Projects (past):

7. VSD systems for near-real-time aseismic structural control
(joint with C. Gantes, National Technical University of Athens)

In this work we seek to develop practical guidelines for both the design and operation stages of variable-stiffness devices, aiming at mitigating seismic hazard in structures.

6. Absorbing boundaries for elastodynamics

In this work we seek to develop efficient methods for modeling unbounded media in both the frequency- and (directly) in the time-domain. Such problems, especially in three dimensions, can quickly become computationally intractable. We seek to minimize the computational cost associated with the modeling of unbounded domains in the presence of elastodynamics or acoustic operators. Of particular interest is the seamless coupling of the artificial boundaries with the underlying numerical scheme. A wide array of engineering problems stands to benefit; such problems include soil-structure interaction, acoustic wave propagation problems (air-borne or underwater), seismic wave propagation, etc.

5. Vehicle rapid hit avoidance scenarios
(joint with R. Longoria, UT; J.L. Tassoulas, UT)

Numerical studies of vehicle-to-ground interaction that allow rapid vehicle movement (within 1-3s) away from an incoming projectile.

4. Scatterer detection in inverse scattering problems

The goal here is the detection of the shape and location of rigid scatterers fully embedded in an acoustic medium using incomplete information from sparsely spaced sensors. Contrary to most approaches, here the sensors do not circumscribe the scatterer. We use amplitude-based continuation schemes that iterate over the wavenumber and direction spaces to arrive at the (global) minimum of appropriately defined misfit functionals. We use boundary integral equations for the resolution of the forward problem, and a PDE-constrained optimization approach for casting the inverse problem. We use both numerical differentiation and a direct scheme based on material derivatives for computing the gradients of the misfit functionals.

3. Fictitious domain methods in elasticity

In this work the goal is to offer a viable alternative to the modeling of geometrically complex domains that would otherwise need extremely fine unstructured meshes for yielding satisfactory results. The approach we follow is based on novel ideas that exploit regular grids and do not need the explicit definition of material boundaries. Problems in all fields of engineering dealing with the modeling of PDEs stand to benefit. Our focus here is a prototype contact problem in elasticity with an application to biomechanics.

2. Multi-domain interface problems using the SGBEM

In this work we develop a unified variational framework for treating (linear) interface problems in mechanics using the symmetric Galerkin boundary element method. Of interest are problems with bi-material interfaces in two and three dimensions.

1. Damage identification in simple structural components

In this work we developed optimization-based algorithms for inferring damage in simple structural components from sparse measurements of dynamic properties. The problem is representative of a more general class of inverse problems with significant applications to structural health monitoring. Preliminary results to date have shown relatively reliable predictions for moderate levels of damage in simple components.

Graduate Student Supervision:

Current:
Seong-Won Na -- PhD candidate
Inverse problems

Aaron Pebley -- MS candidate
Dynamic modeling of cables in cable-stayed bridges

Adam Cryer -- MS candidate
Modeling of vessel impact on bridge piers

Graduated:
Sanghoon Lee -- PhD (now with LG E&C Corporation, Seoul, Korea)
Weakly Non-Local Arbitrarily-Shaped Absorbing Boundary Conditions for Acoustics
and Elastodynamics - Theory and Numerical Experiments

Tanjeet Juneja -- MS (now with Matrix Structural Engineers, Houston, TX)
A symmetric Galerkin boundary element method for multi-domain interface problems

Surapap Prompattaraporn -- MS (now 2nd Lieutenant, Thai Army, Thailand)
An optimization-based algorithm for damage detection in simple structural components