Spring 2008, MET 415 - FEA Applications I

Prof. Dave Johnson, dhj1@psu.edu

Penn State - Erie, The Behrend College

Homework Assignment 3B

Concepts:

• 2D Plane Stress (with thickness) Element Types
  • 2D 8-Node Structural Solid
  • Behavior Option: Plane Stress w/Thickness
  • Real Constant for thickness value
• Model construction with load features
  • For proper placement of loads, edges of the model must be "broken" such that a keypoint or a line is positioned to allow the desired loading.  
  • Lines may be "divided" by various Boolean operations.
  • Keypoints that are NOT end points of a line are also not part of your model and will not produce a useful loading location.
• Concentrated (Point) Loads / Knife-edge supports (singularity)
  • Singularity: (mathematical) point where a solution is undefined (infinite stress)
    • Sharp, inside corners that are not modeled with a fillet radius
    • point loads or point constraints
  • FEA results at and very close to a singularity must be ignored/excluded
• Solution and Postprocessing: Multiple Load Steps
  • Sequential Load Steps:
    • Define loading and constraints
    • Solve, Current LS
    • Change and loads or constraints
    • Solve, Current LS again
    • Repeat, if needed
    • Do NOT leave the solution processor between solves
  • Postprocessing:
    • Summary - to see how much data is available on the results file
    • Read Results to examine each set
    • Plot Legend shows Load Step number / Time
      

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A wood 2" x 4" beam (actual size is 1-5/8" x 3-5/8") and 72" long is simply supported.

Modulus of elasticity: 1.7x10⁶ psi
Density: 0.025 lbm/in³ [consider: are lbm units proper ?]
Poisson's Ratio: 0.25

The loads acting on the beam include:

1. a uniform distributed load of 5 lbf/in centered over 48 in. of the beam
   [2D FEA elements do NOT accept an edge load in lbf/in - convert to pressure (in psi)]
2. two concentrated loads, each  50 lbf, located 20 in. from each end
3. the weight of the beam [simply define material density & gravity for weight]

Consider each load individually, then ALL loads combined.

Turn in:

• A plot showing the elements
• A plot showing constraints, and ALL of the loads.
• A plot showing the normal stress (SX) for each of the load cases (4 cases).
• Make a table to compare the maximum deflection and maximum normal stress (SX) for each load case.  
  • Include in the table, a hand calculation of the vertical force acting on the beam for each load case compared to the ANSYS reaction solution for the corresponding load case.
  • Also, include in the table the mesh error measure for each load case.  (Several load cases may give relatively high SEPC - that may be OK because of point loads and constraints (singularity) - but make sure you have not created a condition of "excessive constraint")
• A hand calculation of the beam deflection at the center of the beam and a calculation of the max. normal stress in the beam for the combined load case COMPARED to the ANSYS solution results.  (Include your reference for the hand calc. formula.  Include any assumptions you make to simplify the hand calculations.)
  • How will you find the deflection at the neutral axis of the beam (use "Selecting" maybe) ?  Use approximate value from a contour plot band for DOF Solution, UY ?

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