Transcript ME160 Sp 16 Project Slides

ME 160 Introduction to Finite Element Method-Spring 2016
Topics for Term Projects by Teams of 2 Students
Instructor: Tai-Ran Hsu, Professor, Dept. of Mechanical engineering, San Jose State University, San Jose, CA, USA
Two-Tier projects for students in ME 160 class
● Tier 1 Projects: Use www.ansys.com/student software (50% bonus marks for using ANSYS code.
Learning and use of the ANSYS code is specified in
the “course goal” in the “green sheet” of ME 160)
● Tier 2 Projects: Use computational methods learned from the course for solutions.
General evaluation criteria for all projects:
1)
2)
3)
4)
Demonstration of learning and understanding of the FEM,
The degree of complexity of the signed up projects ,
Research on missing information required for the projects,
Sophistication in using the FE models to demonstrate the value of this method in solving
advanced analytical engineering problems that cannot be solved by available methods,
5) Demonstrate the wisdom in constructing FE models that make sense to engineering principles,
and interpret FE results correctly and realistically.
6) Quality of project report (limit to 3 printed pages for the text, but with no limit on appendices)
Deadline for submission project report: 4 PM, Tuesday, May 24, 2016. No late submission will be accepted.
Proposed Tier 1 Project topics
Solve the Assigned Projects using ANSYS CODE
(free download from: www.abyss.com/student)
● Description of the project (less than a page)
● Input file
● Material data file
● FE model
● Loading and boundary conditions
● Output file
Show the results in graphic forms
● Interpretation of results
● Discussion on the results
Project 1.1: Determine impact load to crash the helmets (2 teams-one on each)
Project 1.1(a) Cyclist’s helmet
Project 1.1 (b) Football player’s helmet
Project 1.2: Comparison of stress concentration of windows of: “standard shapes”, circular and square with same open areas
Project 1.3: Also use the S/N curve in the next slide to predict the fatigue life of the aluminum fuselage with 3 window
configurations of: circular, square, and rectangular with round corners
2 to 3 teams
• Research on commercial
aircraft windows and
cabin pressure control, and
cabin dimensions will be
desirable.
• Treat windows on thin
aluminum panels subjected to
cabin pressure normal to the
panel.
• One take-off/landing counts
as one loading cycle.
Treat as flat panels with normal pressure loading
Typical S/N curve for aluminum and steel
Use maximum stress in structure as “S” to predict the “Number of cycles for “N”
Project 1.4: Assess the fatigue life of (a) steel shaft (2) aluminum shaft (2 teams)
Predict the fatigue life of the steel (or aluminum) stepped shaft subject to axial tensile force of 20,000 N.
You set your own dimensions on realistic solid structures:
Project 1.5: Determine the maximum stresses in the following perforate panels made of steel
subject to 20,000 N in-plane tensile force along the horizontal coordinate:
(3 teams:
One on each
of the
following):
Multiple holes of the same size
(size-pitch)
Single hole with different diameters
Single or multiple square holes
(size-pitch)
Determine the stress fields and maximum stress in the following 3-D solid structures
with additional 10 bonus marks
Project 1.6: 3-D shell/nozzle assemblies (2 teams)
Project 1.7: 3-D solid plate or alike (2 teams)
Tier 2 Projects
Solve problems using the principle, theories and formulations
of FEM learned from the course
● Description of the problem
● FE formulations used to solve the problem with references to the
lecture notes or other reference sources
● Detailed computations with every major step in computation
● Input data
● Output results with graphical displays
● Verify results if possible
● Interpretation and discussion on numerical results
● Attach computer program, including MS Excel (spread sheets) if applicable
Project 2.1(a) : FE analysis of truss structure (one team)
Determine the displacement components at Node 3 and the
element forces for the plane truss shown in the figure.
Let A = 3 in2 and E = 30x106 psi for all elements.
4
5000 lb
Derive the interpolation function for each element and
show the element equations and the assembly of the overall
stiffness equation with partitioning of the assembled
overall stiffness matrix.
Solution of the overall stiffness equation for nodal
displacements and element stresses using MS Excel
(spread sheets).
20 ft
3
3
1
10000 lb
1
2
40 ft
2
30 ft
30 ft
Project 2.1(b) : FE analysis of truss structure (one team)
2
Determine the displacement components at Node 3 and the
element forces for the plane truss shown in the figure.
Let A = 4x10-4 m2 and E = 210 GPa for all elements.
Derive the interpolation function for each element and
show the element equations and the assembly of the overall
stiffness equation with partitioning of the assembled
overall stiffness matrix.
1
3
3m
2m
1
2
W = 40 kN
Solution of the overall stiffness equation for nodal
displacements and element stresses using MS Excel
(spread sheets).
3
4
Project 2.2(a) : FE analysis of beam structure (one team)
A redundant beam shown in the figure below is subjected to both concentrate force P and uniform distributed load
w per unit length of the beam with total length L = 10 m.
Use the finite element method to determine the deflections along the length of the beam. The beam has a
Young’s modulus of 210 GPa, and has a rectangular cross-section with width b = 10 cm and depth h = 20 cm.
The applied load includes: P = 10 kN, and w = 500 N/m.
Show all FE formulations you used in this project.
Project 2.1(b) : FE analysis of truss (one team)
P
L/2
L
W N/unit length
Project 2.2(b) : FE analysis of beam structure (one team)
A redundant beam shown in the figure below has an internal hinge. There is an applied weight of W = 5 kN at the
hinge. Use the finite element method to determine the deflections at the hinge and point A and B. And also the
bending stresses along the length of the beam. The beam has a Young’s modulus of 210 GPa and a section moment
of inertia I = 2x10-4 m4. Show all FE formulations you used in this project.
2m
2m
B
A
1m
1.5 m
W = 5 kN
Project 2.3(a) : FE analysis of 2-D solid structures (one team)
Use the finite element method to determine the 2 displacement components at each node, and 3 stress components in
each element in the structure shown in the figure below. The structure is made of aluminum with Young’s modulus E =
69 GPa and Poisson’s ratio υ = 0.3. Show all FE formulations you used in this project. 10 bonus points will be allowed
for using MS Excel (spread sheets) for solving the overall stiffness equation of the structure). (Unit for physical
dimensions is m, and the unit for force is N) Tabulate your outputs.
Project 2.3(b) : FE analysis of 2-D solid structures (one team)
Perform FE stress analysis on the 2-D solid structure as in Project 4.1(a) but with 10 times the physical dimensions and
use material properties for steel with E = 210 MPa and the same Poisson’s ratio but is subject to Pm = 50,000 N