Zienkiewicz, Taylor- The Finite Element Method
Liu, Quek, The Finite Element Method: A practical course
Learning Objectives
The aim of the course is to provide the necessary concepts, theories and techniques of the Finite Element Method (FEM) for student to be able to use a FEM package to solve structural analysis.
The focus of the course is on developing a good understanding of the fundamentals and principles of FEM analysis in order to evaluate the degree of confidence of FEM results. The student are called to use a FEM program to solve linear and non-linear problems.
Special focus is placed on non-linear problems
Course program
1. Fundamentals for Finite Element Method (FEM)
Introductions
Strong and weak solution
Galerkin method of approximation
2. FEM procedure
Domain Discretization
Displacement Interpolation, Shape Functions
Properties of the Shape Functions
Assembly of Global FE Equation
Solving the Global FE Equation
3. FEM element type
Shape Function
Assembly of the global Stiffness matrix
Solving the FE matrix equation
Convergence property of the element
4. Modelling Techniques
Geoetry modelling
Mesh Density
Element Distortion
Different Order of Elements
Modeling of supports
Modeling of joints
5. Non-linear structural problems
Geometric nonlinearities
Beyond small displacements
Equilibrium paths
Lagrangian coordinates, conservative systems and potential energy, Lagrange Dirichlet theorem
Stability of discrete systems, local equilibrium path, perturbation equations
Costitutive nonlinearities
No tension material
Costitutive equation for no-tension material
FEM solutions for masonry structures