A series of computer codes are sought that would permit more accurate and efficient three-dimensional inelastic structural analysis of combustor liners, turbine blades, and turbine vanes. Each code embodies a progression of mathematical models for increasingly comprehensive representation of the geometrical features, loading conditions, and forms of nonlinear material response that distinguish these three groups of hot section components

Todd, E. S.

English

The objective of this program is to produce a series of new computer codes that permit more accurate and efficient three dimensional inelastic analysis of selected hot section components - combustor liners, turbine blades and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components

NASA Technical Reports Server

3-D INELASTIC ANALYSIS METHODS 
FOR HOT SECTION COMPONENTS (BASE PROGRAM) 
E. S. Todd 
P ra t  t & Whitney Engineering 
The o b j e c t i v e  of  t h i s  program i s  t o  produce a series of new computer codes t h a t  
permit  more a c c u r a t e  and e f f i c i e n t  three-dimensional  i n e l a s t i c  a n a l y s i s  of s e l e c t e d  
ho t  s e c t i o n  components - combustor' l i n e r s ,  t u r b i n e  b lades  and t u r b i n e  vanes. The 
computer codes embody a progress ion  of mathematical  models and a r e  s t reaml ined  t o  
t ake  advantage of  geomet r ica l  f e a t u r e s ,  load ing  cond i t i ons ,  and forms of m a t e r i a l  
response t h a t  d i s t i n g u i s h  each  group of  s e l e c t e d  components. 
Software i n  t h e  form of stand-alone codes and modules f o r  use i n  General Purpose 
S t r u c t u r a l  Analysis  (GPSA) programs w i l l  be provided by P r a t t  & Whitney A i r c r a f t  
(P&WA) w i t h  a s s i s t a n c e  from t h r e e  un ique ly  w e l l  q u a l i f i e d  subcon t r ac to r s  : MARC 
Analysis  Research Corporat ion (MARC), S t a t e  Univers i ty  of New York a t  Buffa lo  
(SUNY-B), and United Technologies Research Center  (UTRC). Primary development of 
s p e c i a l  f i n i t e  element models w i l l  be accomplished by MARC, whi le  mechanics of  
m a t e r i a l s  models and c o n s t i t u t i v e  formula t ions  w i l l  be assembled by UTRC. Development 
of advanced fo rmula t ion  (boundary e lement )  models w i l l  be  shared  by P&WA and SUNY-B. 
V e r i f i c a t i o n  of t h e  va r ious  a n a l y s i s  packages w i l l  be done by P&WA. 
The t e c h n i c a l  e f f o r t  of  t h i s  program w i l l  be conducted ove r  a pe r iod  of 
twenty-four (24 )  months and w i l l  involve  t h r e e  (3 )  d i s t i n c t  t a s k s :  
Task I - Linear  Theorv 
Under t h i s  t a s k  a l i n e a r  theory w i l l  be developed c o n s i s t i n g  of t h r e e  l i n e a r  
formula t ion  models: 1 )  mechanics of  m a t e r i a l s ,  2) s p e c i a l  f i n i t e  e lements ,  and 3) 
advanced fo rmula t ion  (boundary element)  models. The l i n e a r  theory  i s  def ined  t o  mean 
t h a t :  1 )  t h e  s t r e s s e s  o r  s t r a i n s  and tempera tures  i n  t h e  g e n e r i c  modeling reg ion  a r e  
l i n e a r  f u n c t i o n s  of t h e  s p a t i a l  coo rd ina t e s ,  znd 2) t h e  s o l u t i o n  increments  f o r  load ,  
temperature  and /o r  t ime a r e  e x t r a p o l a t e d  l i n e a r l y  from prev ious  in format ion .  The 
emphasis i n  t h e  l i n e a r  theory  f o r  three-dimensional i n e l a s t i c  a n a l y s i s  w i l l  be on a 
methodology u s i n g  a l a r g e  number of  g e n e r i c  modeling reg ions  and a l a r g e  number o f  
increments ,  bu t  s imple c a l c u l a t i o n s  p e r  increment.  
Task I1 - Polynomial Theory 
This  t a s k  w i l l  involve  t h e  development of a polynomial theory c o n s i s t i n g  of t h r e e  
polynomial fo rmula t ion  models: 1 )  mechanics o f  m a t e r i a l s ,  2) s p e c i a l  f i n i t e  e lements ,  
and 3) advanced fo rmula t ion  (boundary element)  models. The polynomial theory  i s  
def ined  t o  mean t h a t :  1 )  t h e  s t r e s s e s  o r  s t r a i n s  and tempera tures  i n  t h e  g e n e r i c  
modeling r eg ion  a r e  a t  l e a s t  quad ra t i c  f u n c t i o n s  of t he  s p a t i a l  coo rd ina t e s ,  and 2 )  
t h e  s o l u t i o n  increments  f o r  l o a d ,  t empera ture  and/or  t i m e  a r e  ex t r apo la t ed  a t  l e a s t  
q u a d r a t i c a l l y  from prev ious  information.  The emphasis i n  t h e  polynomial theory f o r  
three-dimensional i n e l a s t i c  a n a l y s i s  w i l l  be on a methodology us ing  a s m a l l e r  number 
of gene r i c  modeling r eg ions  w i t h  two i n t e r s e c t i n g  , embedded d i s c o n t i n u i t i e s  and a 
sma l l e r  number o f  increments ,  bu t  more complex c a l c u l a t i o n s  p e r  increment t han  f o r  
https://ntrs.nasa.gov/search.jsp?R=19860002050 2020-03-20T16:13:11+00:00Z
t h e  l i n e a r  theory (Task I). 
Task I11 - Reporting Requirements 
This  t a s k  inc ludes  pe r iod ic  t e c h n i c a l ,  f i n a n c i a l  and schedular  r epo r t ing  and, a t  
t h e  conclus ion  of t h e  t e c h n i c a l  e f f o r t ,  t h e  submi t t a l  o f  a f i n a l  Contractor  Report. 
Optional  Program 
An o p t i o n a l  program, t o  be exe rc i sed  a t  the  d i s c r e t i o n  of t he  Government, w i l l  
extend t h e  base computer codes t o  i nc lude  h igher  o r d e r  r ep re sen ta t ions  of s t r a i n  i n  
space and t ime and t o  d e a l  e f f e c t i v e l y  w i t h  more complex c o l l e c t i o n s  of 
d i s c o n t i n u i t i e s  such a s  coo l ing  ho le s  and c o a t i n g  c racks .  


The 3-D inelastic analysis methods for hot section components (base program)

N87-11208
3-D INELASTIC ANALYSIS METHODS
FOR HOT SECTION CO_,PONENTS (BASE PROGRAM)
E. S. Todd
United Technologies Corporation
Pratt & Whitney
The ohjective of this program is to produce a series of new computer codes that
permit more accurate and efficient three-dimensional inelastic structural analysis
of combustor liners, turhine blades, and turbine vanes. Each code embodies a pro-
gression of mathematical models for increasingly comprehensive representation of the
aeometrical features, loading conditions, and forms of nonlinear material response
that distinguish these three groups of hot section components.
Software in the form of stand-alone codes and modules for use in general purpose
structural analysis programs is being developed by Pratt & Whitney (P&W) with
assistance from three uniauely qualified subcontractors: MARC Analysis Research
Corporation (MARC), United Technologies Research Center (UTRC) and State University
of New York at Buffalo (SUNY-B). Special finite element models are being constructed
by MARC, while mechanics of materials models and constitutive models are heing
assembled hy UTRC. Development of advanced formulation (boundary element) models is
being shared by P&W and SUNY-B. Verification of the various analysis packages is
being done hy P&W.
The technical effort of the Inelastic Analysis Methods program is divided into
two 24-month segments: a base program, and an optional program to be exercised at
the discretion of the government. The first year (Task I) of the base program dealt
with linear theory in the sense that stresses or strains and temperatures in generic
modeling regions are linear functions of the spatial coordinates, and solution in-
crements for load, temperature and/or time are extrapolated linearly from previous
information. Three linear formulation computer codes, hereafter referred to as MOMM
(Mechanics of Materials Model), MHOST (MARC-HOST), and BEST (Boundary Element Stress
Technology), have been developed and delivered to Lewis Research Center.
Three increasingly sophisticated constitutive models are employed by MOMM, MHOST,
and BEST to account for inelastic material behavior (plasticity, creep) in the el-
evated temperature regime. The simplified model assumes a bilinear approximation of
stress-strain response and glosses over the complications associated with strain rate
effects, etc. The state-of-the-art model partitions time-independent (plasticity)
and time-dependent (creep) in the conventional way, invoking the Von Mises yield
criterion and standard (isotropic, kinematic, combined) hardening rules for the for-
mer, and a power law for the latter. Walker's viscoplasticity theory (ref. !), which
accounts for the interaction between creep/relaxation and plasticity that occurs un-
der cyclic loading conditions, has been adopted as the advanced constitutive model.
In brief, MOMM is a stiffness method finite element code that utilizes one-,
two- and three-dimensional arrays of beam elements to simulate hot section component
hehavior. Despite limitations of such beam model representations, the code will be
useful during early phases of component design as a fast, easy to use, corn,
putationally efficient tool. All of the structural analysis types (static, buckling,
vibration, dynamics), as well as the three constitutive models mentioned above, are
provided by MOMM. Capabilities of the code have been tested for a variety of simple
255
https://ntrs.nasa.gov/search.jsp?R=19870001775 2020-03-23T15:01:50+00:00Z
problem discretizations (ref. 2). Work is in progress to establish modeling guide-
lines for simulation of two- and three-dimensional behavior.
The PHOST code employs both shell and solid (brick) elements in a mixed method
framework to provide comprehensive capabilities for investigating local (stress/
strain) and global (vibration, buckling) behavior of hot section components. Over
the last decade, in order to support their commercially available software, the MARC
Corporation has accumulated a great deal of technical expertise creating new, im-
proved algorithms that will significantly reduce CPU (central processing unit) time
requirements for three-dimensional analyses. The MHOST code development has taken
aHvantage of this expertise. First generation (Task I)MHOST code is operational and
has been tested with a variety of academic as well as engine-related configurations
(ref. 2).
Successful assembly of the all new BEST code is possibly the most important ac-
complishment of the Task I effort. The challenge of extending basic theory and al-
gorithms to encompass inelastic dynamic effects in three-space was met by combining
the special skills and efforts of the research and programming teams at SUNY-B and
P?,W. As with MOMM and _IHOST, the initial version of BEST is executable and has been
exercised with both small and large test cases (ref. 2). While MHOST and BEST are
currently viewed as complementary, they are also competitors; and overall performance
on large inelastic models will be watched with interest as the codes mature.
Experimental data from the Benchmark Notch Test program (ref. 3) is being used
to verify the stress analysis capabilities of the Inelastic Methods codes. Nominal
dimensions of the benchmark notch specimen are shown in figure I. Finite element and
boundary element meshes for one-quarter of the specimen gage section are shown in
figure 2. Measured notch root stress-strain behavior for initial uploadings of sev-
eral specimens is summarized in figure 3. Correlation between the MHOST predictions
and the measured strains is very good (fig. 4). Hodest mesh refinement/optimization
in the vicinity of the notch (fiq. 2) is expected to bring the BEST calculations
into close agreement with the data.
The existing models will be extended to include higher-order representations of
deformations and loads in space and time to deal effectively with collections of
discontinuities such as cooling holes and cracks. This will be accomplished during
the second half of the hase program (Task II) and _the optional program (Tasks IV and
V). Work on Task II (polynomial theory) is under way and will be described at the
Fourth Annual HOST Workshop.
l •
.
.
REFERENCES
Walker, K. P.: Research and Development Program for Nonlinear Structural Modeling
With Advanced Time-Temperature Dependent Constitutive Relationships. NASA
CR-165._33, November 25, 1981.
Flilson, P,. B.; Bak, M. J.; Nakazawa, S.; and Banersee, P. K.: 3-D Inelastic
Analysis Method for Hot Section Components (Base Program): First Annual Status
Report. NASA CR-174700, February 1984.
Domas, P. A.; Sharpe, W. N.; Ward; M.; and Yau, J.: Benchmark Notch Test for Life
Prediction. NASA C_-165571, June 1982.
256
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Figure 1 Benchmark Notch Specimen
FINITE ELEMENT MODEL FINITE ELEMENT MODEL_
FINE MESH COARS_
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BOUNDARY ELEMENT MODEL
MIXED VARIATION
L - LINEAR
Q - QUADRATIC
Figure 2 Heshes Used in Benchmark Notch Analysis
257
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X - MHOST, FINE MESH
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CONCENTRATED MICROSTRAIN
Benchmark Motch - Calculated Vs. Measured Strains
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258


The 3-D inelastic analysis methods for hot section components (base program)

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