Nontraditional Applications for Finite Element Analysis

Lorraine Olson
Department of Mechanical Engineeering and Department of Engineering Mechanics
University of Nebraska - Lincoln

Sponsored by the Dept. of Engineering Mechanics

Date: Tuesday, January 30, 2001
Time: 3:30 p.m.
Place: W128 Nebraska Hall


Traditionally, finite element analysis has emphasized solid mechanics, but many of the exciting new areas under development today involve non-traditional and often highly interdisciplinary areas.  My research has evolved from fluid structure interaction problems to these unusual topics, often in collaboration with experts in other fields.  This talk will first give an overview of a number of my previous and current projects, including thermal models for rotational molding, correction of infant skull abnormalities, optimization of thin films, and inverse electrocardiography.  The second part of my talk will focus on my recent work in the solution of inverse problems, particularly inverse heat conduction problems.

Inverse problems occur quite frequently in many different areas of engineering. A properly posed "forward" problem requires complete specification of the governing partial differential equations, knowledge of the material properties, and a definition of all boundary conditions.  In contrast, an "inverse" problem is missing some piece of this information and the goal is to estimate the missing information from measured data.  However, the problems are ill-conditioned so that small changes in the measured data can cause enormous changes in the estimate of the missing data.  To solve these types of inverse problems we have developed a robust formulation based on vector expansions which is quite general and can be used with any set of basis vectors.

In the steady heat conduction area, we are investigating the fusion (combination) of signals which measure temperature with those that measure heat flux for the solution of inverse problems. The types of problems we are examining involve estimating temperature and heat fluxes on one boundary from measurements of temperature and heat fluxes made at remote locations.  We have applied these methods to problems such as identifying heat transfer coefficients on the surface of a pipe from internal measurements of temperature and heat flux, and estimating the tool/chip interface temperature in turning operations from measurements made far from the tool tip.