Daniel A. Tortorelli, - dtort@acm6.me.uiuc.edu
Professor, Department of Mechanical & Industrial Engineering
Most engineering tasks focus on the analysis of engineering systems.
However, analysis is not the primary task of the engineer, rather the
engineer's primary task is to design the system itself. I attempt to
integrate analysis and design synthesis via computational mechanics and
numerical optimization. For the most part, I use continuum mechanics to
derive the governing equations for various engineering systems and then
solve these equations using the finite element method. I also derive the
design sensitivities for these systems, again using continuum mechanics,
and evaluate them, again with the finite element method. Finally, I use
nonlinear programming strategies to update the design so as to minimize a
cost function and satisfy all constraints.
As my list of publications shows, I have published almost exclusively in
the areas of design sensitivity analyses and their applications in
optimization. However, I have also used the sensitivities to solve inverse
heat conduction problems, both transient and steady-state, linear and
nonlinear. Finally, I have an interest in continuum mechanics, a subject in
which I have made few published contributions, but which is central to much
of my research.
The applications of the sensitivity analyses and optimizations are, what I
feel, the most noteworthy aspects of my work and my collaborative efforts
with my colleagues and graduate students. In particular, we have applied
these methods to optimize manufacturing processes, e.g. crystal growth. The
optimization results are generally nonintuitive. In fact, an engineer with
extensive experience in the crystal growth industry had been using the
optimal processing conditions that we computed. However, it took him years
to obtain his results, whereas we obtained our results after several hours
of computing. Similar comments can be said of our experiences in casting,
welding, polymer extrusion and polymer injection molding process
optimizations. In the future, we will improve the simulations which are
used to model these processes, as the optimization results are only as good
as the underlying numerical model. For example, the present casting
analysis only considers heat conduction; therefore to predict distortion
and residual stress development a mechanical model must be developed.
Similarly, the polymer process models neglect thermal effects and cannot
predict fiber orientation or distortion.
We will also investigate other manufacturing processes. At the present
time, we are developing an Eulerian model for continuous processes such as
rolling, extrusion, drawing, continuous casting, laser annealing and
quenching. This model is displacement-based so that residual stress and
distortion can be computed, unlike previously developed velocity-based
Eulerian models. Opposed to displacement-based Lagrangian models, our
computations are steady-state so that costly transient analyses on large
meshes are eliminated. Additionally, since our analyses are steady-state,
we may use proper mesh refinement to obtain more accurate results.
To simplify the use of these optimization techniques, we are developing
graphic interfaces through Pro/Engineer which can be used to parameterize
the design and define cost and constraint functions. This work is being
performed for both finite element and multi-body mechanical system
analyses/optimizations. In the finite element work, we utilize variational
geometry and automatic meshing to parameterize the node coordinates with
respect to the solid model dimensions.
The desire to optimize designs from both a consumer product and
manufacturing process viewpoint motivated the coupled system
analyses/optimizations. This concurrent design concept has been used to
design a weldment, in which both manufacturing and product constraints were
simultaneously considered. We similarly propose to use this concurrent
optimization technique to develop a polymer injection process that will
produce a desired fiber orientation and density to optimize the performance
of composite structures.
In a somewhat similar coupled problem we are combining the finite element
and mechanical multi-body system analyses to optimize linkages, e.g., to
optimize a connecting rod in a slider crank mechanism. The analyses are
coupled because the geometry of the connecting rod determines its mass
properties which are used in a multi-body mechanical system analysis to
evaluate the reaction forces and accelerations which are in turn used as
the loads in a structural finite element analysis.
In multi-body design we are currently studying a unique computationally
efficient means to simulate the flexibility of "rigid body mechanisms.''
Using the theory of pseudo rigid bodies, we can model the flexibility of
each link in the mechanism with only 11 degrees-of-freedom to obtain their
gross motion. Then, a detailed finite element analysis can be performed on
only those links of interest. Thus, we obviate the need to perform a
detailed analysis of every link in the mechanism.
Another interest of mine is to design control strategies which are based on
our open-loop design optimizations. This, for example, can be applied to
trajectory control of flexible bodies and the furnace control in a crystal
growth process. Currently, we are investigating the slewing motion control
of a single flexible link, but in the future these techniques will be
applied to control manufacturing processes such as continuous casting and
polymer extrusion.
Finally, I have always enjoyed the subject of continuum mechanics. We have
several ongoing projects in the elasticity and thermoelasticity of
constrained materials and the linearization of the multi-body equations of
motion.
Present funding for our research comes from The Aluminum Company of America
(ALCOA), Caterpillar Incorporated, Ford Motor Company, the National
Science Foundation and the Department of Energy.Analytical and Computational Mechanics (ACM) Laboratory
Department of Mechanical & Industrial Engineering
College of Engineering
University of Illinois at Urbana-Champaign
Director:
350 Mechanical Engineering Building, (217) 333-5991
Faculty Fellow, Department of Theoretical & Applied Mechanics
Affiliate, Computational Science and Engineering (CSE)
Potential Course Sequences
Group Members
Research Papers
Application to M&IE Graduate Programs
Some useful links
Organizations
Danish Center for Applied Mathematics and Mechanics
Multibody System Dynamics
The International Society for Structural Optimization
United States Association for Computational Mechanics