D-04 (Scordelis-Lo Roof) |
  
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D-04 (Scordelis-Lo Roof) |
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Objective
To verify the membrane and bending behavior of the shell element in a curved structure
Problem Description
The Scordelis-Lo barrel roof below [Ref 1, Ref 2] has a length of 50 ft, a radius of 25 ft, and a sweeping angle of 80 degrees. The roof is supported on rigid diaphragms along its two curved edges (Dx and Dy fixed, but not Dz). The two straight edges are free. A surface load of -90 lb/ft^2 in the global Y direction (self weight) is applied to the entire roof.
Material: E = 4.32e8 lb/ft^2 (3e6 psi); v = 0.0;
Thickness: t = 0.25 ft.
Finite Element Model
36 shell elements
Due to symmetry, one quarter of the roof is modeled with a 6x6 mesh. The boundary conditions are specified in the following table.
Nodes |
Fixed DOFs |
N1 to N6 |
Z, OX, OY |
N7 |
X, Z, OX, OY, OZ |
N14, N21, N26, N35, N42 |
X, OY, OZ |
N43 to N48 |
X, Y, OZ |
N49 |
X, Y, OY, OZ |
Model type: 3D Frame and Shell
Results
The results given by ENERCALC 3D compare well with benchmark values.
Units: displacement – ft; stress - ksf
|
Displacement Dy @ N1
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Displacement Dx @ N1
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Top Principal Stress S1 @ N7 |
Bottom Principal Stress S2 @ N7 |
Top Principal Stress S1 @ N1 |
Bottom Principal Stress S1 @ N1 |
MITC4 Compatible |
-0.291 |
-0.153 |
171.74 |
-197.69 |
242.55 |
349.35 |
MITC4 Incompatible |
-0.307 |
-0.162 |
183.97 |
-210.78 |
225.09 |
352.77 |
Kirchhoff Compatible |
-0.290 |
-0.153 |
174.88 |
-200.62 |
238.73 |
351.68 |
Kirchhoff Incompatible |
-0.306 |
-0.161 |
187.55 |
-214.41 |
224.46 |
352.69 |
Benchmark Value |
-0.302 |
-0.159 |
191.23 |
-218.74 |
215.57 |
340.70 |
Comments
The results given by ENERCALC 3D are comparable to the referenced values.
Reference
[1]. MacNeal & Harder, “A Proposed Standard Set of Problems to Test Finite Element Accuracy”, Finite Elements in Analysis and Design, 1 (1985) 3-20
[2]. Scordelis & Lo, “Computer Analysis of Cylindrical Shells”, Journal of the American Concrete Institute, Volume 61, May, 1964
