Assignment
Projects Project can be done individually or in teams of no more than two students. Each project can be one of two general types of projects: 1) Perform a finite element simulation of a problem for which either an analytical solution or experimental data is available. The analysis must include a mesh convergence study to verify accuracy. 2) Code development Develop and validate source code using Matlab or other programming language to implement some aspect of finite element analysis.
1
Project Deadlines
Submit proposal (approx 1-2 pages) via e-mail to [e-mail] by 3/27. Students submitting ideas already submitted will be asked to submit an alternate topic. Early submission of ideas is therefore encouraged. Proposal shall include: 1) a brief description of the problem to be solved, 2) Discussion of background information including relevant analytical solutions, experimental data, and/or procedure to be implemented (be sure to include references) and 3) preferred date of presentation. Progress reports showing preliminary results, modeling questions, etc. are due Thursday 4/9. Students are encouraged to see me with project questions. In-class presentations (including submission of Powerpoint presentations) are planned for 4/23 & 4/28. Powerpoint presentations will be posted on the course web page. Project reports are due 4/29 (last day of classes). Please submit both hard copy printouts and electronic copies (MS Word or pdf) of your report. The quiz during finals week will include questions related to selected projects.
2
Potential Project Topics
Axial and transverse shear stresses in laminated beams plates under bending Code development implement a particular element formulation in Matlab (or other programming language) Comparison of available 3-D mesh generation algorithms (Abaqus, Cosmos, Hypermesh) Comparison of tetrahedral vs. hexahedral element performance Contact stresses between two cylinders (Hertzian contact) Elastic-plastic beam bending Elastic-plastic torsion Evaluation of column buckling formulas using 2-D & 3-D solid elements (Euler / Johnson)
3
Potential Project Topics (cont.)
Evaluation of transverse properties of fiber reinforced composites Free-edge interlaminar stresses in composite laminates Heat (steady conduction state or transient) Literature review and implementation of a mesh generation algorithm Study of shear coupling effects in composite laminates Thermal stress effects Torsion of non-circular shafts Vibrating string and/or plate Wave propagation
4
Potential Project Topics (cont.)
Sources of other project ideas: texts on Mechanics of Materials (CVE 220), Machine Design (MCE 301 / 302), Advanced Mechanics of Materials (MCE 426), Mechanics of Composite Materials (MCE 440), Heat and Mass Transfer (MCE 448)
5
Chapter 6. Plane Stress / Plane Strain (cont.)
Step 4 Derive Element Equations
p = U + p + S + B
which will be used to derive
[ k ] = tA [ B] [ D][ B]
T
6x6 6x3 3x3 3x6
6
Derive Element Equations (cont.) Strain energy:
7
Derive Element Equations (cont.) Potential energy of applied loads:
8
Derive Element Equations (cont.) Potential energy:
9
Derive Element Equations (cont.) Substitute
to yield
10
Derive Element Equations (cont.)
Apply principle of minimum potential energy
To obtain
11
Derive Element Equations (cont.)
Element stiffness matrix
12
Steps 4-7
4. Assemble global equations 5. Solve for nodal displacements 6. Compute element stresses (constant within each element)
13
Example CST element stiffness matrix
14
CST Element Stiffness Matrix
[ k ] = tA [ B] [ D][ B]
T
where [B] depends on nodal coord...