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
|Intercultural skills||Communication skills||Specialist 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||FEM modeling & meshing issues||Understand the whole procedure of FEM modeling & meshing issues.|
|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||Boundary element method - one dimensional problems||Explain the formulation of boundary element method for one dimensional problem.|
|Class 7||Boundary element method - multidimensional problems||Explain the formulation of boundary element method for multidimensional problem.|
|Class 8||Boundary element method - numerical schemes & examples||Explain numerical schemes of boundary element method, and show some examples.|
|Class 9||Midterm review (exam)||Reviewing BEM and FEM|
|Class 10||FEM implementation: 1D & 2D problems||Students must derive FEM equations: stiffness matrix, loading vector, etc. using energy methods and their implementation|
|Class 11||Triangular & Rectangular elements||Establish formulation for triangular and rectangular elements|
|Class 12||Iso-parametric elements||Establish formulation for iso-parameter elements (e.g., Jacobian matrix, mapping, and its implementation.)|
|Class 13||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 14||Some applications to civil engineering analysis & review||Understand some practical problems in civil engineering analysis using numerical methods|
|Class 15||Final review (examination)||Final review by examination.|
Lecture materials will be uploaded on OCW-i.
Midterm exam (40%) and final exam (60%)
Students must have successfully completed Computers and Fundamental Programming (CVE.M301) and Computers and Applied Programming (CVE.M302), or have equivalent knowledge.