Document
General Disclaimer One or more of the Following Statements may affect this Document This document has been reproduced from the best copy furnished by the organizational source. It is being released in the interest of making available as much information as possible.
This document may contain data, which exceeds the sheet parameters. It was furnished in this condition by the organizational source and is the best copy available.
This document may contain tone-on-tone or color graphs, charts and/or pictures, which have been reproduced in black and white.
This document is paginated as submitted by the original source.
Portions of this document are not fully legible due to the historical nature of some of the material. However, it is the best reproduction available from the original submission.
Produced by the NASA Center for Aerospace Information (CASI) FINAL TECHNICAL REPORT November 1975 Grant NGR 52-012-008 Str'?!ztural Design -..
Wing Automated N76-22188 (NASA-CB-147142) AUTC?9ATED DING 5'T3UCTU.;AL n - DESIGI Final Technical report (T_echnio Unclas Israel Inst. of Tech.) 12 F HC 53.50 CSCI 01A 27711 63/05 Department of Aeronautical Engineering Technion - Israel Institute of Technology Haifa, Israel T4 C\17 Dr. Raphael T. Haftka Principal Investigator: Illinois) at Illinois Institute of Technology, Chicago, (how REPRO?i'C r i',.r?
h ABSTRACT { This report summarizes the work done under NASA grant t NGR 52-012 - 008, entitled Automated Wing Structural Design.
t The work was done during the period of December 1973 to i October 1975.
The main thrust of the effort under the grant is research on the optimization of wing structures under multiple constraint such as strength, displacement, buckling, flutter :^ and divergence limits. Advances were made in improving mathematical programming techniques as well as in improving the efficiency of constraint calculation. The WIDOWAC (Wing Design Optimization With Aeroelastic Constraints) computer program served as the main vehicle for this research.
However, as this program is a research program some effort irected to implement the methods developed in this was•c l This work in a general user oriented finite element program.
effort is expected to be pursued vigorously in the future.
h I INTRODUCTION Current techniques for automated structural design, such as the fully stressed design method, handle well the design for strength of stiff structures under mechanical loads.
For flexible wing structures such techniques often prove inadequate because of two reasons. First, the design of most wing structures is determined by other constraints such as static and dynamic aeroelastic constraints, control effectiveness constraints, and buckling constraints. Second, the external loads,on the wing often depend strongly on the thickness of the structural elements (aeroelastic ' and thermal loads) which ae commonly used';as design variables.
The need to tackle various-design constraints has resulted in design techniques which are suitable for specific constraints. Thus there are methods tailored for stress and displacement constraints, methods tailored for flutter constraint, ans so on. Mathematical programming methods, on the other hand, afford the generality that permits simultaneous design for a multitude of .constraints. The disadvantage of the mathematical programming approach is that it , requires a large number of analyses to be performed. New mathematical programming techni q ues which require a smaller number of analyses, and efficient methods of reanalysis•help overcome th3a disadvantage.
. `, „ Y A The work done under NASA grant NGR 52-012-008 was directed towards these twin goals of better mathematical programming techniques and more efficient structural analysis methods. The main vehicle for implementing the research effort was the WIDOWAC (Wing Design Optimization With Aeroelastic Constraints) computer program (Ref.l) developed by the principal investigator at NASA Langley Research Center during his stay there on an NRC associateship.
Since most of the results of the research pe'rformed under the grant are published as journal or conference papers this report is limited to a short* description of the work with appropriat-a references to the published papers.
_ , ^L g,^pLtc^nUC t I; Optimization Methods a. Mathematical Programuning -The,optimization method used for the WIDOWAC computer program was the Sequence of Unconstrained Minimization Technique (SLIMY) utilizing an interior penalty'function.
Newton's method with approximate second derivatives (Ref. 2) was used for each unconstrained minimization. Even though this optimization method is very efficient compared to other mathematica:. programming methods it was still costly enough to limit the capability of the program to 10-20 design variables. To improve the optimization method three steps were taken. These are described in.detail in Ref. 3 and summarized here.
1.1 Approximate techniques were used for avoiding a full scale analysis at every design point along a search direction.
2. Analytical derivatives of stresses, displacements W and buckling loads were used for saving time in computing search directions and as a basis for the approximate analysis.
3. To make it possible to use efficiently approximation concepts a new quadratic extended interior penalty WIDOWAC.
function was developed and implemented in The use of ar., extended penalty function.permits efficient recovery from excursions into the unfeasible design domain caused by the use of approximation techniques. The use of a quadratic extension for the I penalty function rather than the more common linear extension was mandated for compatibility with the second order Newton method.
The improved optimization procedure was implemented in a version of WIDOWAC that can handle stress, displacement, buckling and minimum gage constraints. The improved capability is reflected in some of the examples in Ref. 3 including a 147 design variables 201 degrees of freedom wing structure.
Optimality Criteria b.
Though the main thrust of the work under the grant ,t was on an optimization procedure based on mathematical a r `r programming methods, some work was done in the area of "x optimality criteria based algorithms. The research reported t in Ref, . 4 was partly funded by' the grant, and it involved a .comparison between mathematical programming and , optimality criteria based methods for wing design under flutter constraints.
An efficient resizing method was developed that is based on the optimality criteria for flutter constraints. When the ii r= only important constraint in the design is flutter the R algorithm developed should prove to be very useful. Ref. 4 is a conference paper, it was also accepted for publication Y s.
in the AIAA journal.
q ,.
r ^ { J ti { F RVROAL'C '.'.":Y OF THE R4' Y: ORIGINAL 11 Constraint Evaluation The goal of improved efficiency in the computation of displacements', stresses, flutter speed's and other constraints has been achieved through two measures. The first is improved method of analysis for each constraint and the second is use of approximation to the constraints during parts of the optimization cycle. This section summarizes these twin o techniques as applied to the individual constraints.
a. Flutter Constraints The first step in developing an efficient flutter analysis capability was to separate the parts of flutter analysis which depend only on the wing planform from the parts that depend on the structure of the wing. The former have to be done only once during the optimization process and'the latter repeated. One of the most important questions in this regard was the most efficient use of vibration modes for the structural representation. Specifically, how often should these modes be calculated. The major part of this work was done before the start of the grant and is documented in Ref. 5.
Additional work on this problem is included in a journal version of Ref. 5 accepted for publication in the Journal of Aircraft.
The problem of computational efficiency for the flutter analysis becomes more important because of the discontinuous nature of the flutter phenomenon. Ref. 2 documents an example of discontinuities of the flutter speed as a'function of ItF'r ! ` structural member thickness. The problem can be solved by monitoring during the optimization the entire V-g diagram rather than just the flutter point. This, however, is very costly. A major part on the effort under the grant, therefore, was the development of a technique to spot and follow the danger points on a V-g diagram. The technique, documented in Ref. 6, obviates the need to'monitor constantly the entire V-g diagram. Rather, only several such calculations are required F while most of the time only a few points on the diagram are monitored.
b. Static Aeroelastic Constraints The calculation of the displacement and stresses on a flexible wing is much more time consuming than such calculation !:y The .reason is the dependence of the loads }- for a rigid wing.
on the displacement.
under An efficient iterative procedure was developed the grant for displacement and stress calculation in wings This work is documented during symmetric pull-up maneuvers.
7, a payer submitted for publication to the Journal ' in`Ref.
c of Aircraft. The paper includes also the development of expressions for the derivatives of the displacements and a : demonstration of the efficiency of the method.
Other Constraints under the grant has also included other constraints Work However, this work has such as buckling and thermal loads, not been completed. It is expected that completion of that
c
part of the work would be followed by documentation in a journal paper or NASA publication in the next year.
F a; x ^ s f F.
F - f 'L } v
r
III. Program Implementation T" work described in the previous two sections.has been implemented in the WIDOWAC program ( Ref. 1). This program is a very useful test bed for optimization procedures and it also provides a reasonable design capability, especially for It is limited however optimization under flutter constraint s c by severe restriction on the generality of the finite element and aerodynamic models.
Recognizing the need to capitalize on the research r effort sponsored by the grant in a more general setting work has started on incorporating the WIDOWAC optimization procedures SPAR is a general finite element code in the SPAR program.
developed by Lockhead with'NASA funding. It combines generality a ^ with high efficiency which makes it an ideal candidate for design work. The effort under the grant was of a prelir.Li.nary' nature directed to assess the feasibility of tying the two programs together. The study of the SPAR program has led to the conclusi o n that, indeed, it is possible to combine it with WIDOWAC to produce a general and efficient design code.
A tE ACKNOWLEDGEMENTS The technical monitor for this grant was Dr. Jates N. Starnes # Jr. of NASA Langley Research Center.
Dr. Starnes participated in the research effort much beyond monitoring it. In effect, a significant part of the work was a cooperative effort of the principal investigator and Dr. Starnes. This is reflected in the authorship ^f several publications resulting from the effort funded by the. grant.
Dr. E. Carson Yates, Jr. and Dr. Sidney C. Dixon of NASA Langley Research Center also contributed to this work. The f principal investigator also gratefully acknowledges the use- ful suggestions, excellent editorial 'help and encouragement Dr.. W. Jefferson Stroud of NASA, Langley Research Center.
of L: REFERENCES Haftka, Raphael T. and Starnes, James .I., Jr. "WIDOWAC 1.
(Wing Design Optimization with Aeroelastic Constrained): Program Manual," TM-X-3071, 1974, NASA.
2. Haftka, Raphael T. "Automated Procedure for Design of Wing Structures to Satisfy Strength and Flutter Requirements," TN D-7264, NASA, 1973.
3. Haftka, Raphael. T. and Starnes, James 17. Jr. "Applications of a Quadratic Extended Interior Penalty Function for Structural Optimization", AIAA Paper No. 75-764, 1975.
4. Haftka, Raphael T., Starnes, James H. Jr., and Barton, Furman W. "A Comparison of Two Types of Structural Optimization Procedures for Satisfying Flutter Requirements, AIAA Paper 74-405, 1974 Haftka, Raphael T., and Yates, E. Carson, Jr. "On 5.
Repetitive Flutter Calculation in Structural Design", AIAA Paper 74-141, 1974.
6. Haftka, Raphael T. "Parametric Constraints with Application to`Optimization for Flutter Using a Continuous Flutter Constraint", AIAA J. Vol. 13, pp. 471-475, 1975.
7. Haftka, Raphael T. "Efficient Analysis of Flexible Wing Structures in Symmetric Maneuvers", (submitted for publication in the Journal of Aircraft).
1.