Spring 2008, MET 415 - FEA Applications I

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

Homework Assignment 1

Concepts:

Basic Modeling		Annotation of Plot
Meshing and Mesh Refinement		Planes of Symmetry
2D Plane Stress Element Types:		PLANE183 vs. PLANE182
Mesh Error Evaluation:	SEPC, Global % Error	SERR, individual element error



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A 12" x 12" x 1" aluminum (6061-T6) plate has a 1" diameter hole at the center.  This plate experiences a (distributed) tensile load of 1000 psi in the horizontal direction.  Determine the stress near the hole. Determine the maximum deflection of the plate.

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This model was developed in class as the "First FEA Model".
For homework:

• Compare results (max. deflection, max. stress, SEPC global mesh error) for the original mesh with both PLANE183 and PLANE182 element types
• Refine the mesh of PLANE182 elements to approach the level of error you had with the PLANE183 model  (at least get < 1%).
• Compare the maximum stress results from the FEA solutions to a hand calculation of the maximum stress at the hole based on classical strength of materials theory.

  Turn in:

• Table of results comparisons (include the model size, i.e., the number of nodes and elements used in each case). At least three FEA analyses are required; more than three may be needed.  
  Results to list: element type, maximum deflection, S Fx, maximum SX stress, mesh error SEPC
• Hand calculation of stress concentration (Include your reference for the formula, etc.)  
  Make a statement comparing the FEA results to the hand calc.
• Hand calculation of the total elongation of the plate in the direction of loading. 
  Make a statement comparing the FEA results to the hand calc.
• An annotated, color (or gray shades) plot of x-direction stress results, SX, from any ONE of your solutions.
• An annotated, color (or gray shades) plot of vonMises stress results, SEQV, from any ONE of your solutions.  
  Write a note comparing the maximum normal stress (SX) to the maximum vonMises stress (SEQV) - why are they similar for this problem ?  why can they be different ?  [Think: How is Mohr's circle used in computing vonMises stress ?]

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