Probabilistic Structural Analysis Methods for Space ... · tural analysis methodology for select Space Shuttle Main Engine (SSME) com- ponents. (1) composite load spectra, (2) probabilistic

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NASA Technical Memorandum 88861

Probabilistic Structural Analysis Methods for Space Propulsion System Components

I N A S A -TM-8886 1) ANALYSIS HE'IiJOCt2 FCB SPACE F I i C F G L 5 I O N SYSfIEEIi

C C f l F C h E N T S ( N E S A ) 25 F CSCL 46E

E &OB A E I L ISI I C S'I3 UCTUR AL N8 7- 1 37 54

U n c l a s G3/39 4 3 9 3 3

Christos C. Chamis Lewis Research Center Cleveland, Ohio

Prepared for the 3rd Space System Technology Conference sponsored by the American Institute of Aeronautics and Astronautics San Diego, California, June 9-12, 1986

https://ntrs.nasa.gov/search.jsp?R=19870004361 2020-01-06T13:14:06+00:00Z

PROBABILISTIC STRUCTURAL ANALYSIS METHODS FOR SPACE PROULSION

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SYSTEM COMPONENTS

Christos C. Chamis National Aeronautics and Space Administration

Lewi s Research Center Cleveland, Ohio 44135

SUMMARY

NASA Lewis Research Center is currently developing probabilistic struc-

This methodology consists of the following program elements: tural analysis methodology for select Space Shuttle Main Engine (SSME) components. (1) composite load spectra, (2) probabilistic structural analysis methods, (3) probabilistic finite element theory - new variational principles, and (4) probabilistic structural analysis application. The methodology has led to significant technical progress in several important aspects o f probabilistic structural analysis. The program and significant accomplishments to date are summarized in this paper.

INTRODUCTION

It is becoming increasingly evident that deterministic structural analysis methods will not be sufficient to properly design critical structural components for upgraded Space Shuttle Main Engines (SSME). Structural components in the SSME are subjected to a variety of complex, severe cyclic and transient loading conditions including high temperatures and high temperature gradients. Most o f these are quantifiable only as best engineering estimates. These complex loading conditions subject the material to coupled nonlinear behavior which depends on stress, temperature, and time. Coupled nonlinear material behavior is nonuniform, is very difficult to determine experimentally, and perhaps impossible to describe deterministically. In addition critical SSME structural components aye relatively small. Fabrication tolerances on these components, which in essence are small thickness variations, can have significant effects on the component structural response. Fabrication tolerances by their very nature are statistical. Furthermore the attachment of the components to the structural system generally differs by some indeterminant degree from that which was assumed for designing the component. In sumnary, all four fundamental aspects - (1) loading conditions, (2) material behavior, (3) geometric configuration, and (4) supports - on which structural analyses are based, are of a statistical nature. One direct way to formally account for all these statistical aspects i s to develop probabilistic structural analysjs methods where all participating variables are described by appropriate probabilistic functions.

NASA Lewis Research Center is currently developing probabilistic structural analysis methods for select SSME structural components. Briefly, the deterministic, three-dimensional, inelastic analysis methodology developed under the Hot Section Technology ((HOST) and R&T Base programs) is being augmented to accommodate the complex probabilistic loading spectra, the ther- moviscoplastic material behavior, and the material degradation associated with the environment of space propulsion system structural components representative

of the SSME, such as turbine blades, transfer duct, and liquid-oxygen posts (fig. 1).

The development of probabilistic structural analysis methodology consists of the following program elements: (1) composite load spectra, (2) probabilistic structural analysis methods, (3) probabilistic finite element theory - new variational principles, and (4) probabilistic structural analysis application. The development of the probabilistic structural analysis methodology is a joint effort of NASA Lewis in-house research, contracts, and grants. highlight significant accomplishments to date.

The objective of this paper is to describe briefly the program and to

PROGRAM DESCRIPTION/PARTICIPANTS

The major part of the program consists of two multiyear contracts. One contract (NASA contract NAS3-24382) is for the development of composite load spectra. The prime contractor is Rocketdyne, a division of Rockwell Interna- tional Corporation, with Battelle Columbus Laboratory, as a subcontractor. Rocketdyne is responsible for the overall program and integrated computer codes while Battelle is responsible for developing probabilistic models. The other contract (NASA contract NAS3-24389) is for the development of probabilistic structural analysis methods. The prime contractor is Southwest Research Institute with several subcontractors. The initial participants on this contract are: Southwest Research Institute - project management and solution strategies development; MARC Analysis Research Corporation - code development for probabilistic finite element methods; Rocketdyne Division, Rockwell Inter- national Corp. - Space Shuttle Main Engine (SSME) design and hardware exper- ience; Prof. Paul Wirsching (University of Arizona) - probabilistic and reliability methods; Prof. Gautam Dasgupta (Columbia University) - stochastic finite elements; and Prof. Satya Atluri (Georgia Tech) - advanced material constitutive models. The remaining part of the program consists of one grant (NAG 3-535) with Northwestern University and the in-house effort which is supported by support service contract personnel from Sverdrup Techn8logy Incor- porated under NASA contract NAS3-24105. The program is summarized in figure 2.

The research activities have led to significant technical progress In several important aspects of probabilistic structural analysis. Technical progress is reported in monthly reports and oral contract progress reviews. In addition, progress was reported at the Structural Integrity and Durability o f Reusable Space Propulsion Systems Conference held at NASA Lewis Research Center on June 4-5, 1985 (refs. 1 to 7). Furthermore, progress was reported i n the ASME Winter Annual Meeting In Miami, Florida, November 1985, where a whole session was devoted to this subject (refs. 8 to 12). The information presented in this paper summarizes progresses repotted in all these sources.

COMPOSITE LOAD SPECTRA

The main thrust of the composite load spectra (CLS) contractual effort is to develop generic probabilistic models for the various individual loads, their probable combinations for the select SSME components and attendant computer codes (refs. 2 and 3). The tasks of the contractural effort are summarlzed in figure 3. The type of available Information to aid in the development of the generic probabilistic models is summarized in table 1 for the high pressure

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fuel turbopumps (HPFTP) blade. Limited but typical measured data for compar- able information is shown in figure 4. The logic chart for analyzing and reducing test or flight measured data is shown in figure 5. The types of individual loads identified to date for four SSME components are sumnarized in table 2 where the source for obtaining data for these individual loads is also shown. tions at least nine individual load conditions.

As can be seen in this table each component is subjected to combina-

The generic probabilistic models for each of the individual loads consist of 4 parts: (1) a steady state load, (2) a periodic load, (3) a random load, and (4) a local spike. Each of thesa parts is formally described with a mean and a variance or a standard deviation. The shape of each part is determined using three different probabilistic distributions. Three probabilistic methods are also used for the phasing of these four parts into a single probabilistic load model. condition will be sufficient to realistically represent present and anticipated individual loading conditions. The shape of each of the four parts is described parametrically with undetermined coefficients. are selected by combinations of known data, computationally simulated data, and Information provided by experts.

It is believed at this time that the four parts for each load

These coefficients

The generic model for the time phasing (or combination) of the individual loads into the composite load spectra is also formulated using three probabilistic methods. The formulation Is based on combinations o f limited known/ anticipated data (of the type shown in fig. 4 for example), information esti- mated by experts, and largely on the probabilistic synthesis of probabilistically occurring events. The rationale for using various levels of progressive sophistication of probabilistic models for both the individual loads and the composite load spectra is to "balance" the uncertainties associated with the various estimates used in the formulations of these models. The models are then validated/adapted by using appropriate structural analyses, and assessing the resulting structural responses. The selection of the structural analyses to be used is obtained from point design information which is either known or computationally simulated by using expert opinions. Structural analyses of these types are also used to determine the reliability and the respective level o f confidence for the composite load spectra to be applied to a specific component.

There are four important considerations in the development of each model: ( 1 ) the ability o f the model to handle nonstandard distributional forms, (2) the treatment of nonstationary processes, (3) the handling of physical dependencies in the model, and (4) the ability of the method to operate effi- ciently so that it will be able to be included in an expert system computer code. The structure for each probabilistic generic model has a distribution fitting routine for the individual loads with a barrier crossing method,. Dis- crete Probability Distribution (DPD) method, and a Monte Carlo method for the combined and composite load models. stationary load processes into stationary processes is also included in the model so that the barrier crossing techniques can be used for a broader spec- trum of problems. function representing the frequency of the various load levels occurring, all forms of load shape curves can be handled including nominal (rectangular pulse), periodic, periodic over nominal, and random over nominal. The case of spike (transient) loads occurring i s handled with a simulation method, or, if

A transformation method for changing non-

Because these models are based on the probability density

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appropr ia te, the b a r r i e r c ross ing method. A t y p i c a l i n d i v i d u a l load record determined us ing t h i s approach I s shown i n f i g u r e 6.

EXPERT SYSTEM COMPUTER CODE

The in tegra ted computer code f o r t h e composite load spect ra i s an execu- t i v e l y d r i v e n modular sof tware system t h a t w i l l i ncorpora te t h e var ious i n d i v - i d u a l and composite load spect ra models. This code i s conf igured as an "exper t system". Modules i n t h i s code w i l l con ta in t h e var ious p r o b a b i l i s t i c models w i t h data dependent c o e f f i c i e n t s and/or func t ions and w i th the inc reas ing l e v e l s of soph is t i ca t i on w i th respect t o p r e d i c t i o n r e l i a b i l i t y and conf idence l e v e l . Associated w i t h these models a re gu ide l ines t o s e l e c t t he c o e f f i c i e n t s and func t ions i n t h e gener ic models t o achieve a s p e c i f i e d p r e d i c t i o n requ i re - ment. t o cons t ruc t spec i f i c load spectra, j u s t i f i e s embedding these models i n an i n teg ra ted software system conf igured as an exper t system t h a t can adv ise users i n the employment o f t h e gener ic load models.

Each subsequent vers ion w i l l add a new engine component, a d d i t i o n a l load types and more sophis- t i c a t i o n t o the p r o b a b i l i s t i c load d e f i n i t i o n and dec i s ion making process. The techn ica l core o f the f i n a l i n teg ra ted system w i l l be an i n t e r a c t i v e exper t system t h a t w i l l : (1) cons t ruc t s p e c i f i c load spectra models based on user suppl ied descr ip t ions o f the component and t h e load environment; (2 ) incorpo- r a t e the p r o b a b i l i s t i c models so as t o enable a d ia logue between the system and t h e user which w i l l he lp the user s e l e c t t he best model parameters f o r h i s problem; and ( 3 ) be ab le t o descr ibe the process o f cons t ruc t i ng a s p e c i f i c load spectra model, i n c l u d i n g dec is ions made by the exper t system and the r a t i o n a l e f o r those dec is ions. The key features o f t h e code a re summarized i n f i g u r e 7.

The p o t e n t i a l complexi ty and the exper t i se inherent i n gener ic models

The code i s being developed i n fou r incremental versions.

The expert system i s being conf igured so t h a t s p e c i f i c s imulated load spect ra models are b u i l t by accessing a knowledge base o f f a c t s and ru les . The knowledge base contains a module o f decision-making data ( f a c t s ) and a module o f ru les and dec is ion c r i t e r i a ( r u l e s ) f o r cons t ruc t i ng the load spect ra model. A l l numerical r e s u l t s needed t o cons t ruc t the s p e c i f i c load spectra model w i l l be computed o r r e t r i e v e d au tomat ica l l y by the exper t system. knowledge base and the in fe rence mechanisms needed t o search the knowledge base w i l l be developed as p a r t o f t h i s p r o j e c t . They w i l l be s t r o n g l y dependent upon the p r o b a b i l i s t i c gener ic load spectra models and engine component loading. A schematic o f the s t r u c t u r e o f the exper t system i s shown i n f i g u r e 8.

The

The expert system i s being const ructed t o e a s i l y accommodate add i t i ons and de le t i ons t o the knowledge base. This a l lows the exper t system t o "get smarter" and t o adapt t o new in fo rmat ion , bo th i n the t e s t and v a l i d a t i o n stage o f each code version and i n t h e expansion of t he exper t system t o incorpora te f u t u r e models i n the l a t e r versions o f the code. The exper t system i s i n t e r - a c t i v e t o a l low the system t o query and guide the user as t o the system opera- t i o n (e.g., required use r ' s i n p u t ) . The knowledge base and in fe rence mechanism i s being designed t o minimize redundant data requests f rom t h e system t o the user. The software system i s modular i n conformance w i t h modern p rog raming p rac t i ce . The source program i s w r i t t e n i n t h e FORTRAN language i n order t o assure a stand alone and p o r t a b l e code.

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PROBABILISTIC STRUCTURAL ANALYSIS METHODS (PSAM)

The focus o f t he PSAM cont rac tua l e f f o r t ( r e f s . 4, 5, and 9 t o 21) i s t o develop ana lys is methods and computer programs f o r p r e d i c t i n g t h e p r o b a b i l i s t i c response of c r i t i c a l s t r u c t u r a l components f o r c u r r e n t and f u t u r e space pro- pu l s ion systems. This methodology w i l l p l ay a c e n t r a l r o l e i n e s t a b l i s h i n g Increased system performance and d u r a b i l i t y . t he development o f a p r o b a b i l i s t i c f i n i t e element code f o r t h e p r o b a b i l l s t i c s t r u c t u r a l ana lys is o f t he se lec t SSME components. The computer code being developed i s NESSUS (Numerical Evaluat ion o f Stochast ic S t ruc tures Under St ress) . It i s based on the I n t e g r a t i o n o f e x i s t i n g technologies ( f i g . 9) .

The i n i t i a l a c t i v i t y o f PSAM i s

The development o f t he NESSUS code i s scheduled t o take 3 years. F i r s t year e f f o r t s i nvo l ve the fo rmula t ion o f t he p r o b a b i l i s t i c ana lys is s t ra tegy and the development o f a p r o b a b i l i s t i c l i n e a r ana lys is code. The u l t i m a t e goal o f t he 3-year program i s t he development o f a f i n l t e element code capable o f performing non l inear dynamic ana lys is o f s t ruc tu res having s tochas t ic m a t e r i a l p roper t ies , geometry, and boundary condi t ions and subjected t o random load ing ( f i g . 10).

Three l e v e l s o f s o p h i s t i c a t i o n are pursued f o r t h e s tochas t ic d e s c r i p t i o n o f the s t r u c t u r a l problem namely:

Level 1: Homogeneous random var iab le f o r s t i f f n e s s , mass, damping, and ex terna l load ing

Level 2: Stochast ic charac ter iza t ion o f var iab les a t t he element l eve l , w i t h spec i f i ed interelement c o r r e l a t i o n s

Level 3: Stochast ic i n t e r p o l a t i o n o f var iab les w i t h i n a f i n i t e element

Two a l t e r n a t i v e p r o b a b i l i s t i c analys is methods a r e being developed, a l l ow ing f o r a l l t h ree l e v e l s o f modeling soph is t i ca t l on . These t w o methods are:

(1 ) A p r o b a b i l i t y i n t e g r a t i o n method, p rov id ing a d i r e c t est imate o f the r e l l a b l l l t y o f the s t r u c t u r a l con f l gu ra t i on under study.

( 2 ) A s imu la t ion method, p rov id ing the means t o v e r i f y t he r e s u l t s obtained w i t h method 1.

The f i n i t e element l i b r a r y o f NESSUS i s shown i n f i g u r e 11 together w i t h the pe r tu rba t i on var iab les and the processors. NESSUS s ta tus i s b r i e f l y descr ibed below t o i l l u s t r a t e PSAM-type o f computa- t i o n a l s imulat ion. The problem chosen I s a curved s h e l l represent ing a.HPFTP blade. The f i n i t e element model f o r t h i s she l l -b lade cons is ts o f 48 b i l i n e a r s h e l l elements, 63 nodes, and 378' o f freedom. The s h e l l i s loaded w i t h random pressure and temperature f i e l d s . the sur face bu t a re s p a t i a l l y cor re la ted through an exponent ia l decay func t ion . Fo r pressure, the c o r r e l a t i o n was assumed st rong i n the spanwise and weak i n the chordwise d i rec t i ons . The opposite was assumed t r u e f o r the temperature f i e l d .

A dernonstratlon problem o f t he

These f i e l d s have a constant mean value over

The o ther random var iab les were she l l th ickness and s t i f f n e s s a t the base. The th ickness v a r i a b i l i t y could come from manufactur ing processes, w h i l e base

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stiffness variatlons may arise from normal assembly procedures. Proper definition of boundary conditions as reflected in the base stiffness may not be well defined and could be a major source of uncertainty in a structural analysis. This would be especially true for an eigenvalue analysis where natural frequency is the critical response variable.

Randomness was included in the elastic modulus and coefficient of thermal expansion of the material by assuming they were deterministic functions of temperature. assumed to be stochastic. The distributions, their means and coefficients of variation for the random variables, were not taken to represent a particular SSME material, structure, or operating environment. They were selected as being representative of what might be expected. variations for the base stiffness factor and the pressure reflect the greater uncertainty these random variables are expected to have in actual service. this analysis the only limitation on the choice of distributions is that the temperature and pressure fields were taken to be normal.

For the strength analysis, material yield strength was also

The higher coefficients of

For

The NESSUS code was executed for a number of preselected perturbations about the deterministic state. In this example, the deterministic solution was defined at the mean value of the random variables. solutions were obtained at i1.5 and 23.0 standard deviations of the 1 1 random variables required for the combined stress performance function (Von Mises criterion). The use of the modified Newton-Raphson iteration method allowed for efficient computation of the perturbed solutions without repeated reformu- lation and resolution of the matrix equations. Clearly the number of perturbations required to construct a performance function depend on the number, of random variables; consequently, for computational efficiency, only the significant variables should be retained in the analysis. The results obtained for excedence of Von Mises type stress are sumnarized in figure 12 (lower right) where the blade-shell finite element model, the NESSUS code flow chart and the input random variables are also shown.

A total of 40 perturbed

VARIATIONAL THEORY FOR PROBABILISTIC FINITE ELEMENTS

A small but Important part of the probabilistic structural analysis methodology is the development of variational principles for formulating probabilistic finite elements. This part is considered to be fundamental and is pursued under a grant (refs. 6 to 8) which focuses on embedding the probabilistic aspects i n a variational formulation. A variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures have been developed, they could easily be adapted to existing general purpose programs. The variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features i n many aspects of the structural problem: (1) displacements, (2) boundary conditions, (3) body forces resulting from acceleration loads and, (4) any other features that cannot be clearly established. For example, the well known dilemna as to whether a shell is clamped or simply- supported at a boundary, could also be treated more rationally by using a probabilistic distribution for this boundary condition. this research effort is summarized below.

Relevant progress of

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A methodology has been completed which can embed t h e p r o b a b i l i s t i c d i s t r i - b u t i o n of t h e c o n s t i t u t i v e p roper t i es and loads ( i .e. , m a t e r i a l u n c e r t a i n t i e s and load u n c e r t a i n t i e s ) w i th a f i n i t e element v a r i a t i o n a l approach. The corresponding p r o b a b i l i s t i c d i s t r i b u t i o n o f t he elemental nodal forces i s assembled i n t o a d e s c r i p t i o n o f t h e p r o b a b i l i s t i c d i s t r i b u t i o n o f t h e nodal fo rces f o r t h e complete model. t o these unce r ta in t i es i s then determined e f f i c i e n t l y . t h i s approach i s t o incorpora te the p r o b a b i l i s t i c d i s t r i b u t i o n s , as r e f l e c t e d i n the variance, o f t he ma te r ia l p roper t ies and the load ing cond i t ions t o ob ta in the corresponding variances i n the elemental nodal forces o f t h e f i n i t e element model. On t h e basts o f t h e variance i n the elemental nodal forces, t he var iance i n the f i n a l s o l u t i o n i s determined i n the usual d e t e r m i n i s t i c solu- t i o n procedures.

The appropr ia te mean s t r u c t u r a l response due The bas ic concept of

E f f i c i e n t numerical a lgor i thms were developed f o r ob ta in ing the probabi- l i s t i c s e n s i t i v i t y element matr ices which r e f l e c t t he e f f e c t s o f randomness on response var iab les such as displacements, stresses, e tc . The randomness i s due t o the preassigned p r o b a b i l i s t i c descr ip t ions o f t he m a t e r i a l p roper t i es and loads.

A p i l o t computer code was completed. So lu t ions obtained us ing t h i s code have been compared t o the Monte Car lo methods and the Hermite Gauss Quadrature i n t e g r a t i o n schemes. The cos t o f the new method i s s u b s t a n t i a l l y lower. This was demonstrated w i t h a ten-bar p r o b a b i l i s t i c non l inear system where the random va r iab les a re the y i e l d stresses. p r o b a b i l i s t i c ana lys is may o f f e r s i g n i f i c a n t savings and warrant f u r t h e r i n v e s t i g a t i o n . together w i t h some representa t ive resu l t s .

E x p l o i t a t i o n o f t h i s c h a r a c t e r i s t i c i n any

A f l o w c h a r t o f t he p i l o t computer code I s shown i n f i g u r e 13

PROBABILISTIC STRUCTURAL ANALYSIS OF SSME TURBOPUMP BLADES

A p r o b a b i l i s t i c study has been i n i t i a t e d in-house a t NASA Lewis Research Center ( r e f . 7 ) . The f i r s t o b j e c t i v e of t h i s study i s t o evaluate the geometric and ma te r ia l p roper t i es to lerances on the s t r u c t u r a l response o f turbopump blades. Dur ing t h i s study, a number o f impor tant p r o b a b i l i s t i c var- i a b l e s have been i d e n t i f i e d which are considered t o a f f e c t the s t r u c t u r a l response of the blade. I n add i t i on , a methodology has been developed t o s ta- t i s t i c a l l y quant i f y the i n f l uence o f these p r o b a b i l i s t i c var iab les i n an opt imized way. The i d e n t i f i e d var iab les inc lude random geometric and ma te r ia l p r o p e r t i e s per tu rba t ions , d i f f e r e n t loadings and a p r o b a b i l i s t i c combination of these loadings. In f luences o f these p r o b a b i l i s t i c var iab les are q u a n t i f i e d by eva lua t ing the blade s t r u c t u r a l response. The s t r u c t u r a l response var iab les i nc lude na tu ra l frequencies, maximum st ress a t the roo t , stage weight and t i p displacements. Geometric and mater ia l per tu rba t ions have been conducted f o r an SSME blade us ing a spec ia l purpose code based on f i n i t e element ana lys is . The geometric per tu rba t ions which s imulate the na tu ra l per tu rba t ions under opera t ing and/or f a b r i c a t i o n condi t ions, a re generated by randomly pe r tu rb ing the x, y, and z coordinates o f a l l the nodes o f t he f i n i t e element mesh. The m a t e r t a l per tu rba t ions were generated by randomly pe r tu rb ing the ma te r ia l pro- p e r t i e s o f a l l f i n i t e elements. These per tu rba t ions represent i n p a r t ma te r ia l v a r i a t i o n r e s u l t i n g from the f a b r i c a t i o n process, and/or any o ther l o c a l i r r e g u l a r i t i e s .

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Probabilistic models have been developed to predict the structural response by perturbating means and variances. abilistic models based only on the significant variances have also been developed. In addition, probability distributions for the structural response have been developed. These distributions provide an assessment of variation in the structural response for selected geometric and material properties perturbations. These provide an estimate of the probability of getting a certain response for a given input. Statistical tests and methods were used to check the developed models. tests indicated that the developed models are good fits. T-tests were used to identify the significant variances of perturbations. autocorrelations of residuals were used to check the goodness-of-fit tests.

Since means are not significant, prob-

Some representative results are shown in figure 14. These

F-tests, plots, and

SUMMARY

NASA Lewis Research Center is currently developing probabilistic structural analysis methods for select SSME structural components. Briefly, the development consists of the following program elements: (2) probabilistic structural analysis methods, (3) probabilistic finite element theory - new variational principles, and (4) probabilistic structural analysis application. The development of the probabilistic structural analysis methodology is a joint effort o f NASA Lewis In-house research, contract, and grants. The research activities have led to significant technical progress in several important aspects of probabilistic structural analysis. The significant technical accomplishments to date demonstrate that structural analyses can be formulated using probabilistic methods where all the participating structural- component-descriptor parameters and variables, and loading conditions are defined probabilistically. An early version of a structural analysis computer code (NESSUS) based on probabilistic finite elements has been completed and is currently used to analyze high pressure turbopump blades. Also the individual loads and composite load spectra can be probabilistically simulated using probabilistic methods with progressive levels o f sophistication, limited available data, expert opinion, and an expert system driven computer code.

(1) composite load spectra,

REFERENCES

1. Chamis, C.C., "Overview o f Structural Response: Probabilistic Structural Analysis," Structural Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381, 1985, pp. 63-66.

2 Newell, J . F . , "Composite Loads Spectra for Select Space Propulsion Structural Components," Structural Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381, 1985, pp. 67-75.

3. Kurth, R., "Composite Loads Spectra for Select Space Propulsion Structural Components: Probabilistic Load Model Development," Structural Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381, 1985, pp. 77-83.

4. Burnside, O . H . , "Probabilistic Structural Analysis Theory Development," - Structural Integrity and Durability of Reusable. Space Propulsion Systems, NASA CP-2381, 1985, pp. 85-92.

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5. Nagtegaal, J., 18Probabilistic Finite Element Development," Structural Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381, 1985, pp. 93-98.

6. Belytschko, T., and Liu, W.K., 'Probabilistic Finite Element: Variational Theory," Structural Integrity and Durability of Reusable Space Propulsion Systems, NASA CP-2381, 1985, pp. 99-107.

7. Nagpal, V.K., "Probabilistic Structural Analysis of SSME Turbopump Blades - Probabi 1 1 stic Geometry Effects, " Structural Intenri ty and Durabil it^ o f Reusable Space Propulsion Systems, NASA CP-2381, 1985, pp. 109-115.

8. Llu, W.K., Belytschko, T., and Mani, A . , "Probabilistic Finite Element for Transient Analysis in Nonlinear Continue," Advances In Aerospace Structural Analysis, edited by O.H. Burnside and C.H. Parr, ASME, New York, 1985, pp. 9-24.

9. Burnside, O.H., "Probabilistic Structural Analysis for Space Propulsion System Components." Advances in Aerospace Structural Analysis, edited by O.H. Burnside and C.H. Parr, ASME, New York, 1985, pp. 87-102.

10. Wirschlng, P.H., and Wu, Y.T. "Advanced Reliability Methods for Structural Evaluation," Advances In Aerospace Structural Analysis, edited by O.H. Burnside and C.H. Parr, ASME, New York, 1985, pp. 75-85.

11. Wu, Y.T., "Demonstration of a New, Fast Probability Integration Method for Reliability Analysis," Advances in AerosDace Structural Analysis, edtted by O.H. Burnside and C.H. Parr, ASHE, New York, 1985, pp. 63-73.

12. Dias, 3.8. and Nagtegaal, J.C., "Efficient Algorithms for Use In Probabilistic Finite Element Analysis," Advances In Aerospace Structural Analysis, edited by O.H. Burnslde and C.H. Parr, ASME, New York, 1985, pp. 37-50.

9

TABLE 1. - INDIVIDUAL LOAD SUMMARY

I n d i v i d u a l l oads

C e n t r i f u g a l

S t a t i c p ressu re and AP

Dynamic p ressu re

Temperature

D e b r i s

How determined

Measured

Pred ic ted f r o m t u r b i n e a n a l y s i s

P red ic ted f r o m t u r b i n e a n a l y s i s and cascade est imates o r t e s t s

P red ic ted f rom t u r b i n e p l u s thermal a n a l y s i s

Predicted, based on h i s t o r y o f i n c i d e n t s

Form a v a i l a b l e

Duty c y c l e and l i m i t s

Pressure p r o f i l e s a t s t reaml ines on a i r f o i l a

Pressure p r o f i l e sca led t o f o r c i n g f u n c t i o n shapea

Temperatures a t l o c a t i o n th roughou t b lade (computer ized da tase t ) a

P a r t i c l e s i z e and ve 1 oc i t y

Degree o f c e r t a i n t y

H igh

1

T o t a l magnitude h i g h ( t o r q u e ) d i s - t r i b u t i o n moderate

Moderate t o l ow

Steady s t a t e - h i g h t r a n s i e n t - l o w

Low

I n p u t t o s t r u c t u r a l a n a l y s i s as values, l i m i t cases o r d u t y c y c l e

I n p u t t o s t r u c t u r a l a n a l y s i s as l i m i t cases o r d u t y c y c l e

I n p u t t o f o r c e d v i b r a t i o n ana lys i s , Campbell d iagram l i m i t s

I n p u t t o s t r u c t u r a l a n a l y s i s

S e n s i t i v i t y a n a l y s i s o r i n c i d e n t i n v e s t i g a t i o n

aLow f requency and t r a n s i e n t

TABLE 2. - SUMMARY MATRIX OF INDIVIDUAL LOAD VERSUS COMPONENT

I n d i v i d u a l l o a d

S t a t i c pressure Dynamic p ressu re

S inus ida l

Random C e n t r i f u g a l Temperature S t r u c t u r a l v i b r a t i o n

T rans ien t

Chugging ( t r a n s i e n t ) Tubul ence

( repeated p u l s e )

S i del oad

Steady s t a t e Pops

Sine Random

D e b r i s Rubbing I n s t a l l a t i o n Fab F r i c t i o n Tolerances

Tu rb ine b lade

T rans fe r d u c t

X

X

X X

X -

X X

X X X - - X X X

Lox p o s t

X

-

-

- X

X -

X X

X X X

X X X X

-

HPOTP DD

How used

Load f o r m

Duty c y c l e a

AMs. s t a t o s

AMS. PSD. s t a t o s AMS. PSD. Duty c y c l e a Duty c y c l e a

AMs. s t a t o s AMs. s t a t o s

AMS. PSD. s t a t o s AMs. s t a t o s H i s t o r y Exper t o p i n i o n Exper t o p i n i o n

PSEUDO l o a d

aLow frequency and t r a n s i e n t

--./ -

S!3E POWERHEAD COMPONENT ARRANGEMENT,

HIGH PRESSURE TURBOPUMP LOX POSTS HA I N COMBUST ION CHAMBER BLADE

FIGURE 1. - PsAM WILL BE INIT IALLY DEVELOPED FOR SELECT S m E STRUCTURAL COMPONENTS.

s I- u W

v) a

W I-

-I- c w

I

0 p: Q v )

a

(I

E s B C

E L

a 2 : I-

t

v) L 2 t

L

I- U E:

2

9 E: d

x

-G L

I-

I

9 0 V I c.( I

L

I- Q 0

E:

L 0

Y 2 .....

z I- < E

2 k oz

L

W

I- CL 0 Q W CL

E

.. 2

3 Y v)

-

0

. s- , I

cv. * 9 09 c9 c

fI1 'Wdll 'No ' V I S d 'Sdd

m

? t

V W (0

ki - ?I- N

0

- in L

L O a - -I- v ) -

X B 8

T

' - I '

v,

B 3 1.72 a e t

1.71 = a

& 1.70 k F %

z PREDICTED

1.69 u Y

1.68 TIME

FIGURE 6. - HPFTP DISTANCE TEMPERATURE.

1. EXPERT SYSTEM 2. DATA ANALYSIS - STANDARD DISTRIBUTIONS AND DISCRETE DISTRIBUTIONS 3. PROBABILISTIC MODEL

0 INDIVIDUAL LOADS 0 COMPOSITE LOADS

4. INDIVIDUAL LOAD SHAPE SIMULATIONS 5. VARIOUS FORMS OF THE LOAD -

A. DUTY CYCLE 0 SLOWLY VARYING 0 RAPIDLY VARYING TRANSIENTS

B. SHOCK C. VIBRATION

0 STEADY STATE PSD. AMs SINUSOIDAL - PSD. ISOPLOT

0 TRANSIENT D. INFREQUENT LOADS

0 DEBRIS 0 RUBBING

6. GENERIC LOADS 0 DEFINITION 0 IMPLEMENTATION IN EXPERT SYSTEM 0 SCALING TECHNIQUES

7. VALIDATION AND VERIFICATION 8. ADDITIONAL COMPONENT.

0 TRANSFER DUCTS 0 LOX POST 0 4TH COMPONENT

FIGURE 7. - KEY TECHNICAL FEATURES OF COMPOSITE LOAD CODE.

COMPOSITE LOAD SPECTRA EXPERT SYSTEM

INPUT

LDEXPT DESIGN

LOAD EXPERT SYSTEM DESIGN PHILOSOPHY

USER SPEC IF lED

REQUIREMENT

J

ENHANCED IMPROVED

METHODS IURABIL ITY b ANALYSES - SPS

PSAM PROGRAM

. DRIVER (USER

INTERFACE NODULE)

EXPERT SYSTEM

COMPOS I TE

SPECTRA OUTPUT

0 RULE-BASE PRODUCTON SYSTEM

0 I F THEN RULES

0 S I R L E INFERENCE SCHEHE

0 INFERENCE NET (DECISION TREE)

0 SOPHISTICATED PROBABILISTIC RTHODS

0 DISCRETE PROBABILITY DISTRIBUTION

0 MONTE CARLO

0 BARRIER CROSSING

0 POWERFUL KNOWLEDGE BASE

0 INFLUENCE COEFFICIENT

0 SCALING COEFFICIENTS

0 DUTY CYCLE LOAD PROFILES

0

0

ENGINE CONFIGURATION AND GEOHETRY DATA

RAW ENGINE FLIGHT AND TEST DATA

FIGURE 8. - COMPOSITE LOAD SPECTRA SIMULATION USING EXPERT SYSTEMS.

HATER I AL MODELS

I SAVE

TECHNOLOGY

ART I F I C I AL INTELLIGENCE

STRUCTURAL

1 PROBABILIST I C

METHODS

FIGURE 9. - PsAM INTEGRATES E X I S T I N G TECHNOLOGIES.

STOCHASTIC r STOCHASTIC MATER I AL I THERMO- PROPERTIES 7 MECHANICAL

STRUCTURAL

CONCEPT OF PROBABILISTIC

STRUCTURAL ANALYSIS

;//' X KUNCERTAIN STRESS CONCENTRATION INPUT PDF

BOUNDARY CONDITIONS

(LOAD, MATERIAL. THE P R O W I L I ST I C STRUCTURAL GEMTRY, BOUNDARY

ANALYSIS PROBLEM CONDITIONS)

r 1. STRUCTURAL PARAMETERS - '\ ARE RANDOM BUT SPATIALLY \, HOMOGENEOUS

PARAMETERS ARE RANDOM

I AND SPATIAL 3. STRUCTURAL VARYING BUT

PARAMETERS ! CONSTANT OVER ARE RANDOM WITHIN A !

A FINITE ELEMENT

Y OUTPUT PDF

FINITE ELEMENT-I THREE LEVELS OF SOPHISTICATION FOR (DISPLACEMENT

PROBABILIST I C F I N I TE ELEMENT ANALYSIS STRAIN, STRESS)

FIGURE 10. - PROBABILISTIC STRUCTURAL ANALYSIS DEFINITION.

v)

5 Y v ) w

d m

v) L

I- 0

I-

El

I3

n I - v

n I

v

w

2 x U

E 2

Y 4

I- v)

n

v) v) W az I- v)

W a

n 4 n m

- n

- > 2 = : v

0 . .

TIP

1.15 I N .

1 .o

lo00 OF

100 PSI

180 KSI

PFEM E X W L E PROBLEM - CURVED SHELL

0.05 LOGNORMAL YES

0.20 EXTREK VALUE YES

0.05 NORML No

0.10 NORML NO

0.05 NORMAL YES

0 RESTART

VON MISES STRESS (NODE 1)

RANDOM VARIABLES FOR CURVED SHELL

E W L E PROBLEM

RANWn VARIABLE

BASE STIFFNESS

FACTOR

TEMPERATURE

PRESSURE

MATERIAL YIELD

I I I

DATA FLOW I N THE NESSUS SYSTEM

v NESSUS/FEM

RTURBATI DATABASE

FH-p OUTPUT NESSUS/FPI

VON MISES STRESS AT NODE 1

0 LINEAR - NORMAL

0 QUAD. - MIXED

1 .o Y 0 QUAD. - NORML 3 .8

w .6

W W

:: B E .4

!i .2 s 0

0 60 80 100 120 140 160 180

VOW MISES STRESS. KSI

FIGURE 12. - PROBABILISTIC F I N I T E ELEMENT STRESS ANALYSIS.

FIN ITE ELERNT SOLUTION OF

UNCERTAINTIES END ASSEMBLY EQUATIONS...

PHYSICAL PROBLEN

DISPLACERNT

E A N UPPER

.8

.6 I= ----- LOWER

f

BOUNDS AT NODE 1 (PFEN)

-----/-

/'

EQUATIONS

PROBABIL lST1 C F IN ITE ELERNT

, , ,REPEATED OVER SINULATION POINTS

MONTE CARLO i--l SINULATION (NCS)

QUADRATURE POINTS

HERNITE GAUSS QUADRATURE (HGQ)

STRESS BOUNDS I N ELEENT 1 (PFEN) 3Ox1O3 r

FIGURE 13. - VARIATIONAL APPROACH TO PROBABILISTIC FINITE ELEMENTS.

EASURED DATA N E W BLADES WITH TOOLING CHANGE

USED BLADES WITH v) 20

8 x 10

0 14 15 16 17 18 19 20

EQUIVALENT ALTERNATING STRESS, KSI

1

BLADE

E A N 3982.9

STANDARD DEVIATION

424.3

3000 3400 3800 4200 4600 x)o FIRST NATURAL FREQUENCY

MEAN 6922.6

STANDARD DEVI AT ION 1023.8

4000 d'l% 5000 6000 7000 8OOO 9OOO

SECOND NATURAL FREQUENCY

PROBABILISTIC MTER 1 AL EFFECTS PROBABILISTIC GEOPETRY EFFECTS

FIGURE 14. - PROBABILISTIC STRUCTURAL ANALYSIS CAN BE USED TO EXPLAIN Sm TURBOPUW BLADE FREOUENCY DISTRIBUTIONS.

1. Report No.

NASA TM-88861

Nat iona l Aeronautics and Space Admin is t ra t ion Washington, D.C. 20546

~ ~ ~

2. Government Accession No. 3. Recipient's Catalog No.

14. Sponsoring Agency Code c

4. Title and Subtitle

P r o b a b i l i s t i c S t ruc tu ra l Analys is Methods f o r Space Propuls ion System Components

7. Author(s)

Chr is tos C. Chamis

9. Performing Organization Name and Address

Nat iona l Aeronautics and Space Admin is t ra t ion Lewis Research Center Cleveland, Ohio 44135

12. Sponsoring Agency Name and Address

I 15. Supplementary Notes

Prepared f o r the 3rd Space Systems Technology Conference, sponsored by t h e American I n s t i t u t e o f Aeronautics and Ast ronaut ics , San Diego, C a l i f o r n i a , June 9-12, 1986.

5. Report Date

0. Performing Organization Code

533-1 3-00 8. Performing organization Report No.

E-301 5

IO. Work Unit No.

11. Contract or Grant No.

13. Type of Report and Period Covered

Technical Memorandum

16. Abstract

NASA Lewis Research Center i s c u r r e n t l y developing p r o b a b i l l s t l c s t r u c t u r a l ana lys is methodology f o r se lec t Space S h u t t l e Main Engine (SSME) components. This methodology consis ts o f t he f o l l o w i n g program elements: (1) composite load spectra, ( 2 ) p r o b a b i l i s t i c s t r u c t u r a l ana lys is methods, (3) p r o b a b i l i s t i c f i n i t e element theory - new v a r i a t i o n a l p r i n c i p l e s , and ( 4 ) p r o b a b i l i s t i c s t r u c t u r a l ana lys is app l i ca t ion . The methodology has l e d t o s i g n i f i c a n t t echn ica l progress i n severa l important aspects o f p r o b a b i l i s t i c s t r u c t u r a l ana lys is . The program and s i g n i f i c a n t accomplishments t o date a re summarized i n t h i s paper.

9. Security Classif. (of this report) Unc lass i f i ed

7. Key Words (Suggested by Author@))

Load conditions; Raterial properties; Boundary conditions; Geanetric configurations; Perturbations; Stat i s t i cal met hods ; Variational pr i nci p l es ; F i ni t e elements; Monte Carlo simulation

20. Security Classif. (of this page) 21. No. of pages 22. Price' Unc lass i f i ed

18. Distribution Statement

Unc lass i f i ed - un l im i ted STAR Category 39

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Documents

Probabilistic Structural Analysis Methods for Space ... · tural analysis methodology for select Space Shuttle Main Engine (SSME) com- ponents. (1) composite load spectra, (2) probabilistic