Civil Engineering and Solid Mechanics: A Computational Mechanical Analysis of Classical Building Structures

Course 17: Civil Engineering and Solid Mechanics: A Computational Mechanical Analysis of Classical Building Structures

I. Course Description

Computational mechanics is a new discipline to solve the practical problems in mechanics according to the theory of mechanics, using the modern electronic computer and various numerical methods. It runs through the various branches of mechanics, constantly expanding the research and application scope of mechanics in various fields, and also gradually developing its own theories and methods. The application scope of computational mechanics has been expanded to solid mechanics, rock and soil mechanics, hydraulics, fluid mechanics, biomechanics and other fields. Computational mechanics mainly studies numerical methods, such as further research on finite difference method and finite element method, and explores some new methods and basic theoretical problems.

The course aims to introduce the application of finite element method and computer simulation in engineering and science. Students will learn how to use computers to solve various mechanical problems, and through theoretical explanations and practical calculation exercises, students will gain the ability to apply computing elements to solve practical engineering and scientific problems.

II. Professor Introduction

Ronaldo Borja – Tenured professor at Stanford University

Professor Ronaldo Borja received his Master of Science in Mechanical Engineering (Applied Mechanics) in 1983 and then continued his PhD at Stanford University and received his PhD in 1984. He soon graduated at Stanford University in 1986 and has been teaching for nearly 40 years. Professor Ronaldo Borja is the author of a textbook called Plastic Modeling and Computing.

He also served as the editor of two important journals in his field, the International Journal of Numerical and Analytical Methods of Geomechanics and the Journal of Rock and Soil Mechanics. The professor received the 2016 Maurice A. Biot Medal from the American Society of Civil Engineers for outstanding contributions to civil engineering and applied mechanics for his research on computational hole mechanics.

III. Syllabus

1. Review of linear algebra
2. The determinant of the matrix
3. The rank of the matrix
4. Finite difference (FD) method
5. Taylor series
6. Precision of the finite-difference equation
7. Finite element (FE) method
8. The Galregin approximation
9. Matrix form
10. Numerical integration