Introduction to Finite Element Analysis 362-1-3091
Prof.
Zohar Yosibash
Fall 2018
Last update, Jan, 29, 2017
Formulas of conventional and trunk shape functions (pdf)
Quadrilateral trunk space shape functions - By Prof. Ernst Rank (pdf)
Homework Assignments:
- Homework 1 (MS/Word doc)
- Homework 2 (MS/Word doc)
- Homework 3 (MS/Word doc)
- Homework 4 (MS/Word doc)
- Homework 5 (MS/Word doc)
- Homework 6 (MS/Word doc)
Collection
of problems assigned in HWs from
Szabo&Babuska book [bmp files]: Intro p.1 p.2 p.3 p.4 p.5 p.6 p.7
Lectures schedule:
· Week 1: The exact solution vis the FE solution and the discretization error.
The classical formulation for a 1-D rod: The 2nd order ODE and three possible
boundary conditions. Formulation of the weak form – the bilinear and linear form,
the strain energy and energy norm.
· Week 2: Formulation of the principle of minimum potential energy. The finite dimension space and
definition of u_FE. Proof that u_FE is closest to u_EX.
· Week 3: Generation of the stiffness matrix and loading vector for a bar with polynomial shape functions along all of it.
The mapping function, the standard element, shape functions, generation the elemental
stiffness matrix,.
· Week 4: Stiffness matrix, mass matrix and the assembly procedure + examples.
· Week 5: The load vector. The concept of h-,p- and hp- extensions. Treatment of non-homogeneous boundary conditions + spring BC.
Rates of convergence, and classification of exact solutions.
· Week 6: Convergence rates for the h-version on uniform and adaptive mesh, p-version
On uniform and adaptive mesh. Computation of the error in energy norm.
Introduction to 2-D elasticity.
· Week 7: Formulation of the principle of virtual work for 2-D elasticity. The energy space.
Conceptual errors – concentrated force/displacement in 2-D elasticity.
Starting finite elements in 2-D.
· Week 8: Shape functions in 2-D. Vertex, edge and bubble modes.
Shape functions for conventional h-elements.
Blending mapping.
· Week 9: Isoparametric mapping – linear and parabolic
Computation of the 2-D elastic stiffness matrix.
· Week 10: Triangular elements.
· Week 11: Load vector – due to tractions and body forces.
· Week 12: Convergence rates for 2-D elasticity problems.
Final
Project: Final project
assignment (Pdf) due ??.2.2019 
Examples of highly graded final
projects in previous years can be received for inspection in Prof. Yosibash's office.
Mid-term Quiz Examples:
Final-term Quiz Examples:
Quiz
2 - 2000 (GIF File)
Answers to Quiz 2 - 1999 (Executable
File)
Previous years Project
Examples (bmp format):
1998: p.1 p.2
1999a: p.1 p.2
1999b: p.1 p.2
