Transcript Project_4240_IFEMdsg.pptx

RPI MANE 4240 Introduction to Finite Element Methods Spring 2014
Study of the Deformation of a Simply Supported
Square Plate Under Uniform Pressure Using the Finite
Element Method and Comparison with Exact Solution
David Grant
Problem Description and Parameters
Simply
Supported
Boundary
Condition
b
Pressure, q
applied to
surface
a
Navier Solution to Simply Supported Plate
𝑛𝜋𝑦
𝑚𝜋𝑥
𝑠𝑖𝑛
𝑠𝑖𝑛
16𝑞0
𝑎
𝑏
𝑤= 6
2
2 2
𝜋 𝐷
𝑚
𝑛
𝑚=1 𝑛=1
+
𝑎2 𝑏2
∞
∞
Finite Element Method Abaqus Results and Comparison to Navier Solution
Conclusions
•
•
•
•
Abaqus maximum deflection solutions converge to 2.52 E-4 m
Abaqus results change little after a mesh of 10 by 10 elements
Navier maximum deflection solutions converge quickly to 2.22 E-4 m
Abaqus and Navier maximum deflection comparison results in more than
a 13 percent error
• Error likely due to approaching limit on thin plate theory
o Ratio of thickness to width for problem given is 0.1, which may explain
the error of using the Navier Solution
o Could use thick plate theory in future analysis for the same problem and
compare results
Questions?
References
1. Abaqus/ CAE 6.13-1, Dassault Systèmes, 2013
2. Timoshenko, Stephen P., Krieger, S. Woinowsky, Theory of Plates and Shells, 2nd Edition, McGrawHill International Editions, 1959
3. Young, Warren C., Budynas, Richard G., Roark’s Formulas for Stress and Strain, 7th Edition,
McGraw- Hill, 2002.