COMPUTATIONAL SIMULATION OF
NONLINEAR STRUCTURES
Proposal to National Science Foundation - NSF97-120
Submitted September 8, 1997
Avi Singhal, Julia Muccino and Han Zhu
Department of Civil Engineering
College of Engineering & Applied Sciences
Arizona State University
Tempe, Arizona 85287-5306
e-mail: avi.singhal@asu.edu
PROPOSAL SUBMITTED TO
NATIONAL SCIENCE FOUNDATION
1.
Name and address of Institution: Office of Research and Creative Activities
Arizona State Universtiy
Box 871603
Tempe, AZ 85287-1603
2.
Type of Organization: Educational
3.
Title: Computational Simulation of Nonlinear Structures
4.
This proposal is submitted pursuant to the NSF Guide to Programs, NSF97-120
5.
Funding requested from NSF: Year 1-$117,614; Year 2-$124,016; Year 3-$41,995:
TOTAL -$283,625.
6.
Duration of effort: 10/1/97-3/31/2000 (Two and a half years)
7.
Principal Investigator: Dr. Avi Singhal
Co-Principal Investigators: Dr. Julia Muccino, and Dr. Han Zhu
Department: Civil Engineering
Area Code/Phone #: (602)965-6901 Fax #: (602)897-0167
8.
Business Personnel:
Ms. Lori Gabriel
Sponsored Projects Officer
Office of Research and Creative Activities
Arizona State University
Box 871603
Tempe, Arizona 85287-1603
9.
Authorized University Official
___________________________
Date of Submission: 9.8.97
Janice D. Bennett, Director
Office of Research and Creative Activities
2
COMPUTATIONAL SIMULATION OF NONLINEAR STRUCTURES
SUMMARY SHEET
Principal Investigators:
Dr. Avi Singhal, P.E., Professor
Department of Civil Engineering
Tel: (602) 965-6901
Fax: (602) 727-6192
Email: avi.singhal@asu.edu
Co-Principal Investigator:
Dr. Julia Muccino, Assistant Professor
Tel: (602) 965-0598
Co-Principal Investigator:
Dr. Han Zhu, Assistant Professor
Tel: (602) 965-2645
Administrative Officer:
Ms. Lori Gabriel
Sponsored Project Officer
Office of Sponsored Projects
Tel: (602) 727-6527
Fax: (602) 965-0649
Proposed Period:
10/1/97 - 3/31/00
Type of Award:
Grant
(No Profit)
3
PROJECT SUMMARY
MODELING AND SIMULATION OF NONLINEAR STRUCTURES
The focus area of this research is to improve and expand fundamental computational mechanics knowledge
in the areas of nonlinear, large deformation behavior of structures subjected to quasi-static and dynamic loadings.
The shift from test base to simulation base design environment requires accurate, robust, and efficient computer
codes, which model large displacements and length and time-scale mechanics. For challenging engineering
simulation problems, this research employs advanced concepts in solid mechanics by using new fundamental
equations for structures undergoing nonlinear large displacement. Effects of large displacement, and large rotations
are included in the compatibility equations. New algorithms will be developed which will be robust, reliable,
efficient and scalable on parallel computing platforms. The results from this analysis will be compared with actual
data already obtained from the experiments. Such a comparison will validate and otherwise support the
development of above computational technology.
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TABLE OF CONTENTS
Page
6
PROJECT SUMMARY
TABLE OF CONTENTS
7
PROJECT DESCRIPTION
8
PRESENT METHODS
9
ACCURACY OF MULTI VALUE METHODS
10
DEFICIENCIES IN PRESENT COMPUTATION CAPABILITY
10
PROPOSED OBJECTIVES
10
SCIENTIFIC APPROACH
11
PROPOSED TASKS
13
BIBLIOGRAPHY
14
FACILITIES AVAILABLE
15
PRINCIPAL INVESTIGATOR AND STAFF
15
MANAGEMENT PLAN
16
TIME SCHEDULE
16
BIOGRAPHICAL SKETCH
17
BUDGET
21
AUTHORIZATION FOR SANDIA LAB
24
5
COMPUTATIONAL SIMULATION OF NONLINEAR STRUCTURES
PROJECT DESCRIPTION
The proposal deals with the simulation of nonlinear structures. Cable structures are taken as an example
case. Cable structures are load adaptive where these structures make a large change in the geometry with the
application of loads rather than a large change in stress. Their geometrical shape changes nonlinearly regardless of
the elastic and linear properties of material and linearity of load with time. The principle of linear superpositions are
not valid because cable structures are flexible and undergo large displacements. Although the cable length may not
change much, there may be large rotation and translation due to the applied loads. Cable dynamics is an
indeterminate problem, which depends upon the shape related to pre-stressing. Kinematics and constitutive
equations are needed to solve the statically indeterminate quasi-static cable problem. Research efforts related to this
proposal include: 1) Hierarchical finite element refinement for the analysis of aerospace structures, 2) Modal
synthesis methods for analysis of large vibrating systems, and 3) Adaptive decomposition method for structural
acoustics modeling. All three research efforts are evolutionary in nature.
There are several physical characteristics of cable systems which can develop extremely nonlinear
relationships in the structural analysis equations (Webster, 1975). These nonlinearities can be classified in seven
categories 1.) Geometric Nonlinearity - Cable systems do not have initial rigidity or spatial stability unless preloads
are imposed, 2.) Position-Dependent Loading - Loads depend heavily on the orientation and position of each
structural element. This is particularly true of fluid-induced loads such as added mass and buoyancy, 3.)
State-Dependent Loading - Fluid-induced loads are nonlinear with respect to the state variables. For example,
fluid-induced drag and associated damping depend on the square of the relative velocity between the structure and
the fluid, 4.) Position-Dependent Constraints - Structural elements may interact with rigid or semi-rigid boundaries
such as the seafloor, 5.) Nonlinear Materials - Constitutive relationships between stress, strain, and strain rate can
be nonlinear in nature for most marine cables particularly synthetic cables, 6.) Physical changes in the Structure The cable structure itself may change. For example, a line may go slack or a line may be paid out from a reel
onboard a ship. 7.) External Structure Interaction - Ships, buoys, underwater vessels, and other relatively rigid
bodies usually interact in a nonlinear fashion with cable systems.
Cable structures can be classified as either terrestrial or marine. Although they possess different loading
environments, the load adaptive nature of these structures is what primarily controls their structural response to these
loads. Unlike the typical terrestrial structure, marine structures are often dominated through necessity by cables,
and thus a fair amount of effort in the marine analysis community has been directed towards improving our capability
to analyze these nonlinear structures. However, too often complex cable analyses fail to converge to a solution
(Webster, 1975). We can sometimes force analyses to converge by making gross simplifications in the physical
modeling. Even when convergence is achievable, analyses of even the smallest structural systems require extreme
computational expense.
For example, it cost about $3 million to analyze the structural response of the near field arrays for the
Intermediate Scale Measurement System (ISMS). Half of this total is spent in solution convergence studies alone.
Another good example is the response analyses for an experimental study of offshore semisubmersible platforms
under the Tactical Air Crew Combat Training System , (TACTS). Such platforms are used by various U.S.
Governmental agencies and the oil industry. In this case, simulation of twenty minutes of structural response took
about one month of computer time. In both of these projects serious limitation in the numerical computational
capabilities were experienced.
A revolutionary change in the computational framework for cable structural simulation is urgently needed.
The proposed research will remove the difficulties associated with the calculation of nonlinear dynamics. The
primary impact of the proposed research would be to improve the mathematical basis for developing computer
software which in turn will improve the design and constructibility of these structures.
Recently reported research work on "Tension Structures" (Abel et al 1994) shows that structural analyses
for many terrestrial cable structures is, in general, advancing to higher and higher levels of sophistication. For
example, dynamic wind analysis, simulation of the step-by-step erection process, and overall stability analysis is
becoming ever more necessary for the kinds of spatial, lattice and tension structures envisioned for the future.
6
PRESENT METHODS: Cable structures are often subjected to non-conservative forces and undergo large
rotations and displacements and exhibit non-linear geometric behavior. Non-linear dynamic equations of motion
can be solved by direct temporal integration using appropriate finite difference techniques. Dynamic equations of
motion are converted into an equivalent quasi-static linearized equations of static equilibrium at each time step by
the introduction of a set of kinematics constraints between the variables of nodal acceleration, velocity and
displacement. The Newmark family encompasses all single step implicit methods including the following: 1.)
constant acceleration, 2.) linear acceleration, 3.) Wilson-theta (a variation of the Newmark), and 4.) alpha (another
variation of the Newmark). Nonlinear dynamic simulation can be achieved through the step-by-step solution of a set
of quasi-static linearized algebraic equations. For linear problems, numerical stability and accuracy of single-step
implicit methods are generally assured, given proper choice of time-step and other parameters. However, for
non-linear problems, stability is not assured. Specific techniques for measuring stability such as energy balance
must be developed. Even if initially stable, Newton-based methods may become ill-conditioned and unstable due to
the transition from one state to the next (Chiou and Leonard, 1994). The interval of convergence is highly problem
dependent, can be very sensitive to changes in the solution procedures, and is not explicitly computable.
To improve the interval of convergence, a number of variations in the advancing and in the correcting phase
have been proposed (Powell & Simon, 1981, Powell, 1984). Variations in the advancing phase include those that
do not require prior knowledge of the load increment and those that control the size of the displacement rather than
the load increment. Strategies that automatically select the load increment in the advancing phase include: 1)
constant force imbalance in the advancing phase, 2) constant number of iterations in the correcting phase. A line
search method can also be used to select the magnitude, and conjugate Newton methods can be used to alter the
direction. In line search methods, a multiple of the computed displacement increment is chosen to minimize some
measure of the force unbalance. In conjugate Newton methods, a set of search directions computed by the conjugate
gradient method are automatically selected to minimize the search.
The technical literature includes extensive reference to local/global methods for static linear analysis. A
particularly relevant reference is that for domain-by-domain algorithms for transient structural dynamics in aerospace
structures (Hajjar and Abel, 1989). In the concluding remarks to this reference, the authors suggested the following
alternate method to their own algorithms: “...use of full sub-structuring with condensation of internal degrees of
freedom followed by an interface solution." Even though most local nonlinearities are quite application-specific, a
sub-structured approach will provide a computational framework that is more generally applicable.
Present capability for general nonlinear analysis of ocean cable systems is principally limited to two similar
finite element codes, SEASTAR (PMB, 1989) and SEADYN (Webster, 1989). Both codes are based on the
displacement method of structural analysis where the primary unknowns are orthogonal translations at nodes of the
structure. The basic finite element used in these codes for modeling cables is the nonlinear truss element. Unlike
traditional linear elements, the elements in these codes are formulated to recognize large displacement kinematics
and equilibrium in the deformed configuration. A Lagrangian approach is used to describe the motion of the system
from the current reference state to a new incremental reference state. Numerous variations of the Newton-Raphson
iteration technique are available to advance the solution using a tangent stiffness estimate. Although developed for
material nonlinearities, specific solution control strategies such as variable step sizing, displacement control,
event-to-event prediction, and viscous relaxation are available on both codes for control of geometric nonlinearities.
Specific numerical representations are provided for ocean-related loads including gravity, hydrostatic pressure,
buoyancy, added-mass, fluid-induced damping, and wave and current-induced hydrodynamic drag and inertia.
Many of these load representations are highly nonlinear and orientation specific, such as wave loading above the
mean water surface. Provisions allow for modeling rigid bodies and their hydrodynamic effect on cable structure
response.
DEFICIENCIES IN PRESENT COMPUTATIONAL CAPABILITY: Although many of the general solution
strategies for material nonlinearites are implemented in a few programs such as SEADYN and SEASTAR, present
analyses are often plagued by modeling and solution inefficiencies due to geometric nonlinearities that are inherent
in cable analysis. These inefficiencies include slow execution, non-convergence of solutions, and inaccurate results.
Other difficulties in dynamic cable analysis include excessive degrees of freedom to model cable shapes accurately.
Structural response output is usually only desired for key nodes in the structure, (e.g. the point where a subsurface
buoy meets several catenaries). Degrees of freedom perpendicular to a catenary line usually have low relative
stiffness, and if eliminated would help tremendously in conditioning the solution.
Most cable structures consist of individual cable catenaries of one or more materials into a two or three
dimensional network. When modeled with finite elements, the structure stiffness matrix is usually sparsely
7
populated and contains terms which differ by several orders of magnitude; this results in poorly conditioned
matrices which are difficult to solve by general matrix methods. Work at NFESC (Navy) has identified several
cable mooring problems that are particularly unstable.
ACCURACY OF MULTI-VALUE METHODS: Multi-value methods are higher order time stepping procedures
that allow a computation to proceed using information only at one level in time to obtain a solution at the next time
level. This is accomplished by solving for approximations to time derivatives of a function as well as the function
itself. These methods are related to multi-step methods, (e.g. Runge Kutta) wherein solutions at a number of time
levels are used to obtain a solution at the new time level. Multi-step methods are said to suffer from inadequacies
when a change in time step is desired because the standard formulas have to be modified to accommodate a change
in time step. Multi-value methods are touted as having the desirable feature that the time step may be changed
arbitrarily as one proceeds in time marching. Conceptually this seems reasonable since information all at one
position in time is used to move to the next position in time. In practice, changes in time step with the standard
coefficients introduce lower order errors. However, coefficients have been developed [Gray and Muccino, 1994] that
allow for a change in time step without sacrifice of order of accuracy. Start-up issues normally associated with
multi-step methods have also been overcome.
Kahaner et al. (1989) attempted to develop multi-value methods from Taylor series expansions. The
development seems to proceed nicely through 4-value methods. However, the authors then demonstrate that the
procedure derived is inherently unstable. Arbitrary and unexplained changes are then made with no indication of
how methods other than the two 4-value methods may be derived. Celia and Gray (1992) adopt a different method
of presentation that leads to appropriate coefficients and not that a change in time step with multi-value methods
seems to introduce a disturbance into the solution that takes a few time steps to die out. However, the derivation is
somewhat obscure and involvessome reasoning that may seem circular.
Current research (Gray and Muccino, 1994) has provided a working method for derivation of algebraic
coefficients needed for multi-value methods that allows for a change in time step; coefficients for error terms have
also been developed so that error assessments may be made as the multi-value computations proceed. These
coefficients have been developed for 2 through 10 value methods using a symbolic mathematics program.
Based on the above discussion, it is proposed to solve the cable dynamics problem by converting nonlinear
differential equations, using higher order Taylor series.
PROPOSED OBJECTIVES: The objective of this study is to break the computational barrier that presently
exists for analyzing the response of large, nonlinear cable structures. It is proposed to abandon the present
mathematical framework and reformulate the structural analysis problem so that it naturally lends itself to full
modeling of nonlinearities. Presently, large, nonlinear structures are represented with one large system of nonlinear
equations that is often extremely sparse and ill-conditioned.
For example, local nonlinearities and the solution stability of one small part of the overall structural system
often control the overall solution strategy (e.g., small step size). The result is a large number of (trivial)
computations. A structural problem can be reformulated in a different way such that the extreme differences in local
solutions are explicitly accommodated, thus making robust simulations possible.
The main task of the proposed research is to formulate the simulation of large, nonlinear structural systems
into a computational framework that is inherently more stable. The basic scientific issues that will be addressed are
related principally to mathematics and mechanics. Time integration methods for local solutions need to be
modified, new numerical methods for local/global iteration need to be developed, different local computational
domains must be addressed, and the stability of the overall computational framework must be assessed. In
summary, we propose to break the computational barrier to structural analysis of large non-linear ocean structural
cable problems by abandoning the present mathematical framework, based on unstable linear approximations, and
involving many diverse and complex unknowns.
SCIENTIFIC APPROACH: Since large structures are assembled from smaller components or sub-structures, it is
logical to synthesize the numerical model into smaller digestible sub-models. Specialized local sub-models, each
with its own local physical behavior, are most suitable for accurate representation of sub-structures. These local
sub-models can be easily developed from existing modeling theories. For example, a deep-water platform can be
represented by the following local sub-models: 1) A rigid-body, large-rotation representation for the surface vessel,
2) an assembly of large-displacement elements for each mooring line and 3) an analytical expression of soil-structure
interaction for each anchor.
8
surface hull
global node
local nodes
cable
global node
anchor
Figure 1. Typical Ocean Buoy
A schematic diagram of a typical ocean buoy moored with three anchor lines is shown in Figure 1. The
present finite element approach for modeling this structure yields a large sparse, ill-conditioned matrix. In the
proposed approach, the structure is broken into three local sub-models, each represented by a set of simultaneous
differential equations. The global matrix, which couples the three local sub-models, condenses to a very small
dense matrix. The key idea here is that the large sparse, ill-conditioned matrix is reduced to smaller, denser, and
inherently more stable matrices. A computational domain specifically turned to the local sub-model best assures
local nonlinear response stability. Local solutions will interact with each other through a well-defined global
interface, as shown in Figure 2
Assume Initial Conditions
Time Step Integration
Time History Solution
t
Nonlinear Iteration
 RU
Local / Global Iteration
 Ri
U
Solve Local Equations
Figure 2 Proposed Local/Global Iterative Solution
The proposed analysis process will be based on the calculation of initial configuration and then the update
of the configuration based on applied static loads and finally calculation of the dynamic structural response as
illustrated in Figure 3.
9
Dead Loads
Static Analysis
Initial Configuration
Static Loads
Static Analysis
Offset Configuration
Dynamic Loads
Dynamic Analysis
Structural
Response
Figure 3. Dynamic Analysis Procedure
For the dynamic analysis, we propose to use a full nonlinear formulation of the dynamic differential
equations of motion with full Morison equation representation of the aero- or hydro-dynamic forces on the cable
structures as shown by equation (1).
Internal Forces = External Forces
M 
r  Cr  K r  R M  R C  R K  R N
where:
(1)
,
r r, r  nodal acceleration, velocity, displacement
M  structural mass
C  structural damping
K  structural stiffness
R M  (,
r u )  equivalent nodal load representing fluid inertia
R C  (,
r u)  equivalent nodal load representing fluid viscosity
R K  (u)  equivalent nodal load representing fluid buoyancy
R N  other applied nodal loads
Structural behavior in cables is often dominated by two basic mechanics principles: large disparities in
stiffnessof cables, and cable behavior which may approach that of a structural mechanism. The driving mechanism
in the solution of catenary shape in cable systems is geometric nonlinearity. In the initial static shape of a cable
system, one cannot prescribe both the shape and the prestress force independently of equilibrium as in most other
structural analyses.
Another method will be pursed in this proposal is to undertake an upper and lower bound analysis on the
basis of a physically sound modeling. Such an analysis may provide a utility in which the physical quantities in the
cable simulation may be pre-determined or pre-defined in a range that can be easily estimated. For example as stated
in this proposal of the cable simulation, it is well known that the slowness in computational convergence is the major
contributor to the extreme computational inefficiencies. A prior knowledge that any possible nodal displacements
10
will be confined in a given range, allows construction of a more effective numerical scheme then could be
constructed based on the information of the limits on those nodal displacements.
The upper and lower bound approach can be applied not only to the physical quantities, but also to the
governing equations that control the cable kinematics and dynamics. The simulation may be formulated in an
inequality form such that many approximation techniques can be introduced to estimate the physical quantities with
limited or no numerical manipulations. Those approximated solutions then can serve as a starting point for a more
vigorous approach.
An upper and lower bound analysis may serve as an alternative to costly and inefficient mathematical
models. The key to success in pursing this alternative is to preserve physics in formulating the bound analysis.
Many such methods like the energy method, weighting function method, or reciprocal principle (Zhu et al., 1996) are
available. An integral representation for the cable simulation could be more suitable with respect to the
effectiveness of computational scheme. In fact, consideration of both integral and differential representations in cable
simulation may yield a desirable and new methodology in cable simulation, and the computational mechanics. This
approach will be pursued in this proposal.
Futher extensions of the multivalue algorithm may lead to an opportunity to vary the time step throughout
the spatial domain so that error of the calculations is uniform. The next step in the development of multi-value
methods for accurate change in time step is implementation of the scheme into a simulation code. Simulation of cable
structures would be an opportunity to examine these issues since local nonlinearities often require a small time step
in a particular region. A large number of trivial computations results if a constant time step is required throughout the
domain.
PROPOSED TASKS: We plan to develop specific nonlinear mathematical techniques appropriate for local
solutions of the dynamic equations of motion a cable substructure constrained by the stability of the global system.
We plan to implement this local cable sub model within an iterative local/global solution procedure as shown in
figure 2. As part of this proposal, we also plan to investigate specific mathematical reformulation for global
solution of an overall reduced system of dynamic motion equations. Mathematical framework will be reformulated
to simulate structures so that local nonlinearities are explicitly accommodated, and solutions will be stable, accurate,
and efficient.
In summary the following tasks are proposed: 1) Development of the mathematical basis for a non-linear
dynamic solution of cable structures, 2) Extentions of this mathematical basis to include complex loading and
boundary contact, 3) Improvement and expantion of fundamental computational mechanics in the areas of nonlinear,
large deformation behavior of new types of flexible structures subjected to various different types of loading, 4)
Development of new algorithms which will be robust, reliable, efficient and scalable on parallel computing platforms
5) Evaluation of stability of the new local model within the computational framework and 6) Numerical testing of the
methods with representative nonlinear cable structures, and published experimental test data. Such comparison will
validate and otherwise support the development of the above computational technology.
Summary
Cable structures are load adaptive where these structures make a change in the geometry with the application of
loads rather than a change in stress. Cables non linearity change their geometrical shape regardless of the elastic
and linear properties of material and linearity of load with time. These structures undergo large displacements and
the principle of linear superposition are not valid. Although the cable length may not change much but there may be
large rotation and displacements due to the applied loads.
Most ocean facilities and many terrestrial structures require extensive engineering analyses for their design and
construction. Highly nonlinear examples include the following analyses: 1) survival of multi-leg vessel moorings,
2) deployment of towed-3D arrays, 3) form-finding for cable structures, 4) seismic capacity of ship dry-dock, 5)
flexibility of aerospace structures, and 6) deployment and behavior of communciation buoys. Research work
shows that structural analyses for many structures have reached a computational barrier. Too often analyses fail to
converge to a solution. Although the analysis can sometimes be forced to converge by making gross simplifications
11
in the physical modeling. Even when convergence is achievable, analyses of even the smallest structural systems
require extreme computational expense. A revolutionary change in the computational framework for cable
structural simulation is urgently needed and will improve the simulation capability for all structures.
The objective of this study is to break the computational barrier that presently exists for analyzing the response
of large, nonlinear structures. With this barrier, gross simplifications (i.e., linearization), computational
inefficiencies often characterize present structural analyses. It is proposed to reformulate the structural analysis
problem so that it naturally lends itself to full modeling of non-linearities. Presently large, nonlinear structures are
represented with one large system of nonlinear equations that is often extremely sparse and ill-conditioned. For
example, local nonlinearities and the solution stability of one small part of the overall structural system often control
the overall solution strategy (e.g., small step size). The result is a large number of computations. A structural
problem can be reformulated in a different way that explicitly accommodates the extreme differences in local
solutions, in this case, robust simulations are possible with greatly reduced computational expense. The solution
algorithms which will be developed here will be robust, reliable, efficient, and scalable on parallel computing
platforms.
Force equilibrium equations for large displacements using orthogonal curvilinear coordinate systems will be
developed. Equilibrium equations are formulated from the deformed state. Solution of multiple structural systems
is formed by simultaneously solving a set of nonlinear differential equations. Solution to the physical mooring
problem is found without using the standard discretization process. As part of this study, nonlinear solutions will be
checked by using 1) Newton-Rapson, 2) modified Newton and 3) Quasi-Newton methods. A numerical efficient
and explicit integration method is developed which is suitable for the geometrically nonlinear dynamic analysis of
flexible cables. This new approach is particularly effective for structures undergoing large extension and rotation.
The focus area of this research is to improve and expand fundamental computational knowledge in the areas of
nonlinear, large deformation, quasistatics and transient dynamics.
12
BIBLIOGRAPHY
Abel J.F., Leonard J.W. and Penalba C.U. "Spatial, latice and tension structures", Proceedings of the IASS-ASCE
International Symposium,ASCE, 1994.
Celia, M. A. and Gray, W. G., Numerical Methods for Differential Equations, Prentice Hall, Englewood Cliffs,
1992.
Chiou R. and Leonard J.W., "Nonlinear modeling of sea floor interactions of mooring cables," Proceedings of the
International Offshore and Polar Engineering Conference, Osaka, Japan, April 1994.
Gray, W. G. and J. C. Muccino, ÒPreservation of Accuracy of Multi-value Methods During Change of Time-step
Size,Ó in Recent Developments in Finite Element Analysis (edited by T. J. R. Hughes, E. Onate, and O. C.
Zienkiewicz), International Center for Numerical Methods in Engineering, Barcelona, pp. 131-140, 1994.
Hajjar J. and Abel J., "On the accuracy of some domain-by-domain algorithms for parallel processing of transient
structural dynamics," International Journal for Numerical Methods in Engineering, August 1989, Vol. 28
N8:1855-1874.
Kahaner, D., Moler, C. and Nash. S., Numerical Methods and Software, Prentice Hall, Englewood Cliffs, 1989.
PMB Engineering Inc., "Near-field array engineering", Intermediate Scale Measurement System Reports, NCEL,
TM No. 44-93-02, April 1993.
Powell G., "Modeling and solution strategies for nonlinear braced frames," Super computing in Engineering
Structures, Edited by Brebbia,C., Computational Mechanics Publications, Southampton, 1989.
Power G. and Simons J., "Improved iteration strategy for nonlinear structures," International Journal for
Numerical Methods in Engineering, John Wiley & Sons, Ltd., 1981.
Webster R.L., “Nonlinear static and dynamic response of underwater cable structures using the finite element
method.” Proceedings of the Offshore Technology Conference, OTC 2322, 1975.
Webster R.L., "On the static analysis of structures with strong geometric non linearity," Computers & Structures,
Vol., No. 1/2, 1980, pp. 137-145.
Webster R.L., "Dynamic response of cables subject to ocean forces," OTC 3854,
Proceedings, Offshore Technology Conference, Houston, Texas, May 1980.
Wriggers P. & Simo J.C., "A general procedure for the direct computation of turning and bifurcation points," Int. J.
Num. Methods. Engineering., 30, 155-176 (1990).
H. Zhu, C. Chang and J.W. Rish, III (1996), "Normal and Tangential Compliance for Conforming Binder Contact.
II: Visco-elastic Binder" Int. J. of Solids and Structures, Vol. 33, pp. 4351-4363.
13
FACILITIES AVAILABLE
Arizona State University has made a major commitment to the development of nonlinear cable dynamics
research capabilities. The University supports full analytical capabilities on both micro or mainframe computers.
PRINCIPAL INVESTIGATOR AND STAFF
Dr. Avi Singhal, Professor of Civil Engineering at ASU will be the principal investigator of this research
effort. Published ocean experimental data on cables will be utilized for numerical to experimental comparison. Dr.
Singhal plans to enlist the assistance of up to two graduate students. The following is a biographical sketch of the key
personnel of the proposed project together with their vitas.
AVI SINGHAL - Dr. Singhal will be the P.I. of the proposed project. He is a Professor of Civil Engineering at
ASU. He has been actively involved in structural dynamics research and education for over 30 years. He was the
principal investigator of multi-year research projects from the National Science Foundation (two projects), U.S.
Army Corps of Engineers Waterways Experiment Station project, Engineering Foundation, and U.S. Bureau of
Reclamation project on large structures. Dr. Singhal has extensive project management experience and was a
project manager of TRW, a senior level manager at General Electric Co., served as Director of Central Building
Research Institute and recently worked as a fellow at Naval Facilities Engineering Service Center.
For the last 20 years, Dr. Singhal has been involved with the non-linear analysis of structures. He has an
extensive publication record on this subject (over 100 technical papers) which includes design, analysis, structural
dynamics and cable systems. Dr. Singhal has focused his research on the implementation of nonlinear behavior of
structures and stresses and deflections in structural systems. During his research several new computer programs
were developed which model the nonlinear behavior of structures.
Dr. Singhal joined Arizona State University in 1977 and established a structural testing facility at ASU with
support from the National Science Foundation. Dr. Singhal has 10 years of experience with instrumentation,
laboratory testing and field testing. As a professor at ASU, Dr. Singhal has been teaching various engineering
materials, mechanics of materials, and design of structures courses. He has been consultant and expert witness in
areas of solid mechanics and behavior including dynamic stresses, strains and deformations. He is a registered
engineer and is active in several professional societies, including the American Society of Civil Engineers and the
American Society of Mechanical Engineers.
JULIA MUCCINO - Dr. Muccino is an Assistant Professor in the Civil and Environmental Engineering Department
at Arizona State University. She received an M.S.C.E. and a Ph.D. at the University of Notre Dame in 1992 and
1995, respectively. Part of her Ph.D. research was conducted at the Institute of Ocean Sciences in British Columbia,
CANADA. Funding for her Ph.D. was obtained from a three year National Science Foundation Graduate Research
Fellowship and Rice University subcontract of NSF funding R34111-77600094. She obtained further experience
with postdoctorate appointments at the National Tidal Facility in South Australia and the University of Notre Dame.
Dr. Muccino's field of expertise is numerical modeling of surface water systems, particularly large scale
(tens to hundreds of kilometers) circulation due to tidal fluctuations, wind stress and density variations. Because the
domains are so large and flexibility in grid resolution is paramount, finite element methods were the method of
choice for these studies. Specific aspects of study included grid resolution requirments as well as implementation of
data assimilation techniques. She has also participated in the development of multivalue methods for solution of
temporal differential equations which may lead to the opportunity to vary the time step throughout the spatial domain
such the error of the calculation is uniform.
HAN ZHU - Dr. Zhu is an Assistant professor of Civil Engineering Department at Arizona State University. His
research interests include testing and characterizing engineering materials. He was the principal investigator for a
number of projects sponsored by AFOSR, DOE, etc. He has authored or co-authored about 25 peer-reviewed
professional journal articles.
MANAGEMENT PLAN
14
The management organization represents a general structure that has been used successfully by Arizona
State University (ASU) on numerous projects of similar size, duration and complexity. ASU will be the prime
contractor of the project. The ASU administrative officer will be Ms. Lori Gabriel, a Sponsored Project Officer at
the Office of Sponsored Projects at ASU. The P.I. of the project will be Dr. Avi Singhal who will be responsible for
the technical content, conducting research, progress of the project and preparing the final report. Dr. Singhal will be
responsible for communicating with the NSF and timely accomplishment of various tasks of the project. Sea data
from the past experiments will be obtained from existing Navy reports, and publications, (PMB, 1993). Graduate
students will participate in the literature search, computer analysis and other activities as needed.
Due to the limited size of the staff that will participate in the project, an organizational chart is not included with the
proposal. Also the P.I. is currently without any "current or pending" support, therefore NSF form 1239 is not
included with the proposal.
TIME SCHEDULE
The project will run for 2.5 years. Dr. Singhal has the time availability to meet this schedule. Should
ASU be selected for this project, future teaching loads for the P.I. will be adjusted to meet the demands of this
project. We stand prepared to negotiate the time schedule of the project to better meet the needs of the government.
15
BIOGRAPHICAL SKETCH
Avi C. Singhal
ADDRESS:
Office:
Arizona State University
Professor of Civil Engineering, ECE 5306
Tempe, Arizona USA 85287-5306
Fax: (602) 965-0557 (Office)
Phone: (602)965-6901(Direct)
(602)867-0167(Fax)
(602)839-1652(Home)
E-Mail: avi.Singhal @ asu.edu
EDUCATION: 1) Sc.D.(1964), Massachusetts Institute of Technology, (Civil Engineering-Majors:Structures,
Geotechnique and Fluid Mechanics, Minor: Mathematics), 2) C.E. (1962), Massachusetts Institute of Technology,
(Structures), 3) S.M. (1961), Massachusetts Institute of Technology, (Structures), 4) B.Sc.(1960), Honors, St.
Andrews University, Scotland, (Civil Engineering-Fluid Mechanics), 1st Class, 1st Rank, Top (Gold) Medalist, 5)
B.Sc.(1959), St. Andrews University, Scotland (Civil Engineering).
ACADEMIC EXPERIENCE: 1) Professor (1984 +), Civil Engineering, Arizona State University, 2) Graduate
Coordinator (91-92), Structural Engineering, Arizona, State University, 3) Director (78-89), Earthquake Research
Laboratory, Arizona State University, 4) Associate Professor (77-84), Civil Engineering, Arizona State University,
5) Professor and Director of Laboratories (65-69), Laval University.
MAJOR TEACHING-EMPLOYMENT SUMMARY: 1) Professor of Civil Engineering (1977 +), Arizona
State University. Graduate Coordinator to Structural Engineering Program at ASU, responsible for graduate
admissions. Taught ninety-eight (98) graduate and undergraduate classes in Computer Applications & Graphics,
Mechanics of Material, Advanced Stress Analysis, Dynamics of Structures, Statics, Structural Analysis, Systematic
Structural Design, Reinforced Concrete Structures, Steel Structures, Seismic design, Partial Differential Equations
Computer Aided Engineering, Engineering Materials, and Advanced Steel Structures. Over the past 20 years at
ASU, devoted time to develop, install and direct earthquake laboratory, and other funded sponsored research
projects. 2) Director (92-93), Central Building Research Institute. A major research institute with 15 laboratories
and employing over 787 engineers and support staff. Managed a $2M annual budget and significantly contributed
to development of new building materials. Promoted to Nodal Directorship in charge of a national program on
building, integrating seven large national research institutes. 3) Project & Design Engineer (74-77), Weidlinger
Associates, New York, Directly supervised ten engineers working on structural and dynamic analysis of complex
structures. Also developed computer programs. 4) Manager, Systems Services (72-74), Engineers India Limited.
Top management position and supervised 38 senior level technical personnel, other supervisors and managers. Was
responsible for overall administration, and technical supervision. Primarily responsible for systems and computer
engineering. 5) Manager (71-72), Systems Engineering, General Electric Corporation, Philadelphia. This was a
senior level direct management position with three layers of managers reporting. Supervised over 24 technical
personnel. Primarily responsible for ocean systems, building and missile systems and engineering.
RESEARCH SUPPORT FROM GOVERNMENT & FUNDING AGENCIES: 1) Council of Scientific and
Industrial Research: Received large research allocation to develop a substitute for wood and manage 15
laboratories researching on building materials. Reviewer of research proposals for CSIR, a research funding agency
in India, 2) National Science Foundation: Host - NSF research grantee workshop (August 1991). Chairman - NSF
Workshop on "Research on Lifeline Earthquake Engineering," member-research needs in lifelines, Member - large
experimental facility workshop, Received NSF research support at MIT for creep of concrete columns, Received
large equipment NSF research grants to establish two-axes multi-shake tables at Arizona State University, Received
NSF research grant for strength characteristics of pipeline systems, 3) U.S. NAVY: ASEE - Navy Senior Faculty
Fellow (1994), worked at Naval Facilities Engineering Service Center on Nonlinear Cable Dynamics, 4) U.S. Army:
Received funding on five separate research projects related to: a) Nonlinear Finite Element Models, b) Influence of
Creep, Temperature, Geometrical Imperfections on Stress-Field, 5) U.S. Department of the Interior: Received
multi-year support for research on earthquake analysis of various dam structures. Participated in a workshop on
seismic effects on Arch Dams held at Beijing, China, 6) Department of Defense (Canada): Received several
research grants on the effects of high intensity nuclear and conventional explosives on various complex structures
16
(missiles & submarines), 7) National Research Council (Canada): Received several research grants for theoretical
and experimental work on creep studies for radome structures, and equipment grants to establish testing facilities, 8)
U.S. National Oceanographic & Atmospheric Administration (NOAA): Received support as a part of General
Electric manager to develop a major instrumentation system, 9) Central Building Research Institute. CSIR, India:
As a Director, acquired funding of $2,000,000 for 1992-1993 for research work at CBRI. Worked as Director
CBRI and invented new building materials for wood substitute.
RECENT SPONSORED RESEARCH WORK: 1) Primary interest in structural engineering and structural
dynamics, 2) Worked with the Bureau of Reclamation (Denver) on the computer analysis of gravity and arch dams.
Have written several finite element codes, 3) Worked with the Corps of Army Engineers on overall instrumentation
plan for various concrete dams, canals and hydraulic structures. Performed stability calculations. Participated in
the review of specifications prepared by FERC, U.S. Army, Bureau of Reclamation on the seismic performance and
evaluation of dams. Prepared reports for the Waterways Experiment station (WES) on the instrumentation and
stability of dam structures, 4) Performed research at McDonnell Douglas on the effect of flexibility on the
transmission of blast forces within an aerospace structure. Defined explosive loads including diffraction.
Developed computer programs based on structural dynamics, gas and compressible gas flow dynamics.
SUPERVISION OF GRADUATE STUDENT (M.S./Ph.D): 1) Dr. M.P. Chung, Ph.D (1984), 2) Dr. G. Dhatt,
Ph.D (1969), 3) M. Zuroff, Ph.D (1991), 4)M.S. Zuroff, M.S. (1986), 5) V. Veliz, M.S. (1986), 6) W. Korp, M.S.
(1985), 7) W.S. Li, M.S. (1983), 8) C.L. Meng, M.S. (1982), 9) J.C. Benavides, M.S. (1982), 10) M. Gagnon, M.S.
(1968), 11) C. Tahiani, M.S. (1968), 12) G. Bonnes, M.S. (1967), 13) A.C. Menlo, M.S., 14) V. Karmakar, M.S.
(1991), 15) Dr. M.P. Chung, Post Doc. (1985), 16) John Sims, M.S. (1985), 17) E. Artsi, M.S. (1983), 18) S.
Aljaweini, M.S. (1980), 19) S. Bandityanand, M.S. (1978), 20) Dr. S. Govil, Ph.D (1991), 21) J. Pyne, M.S. (1987),
22) Ray Peterson, M.S. (1986), 23) D. Furstenau, M.S. (1986), 24) P. Nichol, M.S. (1986), 25) T. Kwalik, M.S.
(1978), 26) E. Castillo, M.S. (1992), 27) T. Wolf, M.S. (1991), 28) Dr. M. Zuroff, Post Doc. (1987), 29) I. Jiblawi,
M.S. (1993), 30) J.A. Schrieber, M.S. (1994), 31) M. Muthial, M.S. (1994), 32) T.S. Hu, M.S. (1994), 33) R.
Ringwald, M.S.E. (1995), 34) S. Kordt, M.S.E. (1996), 35) Q. Yuwei, M.S.E. (1996), 36) N. del Prado, M.S.E.
(1996), 37) J. Corpuz, M.S.E. (1997), 38) A. Malhotra, Post Doc. (1997)
PUBLICATION LIST
1)
Computer Modeling, Burgess Publishing Inc., 1997, ISBN 0-8087-99495.
2)
"Simulation of Blast Pressures on Flexible Panels", (with D. Larson, S. Govil and V. Karmakar), Journal of
Structural Engineering, American Society of Civil Engineers, New York, July 1994.
3)
"System Flexibility and Reflected Pressures", (with K.S. Fansler and M. Toossi), Journal of Aerospace
Engineering, American Society of Civil Engineers, New York, Vol. 6, No. 3., pp299-313, July 1993.
4)
"Nonlinear Seismic Analysis of Arch Dams Using Slip Joint Elements", (with M. Zuroff), Soil Dynamics
and Earthquake Engineering, Vol VI, Edited by IBF, Elsvier Applied Science, Oxford, England, Feb., 1992.
5)
"Computer Simulation of Weapon Blast Pressures on Flexible Surfaces", (with D. Larson) Journal of
Computers and Structures, Pergamon Press, Oxford, England, Vol. 41, No. 2, Oct., 1991.
6)
"Analysis of Underground and Underwater Space Frames with Slip Joints". Journal of Computers and
Structures, Pergamon Press, Oxford, England, Vol 35 No. 3, pp 227-237, 1990
7)
Stiffness, Structural Analysis of Buried, Flexibly Jointed Frames, (with M. Zuroff) Part Contributor to a
Book, Earthquake Behavior of Buried Pipelines, Storage, Telecommunication, and Transportation
Facilities, American Society of Mechanical Engineers, Book No. H00477, PVP, Vol. 162, New York, pp
121-131, July 1989
8)
"A Numerical Simulation for the Expansion Diaphragm within Creeping Salt Deposits", Journal of
Computer and Structures , Vol. 29, No. 3 Pergamon Press, Oxford, UK, pp. 393-402, July 1988
9)
Recent Advances in Lifeline Earthquake Engineering (Edited by A.C. Singhal et al.), Computational
Mechanics, Page 288, Southampton, UK, 1987
10)
"Nonlinear Dynamic Response of Multi-Rings", Proceedings of Canadian Centennial Congress of Applied
Mechanics, Laval University, Quebec, May 1967.
Julia Muccino
17
EDUCATION:
1996
1993
1990
Ph.D. - University of Notre Dame - Civil Engineering
M.S.C.E. - University of Notre Dame - Civil Engineering
B.C.E. - Villanova University - Civil Engineering
ACADEMIC EXPERIENCE:
1997
Assistant Professor, Arizona State University
1996-1997
Postdoctoral Research Associate, University of Notre Dame
1995-1996
Visiting Research Fello, National Tidal Facility, South Australia
Summer 93, 94 Visiting Scientist, Institute of Ocean Sciences, British Columbia
AWARDS, HONOR SOCIETIES:
Eli J. and Helen Shaheen Graduate School Award in Engineering (1996)
National Science Foundation Graduate Research Felloship (1992-1995)
Dondanville Award for Outstanding Teaching Assitant (1991)
Dehner Felloship (1990)
Magna Cum Laude Graduate, Villanova University (1990)
Dean's Award for Academic Excellence (1990)
Phi Kappa Phi (National Interdisciplinary Honor Society)
Tau Beta Pi (National Engineering Honor Society)
Chi Epsilon (National Civil Engineering Honor Society)
PRINCIPAL AREAS OF RESEARCH AND TEACHING:
Numerical Methods
Finite Element Methods
Data Assimilation
SELECTED PUBLICATIONS
Muccino, J. C., W. G. Gray, L. A. Ferrand, "ÔDevelopments in Theoretical Tools for Deterministic Modeling of
Two-Phase Flow in Porous Media," submitted to Reviews of Geophysics, May, 1997.
Muccino, J. C., W. G. Gray and M. G. G. Foreman, "Calculation of Vertical Velocity in Three-Dimensional, Shallow
Water Equation, Finite Element Models," International Journal for Numerical Methods in Fluids, in press.
Muccino, J. C., W. G. Gray and M. G. G. Foreman, "Vertical velocity calculation in a finite element model,"
Proceedings of the Ocean and Atmosphere Pacific International Conference, pp. 225-230, April 1996.
Gray, W. G. and J. C. Muccino, "Preservation of Accuracy of Multi-value Methods During Change of Time-step
Size," in Recent Developments in Finite Element Analysis (edited by T. J. R. Hughes, E. Onate, and O. C.
Zienkiewicz), International Center for Numerical Methods in Engineering, Barcelona, pp.131-140, 1994.
Muccino, J.C., W.G. Gray and M.G.G. Foreman, "Calculation of Vertical Velocity in a Three-Dimensional Model
Using a Least Squares Approach," Computational Methods in Water Resources X, Volume 2, pp.1105-1112, 1994.
18
Westerink, J.J., R.A. Luettich, and J.C. Muccino, "Modeling Tides in the Western North Atlantic Using Unstructured
Graded Grids," Tellus, v46A, pp.178-199, 1994.
Westerink, J.J., J.C. Muccino and R.A. Luettich, "Resolution Requirements for a Tidal Model of the Western North
Atlantic and Gulf of Mexico, "Computational Methods in Water Resources IX, Vol 2: Mathematical Modeling in
Water Resources, pp.637-648, 1992.
Westerink, J.J., J.C. Muccino, and R.A. Luettich, "Tide and Hurricane Storm Surge Computations for the Western
North Atlantic and Gulf of Mexico," Estuarine and Coastal Modeling, edited by M.L. Spaulding et al., ASCE, New
York, 1991.
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Han Zhu
ADDRESS:
Office: Arizona State University
Phone: (602) 965-2745 (Direct)
Assistant Professor of Civil Engineering, ECE 5306
(602) 965-0557 (Fax)
Tempe, Arizona, USA 85287-5306
E-mail: han.zhu@asu.edu
EDUCATION:
1990
Ph.D. - Northwestern University – Theoretical and Applied Mechanics
1984
M.S. - Fudan University, China - Applied Mechanics
1982
B.S. - Fudan University, China – Mathematics and Mechanics
ACADEMIC AND WORKING EXPERIENCE
Assistant Professor: 08/97-present
Civil Engineering Department, Arizona State University, Tempe AZ 85287-5306
Computer Consultant: 04/97-08/97
MIS Department, Turbulence Component Center, Pratt & Whitney, 109600 Beelines Hwy.
West Palm Beach, FL 33410.
Senior Engineer: 09/93-04/97
Applied Research Associates Inc., 1142 Mississippi Road, Tyndall AFB, FL 32403
Research Assistant Professor: 07/92-08/93; Post-Doctoral Fellow: 07/90-06/92
Dept. of Engineering Sciences and Mechanics, The Univ. of Tennessee, Knoxville, TN 37996
AREAS OF RESEARCH INTEREST:
First principle based thermal-mechanical modeling; analytical and computational analysis of macro-micro
stress-strain relationships; asphalt pavement performance theory, specification, testing and design criteria
development; structural and material characterization of particulate and fiber-reinforce ceramic composites; creep
and viscous behavior study; interface/binder evaluation; fracture and damage estimation; NDE method and wave
propagation; Weibull statistical approach; finite element method (FEM) and boundary element method (BEM).
Experimental investigation of asphalt pavement, asphalt binder and viscous media, testing of composite
structures; dynamic signal process in engineering applications.
RECENT SPONSORED RESEACH PROJECTS:
1. Fundamental understanding of asphalt concrete by AFOSR (1993-1997, Principal Investigator)
2. Thermal-mechanical analysis and damage characterization of CAS/SiC ceramic composites by
DOE (1990-1993, Co-principal investigator)
SELECTED PUBLICATIONS:
(1) C. Ouyang and H. Zhu (1986), "Computations for Deep Boundary Cracks," Theoretical and Applied Fracture,
Vol.5, No.3, pp.163-172.
(2) J.D. Achenbach, D.A. Sotiropoulos and H. Zhu (1987), "On the Direct and Inverse Elastic Wave Scattering
Problem to Characterize Damage in Materials," Review of Progress in Quantitative Nondestructive Evaluation, D.O.
Thompson Eds., Plenum, New York.
(3) D.A. Sotiropoulos, J.D. Achenbach and H. Zhu (1987), "An Inverse Scattering Method to Characterize
Inhomogeneities in Elastic Solids," J. Appl. Phys., Vol.62, pp.2771-2778.
(4) J.D. Achenbach, D.A. Sotiropoulos and H. Zhu (1987), "Characterization of Cracks from Ultrasonic Scatter
Data," J. Appl. Mech., Vol.54, pp.753-760.
(5) J.D. Achenbach and H. Zhu (1989), "Effect of Interfacial Zone on Mechanical Behavior and Failure of
Fiber-Reinforced Composites," J. Mech. Phys. Solids, Vol.37, pp.381-394.
20
(6) J.D. Achenbach and H. Zhu (1990), "Effect of Interphases on Micro-Macro Mechanical Behavior of Hexagonal
Array Fiber Composites," J. Appl. Mech., Vol.57, pp.956-963.
(7) H. Zhu and J.D. Achenbach (1991), "Effect of Fiber-Matrix Interphase Defects on Microlevel Stress States as
Neighboring Fibers," J. of Composite Matls., Vol.25, pp.225-238.
(8) H. Zhu (1991), "Slowly Varying Method for High Frequency Scalar Scattering Problems," J. Acoustical Soc.
Amer., Vol.90(2), pp.1138-1143.
(9) H. Zhu and J.D. Achenbach (1991), "Radial Matrix Cracking and Interphase Failure in Transversely Loaded
Fiber Composites," Mechanics of Materials, Vol.11, pp.347-356.
(10) H. Zhu and J.D. Achenbach (1992), "Matrix Cracks and Interphase Disbonds in Hexagonal Array Fiber
Composites," ASTM STP, No.1131, pp.381-394.
(11) H. Zhu (1992), "A Method to Evaluate 3-Dimensional Time Harmonic Elastodynamic Green's Functions in
Transversely Isotropic Media," J. Appl. Mech., Vol.59, s96-101.
(12) J. Weitsman and H. Zhu (1993), "Multi-Fracture of Ceramic Composites," J. Mech. Phys. Solids, Vol.42,
No.2, pp.351-388.
(13) J. Weitsman and H. Zhu (1993), "On the Minimization of Residual Thermal stresses in Viscoplastic
Materials," International J. of Solids and Structures. Vol.30, pp.2813-2817.
(14) H. Zhu and J. Weitsman (1994), "The Progression of Failure Mechanisms in Unidirectionally Reinforced
Ceramic Composites," J. Mech. Phys. Solids, Vol.42, pp.1601-1632.
(15) H. Zhu, C. Chang and J.W. Rish, III (1996), "Normal and Tangential Compliance for Conforming Binder
Contact. I: Elastic Binder" Int. J. of Solids and Structures, Vol.33, pp.4337-4349.
(16) H. Zhu, C. Chang and J.W. Rish, III (1996), "Normal and Tangential Compliance for Conforming Binder
Contact. II: Visco-elastic Binder" Int. J. of Solids and Structures, Vol.33, pp.4351-4363.
(17) H. Zhu, C. Chang and J.W. Rish, III (1996), "Rolling Compliance for Elastic and Visco-elastic Conforming
Binder Contact," Int. J. of Solids and Structures, in press.
(18) H. Zhu, J.W. Rish, III and W.C. Dass (1997), "A Constitutive Study of Two-phase Particulate Materials. I:
Elastic Binder," Computers and Geotechnics, Vol.20, No. 3, pp303-323.
(19) H. Zhu, J.W. Rish, III and W.C. Dass, (1996), "A Constitutive Study of Two-phase Particulate Materials. II:
Maxwell Binder," Computers and Geotechnics, accepted.
(20) H. Zhu, J.R. Porter and W.C. Dass (1996), "Analysis of Asphalt Mortar," ASCE J. Materials in Civil
Engineering, In the public release procedure.
(21) H. Zhu, C. Chang and J.W. Rish, III (1996), "Torsion Compliance for Elastic and Visco-elastic Conforming
Binder Contact," ASCE J. Engineering Mechanics, Submitted.
21
AUTHORIZATION TO DISCLOSE PROPOSAL
AND REVIEW MATERIAL TO
SANDIA NATIONAL LABORATORIES
I acknowledge by signing below that I understand the program announcement for Engineering Sciences for Modeling
and Simulation-Based Life-Cycle Engineering is a joint initiative of the National Science Foundation and the Sandia
National Laboratories (Sandia), and that submitted proposals and review materials will be shared with Sandia for
purposes of proposal evaluation. I authorize the NSF to disclose my proposal and all associated materials and review
documents concerning my proposal, to Sandia and its representatives for the purpose of evaluation and selection of
proposals.
________________________________________
PI Signature Date
________________________________________
Co-PI Signature Date
________________________________________
Co-PI Signature Date
22