Introduction to Integrative Engineering

Guigen Zhang, Ph.D., is Professor of Bioengineering and Professor of Electri- cal and Computer Engineering at Clemson University. He is also the Executive Director of the Institute for Biological Interfaces of Engineering, a research and education/training institute designated by the South Carolina Commission on Higher Education. Professor Zhang is a fellow of the American Institute for Medical and Biological Engineering (AIMBE). He has published extensively in the areas of biosensors, biomechanics, biomaterials and computational modeling. Over the years, his research has been funded by diverse funding sources ranging from federal agencies such as National Institutes for Health and National Science Foundation, to private foundations like the Bill and Melinda Gates Foundation, to venture groups and state-level startup funds, as well as industries in the health-care, semiconductors, and data-storage sectors. Professor Zhang holds numerous patents in nanotechnology-enhanced structures and biosensors. Aside from his services on the editorial boards of numerous scientific journals, Pro- fessor Zhang is also active in serving leadership roles in professional societies. He is currently the Executive Editor of the Biomaterials Forum of the Society For Biomaterials (SFB), and President of the Institute of Biological Engineer- ing (IBE), a professional society that supports the community of scientists and engineers who are at the forefront of creating new linkages between biology and engineering and seeking new opportunities through Biology-Inspired engineering.

I Readying the Integrative Mindset

1 From Compartmentalized Disciplines to Transdiscipline

II Cracking Open the Blackbox of Computational Modeling

2 Engineering Problems and Partial Differential Equations

3 Where Do Differential Equations Come From?

4 Approximate Solutions to Differential Equations

5 Discretization of Physical Domains

6 Solving Differential Equations Computationally

7 Scalar Field Problems in Higher Dimensions8 Vector Field Problems in Higher Dimensions

9 Axisymmetric Scalar and Vector Field Problems

10 Isoparametric Elements

11 Gauss Quadrature and Numerical Integration

12 Dealing with Generalized PDEs13 Errors in FEM Results

III Developing Hands-On Modeling Skills 327

14 A Quick Tour of the COMSOL Modeling Environment

15 A Glimpse of the ABAQUS and ANSYS User Interfaces16 Dealing with Problems of Biomedical and Regulatory Interest

IV Useful Knowledge

A Mechanics of Materials

B Useful Mathematic Knowledge

Index