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This paper examines various first order approximation methods commonly used in structural optimization. It considers several attempts at improving the approximation by using previous analytical results and introduces an adaptation of a first order approximation method using an exponent adjusted to better fit the constraints and reduce the overall number of iterations needed to attain the optimum.
This report describes a structural optimization procedure developed for use with the Engineering Analysis Language (EAL) finite element analysis system. The procedure is written primarily in the EAL command language. Three external processors which are written in FORTRAN generate equivalent stiffnesses and evaluate stress and local buckling constraints for the sections. Several built-up structural sections were coded into the design procedures. These structural sections were selected for use in aircraft design, but are suitable for other applications. Sensitivity calculations use the semi-analytic method, and an extensive effort has been made to increase the execution speed and reduce the storage requirements. There is also an approximate sensitivity update method included which can significantly reduce computational time. The optimization is performed by an implementation of the MINOS V5.4 linear programming routine in a sequential liner programming procedure.
Mechanical property characterization tests of a directionally solidified Ni-20 percent Cb-2.5 percent Al-6 percent Cr cellular eutectic turbine blade alloy demonstrated excellent long time creep stability and indicated intermediate temperature transverse tensile ductility and shear strength to be somewhat low for turbine blade applications. Alloy and structural optimization significantly improves these off-axis properties with no loss of longitudinal creep strength or stability. The optimized alloy-structure combination is a carbon modified Ni-20.1 percent Cb-2.5 percent Al-6.0 percent Cr-0.06 percent C composition processed under conditions producing plane front solidification and a fully-lamellar microstructure. With current processing technology, this alloy exhibits a creep-rupture advantage of 39 C over the best available nickel base superalloy, directionally solidified MAR M200+ Hf. While improved by about 20 percent, shear strength of the optimized alloy remains well below typical superalloy values.
This paper outlines the development of methods for the combined control-structure optimization of physical systems encountered in the technology of large space structures. The objectives of the approach taken in this paper is not to produce the 'best' optimized design, but rather to efficiently produce a family of design options so as to assist in early trade studies, typically before hard design constraints are imposed. The philosophy is that these are candidate designs to be passed on for further considerations, and their function is more to guide the development of the system design rather than to represent the ultimate product. A homotopy approach involving multi-objective functions is developed for this purpose. Analytical and numerical examples are also presented.
This paper addresses the application of a formal optimization technique in rotorcraft airframe structural design studies to reduce the structural weight, to lower airframe vibrations, and to enhance fatigue life of the structure. Vibration and fatigue considerations in airframe design are described. An optimization methodology based on the use of a nonlinear programming technique to size airframe structural members subjected to constraints on weight, vibration response and fatigue stresses under dynamic loads, are described. The paper focuses on the development of necessary computational tools for airframe structural optimization and describes the sensitivity analysis procedure for these types of design constraints. Further, the paper describes the optimization procedure as implemented in a computer code called DYNOPT which is a unique operational combination of several newly developed Fortran codes as well as modification of existing codes consisting of the direct matrix abstraction modules of the MSC/NASTRAN Program and CONMIN optimizer. The application of the optimization procedure is demonstrated using an elastic-line model of the Bell AH-1G helicopter airframe structure and computational results are discussed.
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.
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.
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.
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.
We present a new algorithmic paradigm for the decentralized solution of graph-structured optimization problems that arise in the estimation and control of network systems. A key and novel design concept of the proposed approach is that it uses overlapping subdomains to promote and accelerate convergence. We show that the algorithm converges if the size of the overlap is sufficiently large and that the convergence rate improves exponentially with the size of the overlap. The proposed approach provides a bridge between fully decentralized and centralized architectures and is flexible in that it enables the implementation of asynchronous schemes, handling of constraints, and balancing of computing, communication, and data privacy needs. The proposed scheme is tested in an estimation problem for a 9241-node power network and we show that it outperforms the alternating direction method of multipliers.
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.
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.
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
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.
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.
Reversible protonic ceramic electrochemical cells (R-PCECs) have emerged as a novel technology for clean and efficient energy generation and storage. Improving the oxygen and proton conduction characteristics and stability of air electrodes at intermediate temperatures is crucial for achieving a high performance. Herein, we optimize the electronic structure of a state-of-the-art PrBa 0.8 Ca 0.2 Co 2 O 5+δ (PBCC) air electrode via doping IIIA cations (Al 3+ , Ga 3+ , and In 3+ ). Also, it is shown that PrBa 0.8 Ca 0.2 Co 1.9 Ga 0.10 O 5+δ (PBCCGa 0.10 ) exhibits improved oxygen reaction activity and hydration capability. Density functional theory calculations confirm that Ga doping provides the most favorable electronic structure. An R-PCEC with PBCCGa 0.10 achieves a peak power density of 2.21 W cm -2 and a current density of −4.64 A cm -2 at 1.3 V at 650 °C. Additionally, the PBCCGa 0.10 electrode performs good operational stability in FC mode (for about 100 h), EC mode (for about 100 h), and reversible cyclic testing (over 200 h) at 600 °C.
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.
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.