Fall 2005, METBD450 - FEA Applications II

Constraint Equations

Prof. Dave Johnson, dhj1@psu.edu, Penn State - Erie, The Behrend College

Homework Assignment 4-B

Concepts:

• Constraint Equations (CEQN's) can connect models with dissimilar DOF's
• 2D 4-node Quad (UX, UY) and 2D Elastic Beam (UX, UY, ROTZ)
• Beam element properties and real constants
• Rigid Region (CERIG)

A 20 mm. x 40 mm. x 10 mm. solid block of aluminum has a 10mm. square x 30 mm long solid steel "breaker bar" attached rigidly to the top edge.
Aluminum material: E = 73,000 MPa, Poisson's ratio = 0.32
Steel material: E = 207,000 MPa, Poisson's ratio = 0.30
A concentrated force load (FX) of 500 N acts on the far end of the bar.
The lines of the base are constrained in UY
The keypoint at the center of the base is fixed in UX.

Use the RIGID Region to attach the base of the steel beam to all nodes on the top of the aluminum.  (CERIG option:  UXYZ , should be set for the 2D translational DOF of the solid elements to the 2D translations + rotation DOF of the beam).  The steel beam's base node should be the "master" for the rigid region, all the other nodes along the top of the aluminum block are to be the "slaves" for the rigid region. 

What symmetry exists in this system ?

Turn in:

• Element plot or plots showing the mesh for your model, showing: 
  • the different REAL constants and 
  • showing the different MATerial assignments
• An node plot showing all boundary conditions including the CEQN's.
• An ANSYS listing of the constraint equations which were generated (CELIST).
• A contour plot of the vonMises stress
•  A contour plot of the y-direction (SY) stress in this part.
• A plot showing the maximum stress in the BEAM elements
• Plots illustrating the mesh discretization error (to support the max. stress results).
• Check sum of forces (FSUM) by selecting only the nodes of the solid, i.e., 0 <= y <= 40 mm. to verify the bending moment used in the hand calc.
• Hand Calculation of the maximum stress at the fixed end (or base) of a cantilever beam with a tip load.
• Include the annotated log file, showing the model generation and solution.

ANSYS Workbench (3D model using "bonded" contact)

Turn in:

• A solid model plot showing ALL boundary conditions
• A solid model plot (or plots) showing all bonded contact regions
• A plot of the element mesh (record the number of nodes and elements, and the element types used for the simulation)
• A contour plot of the vonMises stress.
• A contour plot of the y-direction (SY) stress in this part.
• A plot showing the total deformation of the model.
• A plot showing contact "pressure" distribution between the two parts
• Plots illustrating the mesh discretization error (to support the max. stress results).  Also, report SEPC (the overall % error in the mesh)
• Check sum of forces (FSUM) by selecting only the nodes of the solid, i.e., 0 <= y <= 40 mm. to verify (confirm) the bending moment used in the hand calc.
• Hand Calculation of the maximum stress at the fixed end (or base) of a cantilever beam with a tip load compared to the appropriate FEA model results.
• ANSWER this question:  Based on SEPC and SERR results, can you expect a good comparison of the hand calc to the FEA model results ?