Research
My research interests are in the field of Computational Mechanics, although I have worked on a wide variety of projects. Below is a list of the projects starting with the most current.
Geometry Representation with Reproducing Kernel Element Method (RKEM) Interpolants
Current analysis methodologies solve approximate problems on approximate geometries. A finite element solution is actually an approximate solution on an approximate geometry. This approximate geometry is piecewise linear. While this approximation may not be of concern for a wide range of problems, it could be a source of error in problems involving fluid-structure interaction, nanomechanics, and life science applications.
The aim of this research is to use RKEM interpolants to better represent the geometry. The RKEM interpolants are globally smooth and can reproduce polynomials of arbitrary order.
Isogeometric Analysis using RKEM
A further application of geometry representation using RKEM, is to solve problems isogeometrically, that is, to use the same basis functions in representing the geometry in the analysis.
Meshfree Crack Propagation in Ductile Materials
Meshfree methods are well suited for crack propagation algorithms because their basis functions are defined by support windows as opposed to elements. These windows can be dynamically modified and the functions recomputed as needed. Thus a crack can propagate through a meshfree domain via a particle splitting algorithm and we can use a visibility criteria to modify the supports of nearby particles.
Quasi-Uniformity for RKEM Meshes
RKEM was invented as an effort to maintain the higher order smoothness of meshfree-type interpolants while also achieving the Kronecker-delta property common to finite elements. This adds regularity contraints on the RKEM mesh. These contraints relate to the support size of each RKEM Node.
This project explored and described this condition as well as developed a test for a passing mesh. These tools are used to develop and refine meshes for the aforementioned RKEM projects.
Optimal Utility Placement in the Right of Way
The Florida Department of Transportation is responsibile for regulating the installment of utilities in the underground portion of the Right of Way. They have little basis for what might be a good placement of utilities, nor is there a good record kept of where utilities are placed. The result is expensive relocations during roadway expansions as well as outages due to damaged utilties during installations.
This research proposed a costing algorithm and exhaustive search method to determine optimal placement of utilities. The cost of installing a utility included installation costs, maintenance costs, probably accident costs (the cost of an accident if the utility has a above ground component), probable damage costs, and relocation costs. All of this was incorporated into a tool the FDOT could use to assess a right of way and determine "good" utility placement.
Spread Calculation for Water Flowing Past Concerte Barrier Walls
The Florida Department of Transportation funded research concerning water flow past concrete barrier walls commonly seen in roadway construction. The inlets cut at the bottom of these walls are designed to remove water from the road surface produced by rain. The barrier walls can stretch for miles and are sometimes positioned close to travel lanes.
I took a flow relationship developed by Dr. Kranc and created a Visual Basic program capable of taking in barrier wall information as well as roadway/rainfall information and predicting the amount of water spread back onto the lanes of travel. This tool is used by FDOT to assess safety of their construction plans prior to approval.
Holistic Numerical Methods Institute Simulation Development
This project is designed to bring undergraduates and instructors alike resources for teaching and learning Numerical Methods. For a better project description, visit the project site here. Part of the project is to generate step by step simulations of the methods studied. A student can then see and check intermediate results as they try to understand what is going on in each method. Due to students coming from different schools and having different backgrounds, the simulations were programmed in 4 different languages (Maple, Mathcad, Mathematica, and Matlab).
Numeric Comparison of Cooling Methods in Shrink Fitting of Composite Cylinders
This projected related to a problem presented by the FDOT in the construction of bascule bridges. The fulcrum of the bridges is a long shaft inserted into the main bridge assembly. The shaft is shrink-fitted into the girder using liquid nitrogen. On assembly, the shaft was observed to crack. For more details, read here.
My masters thesis modeled the shaft as a cylinder and used finite differences to solve the thermo-mechanical problem with temperature dependent material properties using finite differences. I compared different cooling methods by stages to reduce likelihood of a crack developing.
