This course aims to teach concepts, fundamental knowledge and implementation of advanced numerical approaches for civil engineering problems analysis. In particular, the lecture details the formulation of numerical approaches including variational methods, which are closely related to the most popular numerical methods, i.e., boundary element methods (BEM) or finite element methods (FEM). Fundamental concepts and detail on some implementation aspects of both BEM and FEM in 1-D and 2-D are taught. Some practical aspects on the BEM and FEM, e.g., model generation, meshing issues, validation and verification, results, documentation, computer programming, and typical examples in civil engineering problems are also given.
This is an entry level graduate course, which is to give introduction to most popular numerical methods (e.g., BEM, FEM) through applications to several civil engineering problems. The emphasis will be on theories, numerical schemes in linear analysis and applications. The course is expected to provide fundamental concepts of computational methods, and more importantly, to lay foundation for students beginning to engage in research projects that involve implementations of engineering problems using numerical methods.
Upon completion of the course, the students will be able to:
1. Describe and apply basic numerical methods for solving civil engineering problems.
2. Understand and explain the relationship among variational methods, weighted residuals, Galerkin methods, FEM, and BEM.
3. Explain theories and numerical schemes of BEM and linear FEM.
4. Develop algorithms and programs of FEM and BEM for simple problems
5. Understand the importance of numerical simulations of engineering problems using advanced numerical methods, particularly civil engineering problems.
weighted residual method, numerical analysis, approximation, finite element method, boundary element method, computational engineering, numerical methods
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
This course will be mainly provided in lecture style. However, practical exercises with programming for finite element method and boundary element method are included to allow students to get a good understanding of fundamentals for numerical analysis.
|Course schedule||Required learning|
|Class 1||Introduction to the course theme & math review||Understand the course’s objective and fundamental of mathematics used for numerical methods .|
|Class 2||Direct stiffness method (bar & truss elements)||Students must solve some examples for bar & truss using DSM.|
|Class 3||Stress-strain analysis & FEM modeling||Understand the whole procedure of stress-strain analysis and FEM modeling.|
|Class 4||Variational method -1 (Weight residual methods, Galerkin method)||Students must explain weight residual method (Galerkin method) and solve some related problems.|
|Class 5||Variational method – 2 (Energy method)||Student must explain FE approximation, formal procedure, energy method and solve some examples.|
|Class 6||Basic programming FEM: 1D & 2D problems||Students must gain basic programming skill of FEM for 1D and 2D problems.|
|Class 7||Triangular & Rectangular elements||Establish formulation for triangular and rectangular elements|
|Class 8||Iso-parametric elements||Establish formulation for iso-parameter elements (e.g., Jacobian matrix, mapping, and its implementation.)|
|Class 9||Numerical integration in FEM & some special elements||Students must calculate the numerical integration in FEM (Gaussian technique) & establish formulation for some special elements (e.g., 3D elements, polygonal element, adaptive algorithm)|
|Class 10||Review & Examples on Civil Engineering Analysis||Understand some practical problems in civil engineering analysis using numerical methods|
|Class 11||Exam for review||review by exam|
|Class 12||Boundary element method - one dimensional problems||Explain the formulation of boundary element method for one dimensional problem.|
|Class 13||Boundary element method - multidimensional problems||Explain the formulation of boundary element method for multidimensional problem.|
|Class 14||Boundary element method - numerical schemes & examples||Explain numerical schemes of boundary element method, and show some examples.|
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Lecture materials will be uploaded on OCW-i.
Review(exam) (70%) and assignment (30%)
Students must have successfully completed Computers and Fundamental Programming (CVE.M301) and Computers and Applied Programming (CVE.M302), or have equivalent knowledge.