvements of the hinge fold region.

D. P. Schrage↗

NASA NTRS2002

Structural Optimization of a Force Balance Using a Computational Experiment Design

This paper proposes a new approach to force balance structural optimization featuring a computational experiment design. Currently, this multi-dimensional design process requires the designer to perform a simplification by executing parameter studies on a small subset of design variables. This one-factor-at-a-time approach varies a single variable while holding all others at a constant level. Consequently, subtle interactions among the design variables, which can be exploited to achieve the design objectives, are undetected. The proposed method combines Modern Design of Experiments techniques to direct the exploration of the multi-dimensional design space, and a finite element analysis code to generate the experimental data. To efficiently search for an optimum combination of design variables and minimize the computational resources, a sequential design strategy was employed. Experimental results from the optimization of a non-traditional force balance measurement section are presented. An approach to overcome the unique problems associated with the simultaneous optimization of multiple response criteria is described. A quantitative single-point design procedure that reflects the designer's subjective impression of the relative importance of various design objectives, and a graphical multi-response optimization procedure that provides further insights into available tradeoffs among competing design objectives are illustrated. The proposed method enhances the intuition and experience of the designer by providing new perspectives on the relationships between the design variables and the competing design objectives providing a systematic foundation for advancements in structural design.

Parker, P. A.↗

NASA NTRS1992

Conditions for continuation of the efficient curve for multi-objective control-structure optimization

The paper describes the conditions for continuation of the efficient curve for bi-objective control-structure optimization of a ten-bar truss with two collocated sensors and actuators. The curve has been obtained with an active set algorithm using a homotopy method. The curve is discontinuous. A general stability theory has been implemented to determine sufficient conditions for the persistence of minima, and bifurcation theory has been used to characterize the possible points of discontinuity of the path.

Rakowska, Joanna↗

NASA NTRS2015

Targeted Structural Optimization with Additive Manufacturing of Metals

The recent advances in additive manufacturing (AM) of metals have now improved the state-of-the-art such that traditionally non-producible parts can be readily produced in a cost-effective way. Because of these advances in manufacturing technology, structural optimization techniques are well positioned to supplement and advance this new technology. The goal of this project is to develop a structural design, analysis, and optimization framework combined with AM to significantly light-weight the interior of metallic structures while maintaining the selected structural properties of the original solid. This is a new state-of-the-art capability to significantly reduce mass, while maintaining the structural integrity of the original design, something that can only be done with AM. In addition, this framework will couple the design, analysis, and fabrication process, meaning that what has been designed directly represents the produced part, thus closing the loop on the design cycle and removing human iteration between design and fabrication. This fundamental concept has applications from light-weighting launch vehicle components to in situ resource fabrication.

Burt, Adam↗

NASA NTRS1988

Structural optimization with aeroelastic constraints of rotor blades with straight and swept tips

This paper describes a study in which structural optimization techniques are used to minimize the n/rev vertical hub shears in forward flight, subject to aeroelastic stability constraints and frequency placement constraints. A special technique is used to build a sequence of approximate, inexpensive to solve optimization problems, the solutions of which converge to the solution of the exact, expensive to solve optimization problem. Blade configurations with both straight and swept tips, and single- and double-cell cross sections are analyzed. The results show that the approach used in this study is very efficient, and produces improved designs with a very small number of blade aeroelastic analyses.

Celi, R.↗

NASA NTRS1989

Recent experience in simultaneous control-structure optimization

To show the feasibility of simultaneous optimization as design procedure, low order problems were used in conjunction with simple control formulations. The numerical results indicate that simultaneous optimization is not only feasible, but also advantageous. Such advantages come at the expense of introducing complexities beyond those encountered in structure optimization alone, or control optimization alone. Examples include: larger design parameter space, optimization may combine continuous and combinatoric variables, and the combined objective function may be nonconvex. Future extensions to include large order problems, more complex objective functions and constraints, and more sophisticated control formulations will require further research to ensure that the additional complexities do not outweigh the advantages of simultaneous optimization. Some areas requiring more efficient tools than currently available include: multiobjective criteria and nonconvex optimization. Efficient techniques to deal with optimization over combinatoric and continuous variables, and with truncation issues for structure and control parameters of both the model space as well as the design space need to be developed.

Salama, M.↗

NASA NTRS1993

Stochastic search in structural optimization - Genetic algorithms and simulated annealing

An account is given of illustrative applications of genetic algorithms and simulated annealing methods in structural optimization. The advantages of such stochastic search methods over traditional mathematical programming strategies are emphasized; it is noted that these methods offer a significantly higher probability of locating the global optimum in a multimodal design space. Both genetic-search and simulated annealing can be effectively used in problems with a mix of continuous, discrete, and integer design variables.

Hajela, Prabhat↗

NASA NTRS1990

Accumulated approximation: A new method for structural optimization by iterative improvement

A new method for the solution of non-linear mathematical programming problems in the field of structural optimization is presented. It is an iterative scheme which for each iteration refines the approximation of objective and constraint functions by accumulating the function values of previously visited design points. The method has proven to be competitive for a number of well-known examples of which one is presented here. Furthermore because of the accumulation strategy, the method produces convergence even when the sensitivity analysis is inaccurate.

Rasmussen, John↗

NASA NTRS1989

First and second order convex approximation strategies in structural optimization

In this paper, various methods based on convex approximation schemes are discussed that have demonstrated strong potential for efficient solution of structural optimization problems. First, the convex linearization method (Conlin) is briefly described, as well as one of its recent generalizations, the method of moving asymptotes (MMA). Both Conlin and MMA can be interpreted as first-order convex approximation methods that attempt to estimate the curvature of the problem functions on the basis of semiempirical rules. Attention is next directed toward methods that use diagonal second derivatives in order to provide a sound basis for building up high-quality explicit approximations of the behavior constraints. In particular, it is shown how second-order information can be effectively used without demanding a prohibitive computational cost. Various first-order and second-order approaches are compared by applying them to simple problems that have a closed form solution.

Fleury, C.↗