Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering

Committee Chair(s)

Wenbin Yu


Wenbin Yu


Steven L. Folkman


Thomas H. Fronk


Ling Liu


Marvin W. Halling


The applications of heterogeneous materials and other materials with engineered microstructures growth rapidly in all industries to achieve better performance. These materials and structures are defined such as composites and nanotube. With the increasing of computing power, though the well-established commercial finite element analysis (FEA) has the ability to analyze such material of a small portion. It is not feasible for the structure level, since the computing requirements of a finite element model can easily exceed the bearable time in analysis or the capability of the best mainstream computers. To reduce the computational efforts, an efficient way is to use a simpler and coarser mesh at the structure level with the micro level complexities captured by a homogenization method.

The homogenization method covers two parts. The first one is to calculate the equivalent material properties from heterogeneous materials or structures as an input for structural level analysis, and the second one is to use the behaviors from the structural lever to recover the local behavior in the heterogeneities.

The main point in the dissertation is to extend the application of homogenization method, which is based on variational asymptotic method developed recently as the Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), to some real engineering structures and materials. A unit cell could be a small potion of heterogeneous material or a representive microstructure, which is further defined as a representative structural element (RSE). In the present research, the following problems are presented: (1) Maximizing the flexibility of choosing a RSE; (2) Bounding the effective properties of a random RSE; (3) Obtaining the equivalent plate stiffnesses for a corrugated plate from a RSE; (4) Extending the shell element of relative degree of freedom to analyze thin-walled RSE.

These problems covered some important topics in homogenization theory. Firstly, the rules need to be followed when choosing a unit cell from a structure that can be homogenized. Secondly, for a randomly packed structure, the efficient way to predict effective material properties is to predict their bounds. Then, the composite material homogenization and the structural homogenization can be unified from a mathematical point of view, thus the repeating structure can be always simplified by the homogenization method. Lastly, the efficiency of analyzing thin-walled structures has been enhanced by the new type of shell element. In this research, the first two topics have been solved numerically through the finite element method under the framework of VAMUCH. The third one has been solved both analytically and numerically, and in the last, a new type of element has been implemented in VAMUCH to adapt the characteristics of a thin-walled problem. Numerous examples have demonstrated VAMUCH application and accuracy as a general-purpose analysis tool for real engineering problems.



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