Introduction to Finite Element Analysis 362-1-3091
Prof.
Zohar Yosibash Spring 2012
Last update, April, 29, 2012
Formulas of conventional and trunk shape functions (pdf)
Quadrilateral trunk space shape functions - By Prof. Ernst Rank (pdf)
Links to other Tutorials:
A very good tutorial on xxxxx can be found
HERE.
A very good tutorial on yyyyy can be found HERE.
Homework Assignments:
- Homework 1 (MS/Word doc) assigned ??/2009 due ??/2009
- Homework 2 (MS/Word doc) assigned ??/2009 due ??/2009
- Homework 3 (MS/Word doc) assigned ??/2009 due ??/2009
- Homework 4 (MS/Word doc) assigned ??/2009 due ??/2009
- Homework 5 (MS/Word doc) assigned ??/2009 due ??/2009
- Homework 6 (MS/Word doc) assigned ??/2009 due ??/2009
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: Load vector – due to tractions and body forces.
.
· Week 11: Convergence rates for 2-D elasticity problems.
Final
Project: Final project
assignment (Pdf) due 25, July, 2012 
The parasolid file of the femur 
can be downloaded here.
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
