METBD 451 - Lab 4

Fall 2000, METBD 451 - FEA Dynamic Applications

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

FEA Lab Final Project

General Transient Dynamics FEA Models

Concepts:

Contact finite elements/Impact
Full Transient Dynamic Analysis
Time Integration and Initial Conditions
Time History Postprocessor
Animation, Over Time

A solid block, 6 in. by 6 in. cross-section, is dropped from 100 in. above a flexible base. The block is released from rest at a position which is off-center with respect to the base.

Treat this as a 2D system:

use 2D plane stress triangle elements (unit thickness) to model the block (obviously, we are not concerned with the stresses developed in the block), Set the element size to one element per line when you mesh the block area.

use 2D beam elements, each 5 in. long, to model the 100 in. long base.

The beam cross-section is 0.5 sq. in., the area moment of inertia is 0.0521 in⁴, and the beam height is 0.5 in.

Handle the "interaction" of the block and base with 2D general contact and target elements. Create general contact elements from all surfaces of the block (contactors) to all upper faces on the beams (targets). Use a coefficient of friction of 0.1 for this assignment.

The material of both the block and the base has: Modulus = 1x10⁶ psi, Mass Density = 0.001 lbf-s²/in⁴, Poisson's Ratio = 0.3

Use a damping multiplier of 0.0003 based on the stiffness matrix (Beta damping factor) and of 2x10^-6 based on the mass matrix (Alpha damping factor).

Hand calculations:

Time of impact based on free-fall behavior
Transverse (or bending) natural frequencies of the "clamped-clamped" beam
What effective damping ratio, x, is produced at each of the beam's modes by the beta damping value of 0.0003 and the alpha damping value of 2x10^-6 ?

Initial Conditions:

Starting from rest (static), no initial velocity
Gravity load acts on the entire structure.

Solution:

Establish initial static (no time integration) state (load step 1) over a very short time interval.
Then, simulate 5 seconds of dynamic response after releasing the block (load step 2). Gravity remains on for this step.
Include large deflection/large rotation effects.
Choose integration times step size based on the expected response frequencies of the base.
Make (and document) your own decisions on nonlinear solution controls: equilibrium iterations, convergence criteria, automatic time stepping and ranges, contact element options, output controls for your results file.

Animate, Deformed Shape, Over Time (for an in-class homework grade)

Report:

Include plots showing the model (different element types) and the boundary conditions
Include time history plots of the vertical motion of the center of the beam, of a corner of the block, and of the vertical reaction forces at both ends of the beam. What response frequency can you determine from the time history plots ?
Include time history plots of the integration time step size, no. of equilibrium iterations, and response frequency
Describe the vibration of the base that is observed in the animation (is it 1st mode bending or higher modes ?). Compare to the calculated natural frequencies of the base. Does this response match the hand calculations ?
Include a session log file (of Essential Commands ONLY), to which you have added comments describing the process of modeling, loading, and solving the transient analysis.

Reminder: All project reports will be typed, and include:

a cover page with course name, project name, team names, and date
a brief objective statement (2-3 sentences, maximum)
a summary of procedures (bulleted items: assumptions, data, analysis steps)
a conclusion statement, which includes:
- (what was learned, perhaps an evaluation of the design)
- describe what the plots of the solution summary items tell you about the model and solution
a copy of the project statement (this web page) may be attached.