Seminar Series - 1999-2000

Shape Optimization of Elastic and Thermoelastic Materials Using a Meshless Method:  Optimization of Shape and Structure of Functionally Graded Materials

Florin Bobaru, Doctoral Candidate
Dept. of Theoretical and Applied Mechanics
Cornell University

Sponsored by the Dept. of Engineering Mechanics

Date:  Tuesday, May 2, 2000
Time:  3:30 p.m.
Place:  N129 Walter Scott Engineering Center


A major current theme in structural and non-structural materials research is the study of a special type of composites, namely Functionally Graded Materials (FGM's). Successful design of FGM's for particular application requirements depends crucially on the analytical and numerical models used. Of primary importance is the combination of shape, structure and topology optimization of this new generation of “smart” materials for applications ranging from engine components to implants for humans.

In my talk I will present some recently obtained results in shape optimization of elastic structures using a meshless method (namely the Element-Free Galerkin method - EFG), current progress in shape optimization of thermoelastic materials, and future plans aimed at the combination of shape and composition optimization of FGM's using a meshless method.

Meshless methods have been a very intense area of research for the past six-seven years. They offer greater flexibility than the FEM or BEM but often at a higher computational cost. However, in certain problems, such as shape optimization, large deformation plasticity, etc., they represent a better choice since remeshing can be avoided.

A variational formulation for shape design sensitivity was derived and implemented using the EFG. This was subsequently applied to shape optimization of an elastic system.  My current research extends the EFG shape optimization to steady-state and transient thermoelastic problems, as a first step toward optimization of FGM's. By the nature of their applications, FGM's have to sustain high thermal stresses and thermal shocks. Minimizing these stresses by grading the composition of the composite is one of the targets in designing FGM's.

Two main options for modeling FGM's have been used in the literature:  discretization to the level of the microstructure and homogenized models. The former are often times impractical and consequently the latter are chosen for analytical and/or numerical solutions. In a homogenized model the FGM is discretized in several homogeneous layers which have their corresponding effective elastic, thermal, etc. properties evaluated using an averaging method. Popular “homogenization” choices are: the rule of mixture, the Mori-Tanaka theory, and self-consistent methods. Recent results (Reiter and Dvorak (1999)) based on the FEM suggest that, in some instances, a combination of the Mori-Tanaka theory and self consistent method gives close results to the ones obtained by discretization to the level of the microstructure.

I will highlight some key points where meshless methods can be very helpful in the combined structure shape optimization of FGM's.


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