4. Scordelis-Lo Roof

The Scordelis-Lo roof is a classical test case for linear static analysis named after the authors who first reported it.[5]The test has been proposed as a standard FE test by MacNeal and Harder[6] and it can be found in the NAFEMS test case description.

The structure consist of a concrete cylindrical shell roof supported by rigid diaphragms on both curved sides. The structure is loaded by its own weight of 90 per unit surface. The length of the cylinder is 50, radius is 25, thickness is 0.25. Material properties are isotropic, with E=4.32108 and ν=0.

The diaphragms are defined such that a simply supported boundary condition results: Displacements in x- and y-directions are suppressed. The figure below shows the FE mesh modeling a quarter of the structure, taking advantage of double symmetry.

Scordelis-Lo Roof: Mesh and boundary conditions (1/4 of structure modeled), 6 by 6 Q4 mesh.

Figure 8. Scordelis-Lo Roof: Mesh and boundary conditions (1/4 of structure modeled), 6 by 6 Q4 mesh.


The test is run with Q4S.MITC.E4, Q8.S.MITC, and Q9.S.MITC shell elements, comparing the global y-displacement at point A to the reported solution of 0.3024.

Scordelis-Lo Roof: Deformed shape (y-displacements), 10 by 10 Q4 mesh.

Figure 9. Scordelis-Lo Roof: Deformed shape (y-displacements), 10 by 10 Q4 mesh.


The convergence behaviour of the y-displacement at point A for the selected shell elements is displayed below (reference solution: 0.3024):

Convergence behaviour

Figure 10. Convergence behaviour




[5] A. C: Scordelis, K. S: Lo; Computer analysis of cylindrical shells; J. Amer. Concr. Inst 61, pp. 539-561 (1969).

[6] R. H. MacNeal, R. L. Harder; A proposed standard set of problems to test finite element accuracy; Finite Elements in Analysis and Design 1 (1985) pp. 3-20.