## 4. Cylinder with Square Cutouts

A cylinder with two opposite square cutouts is clamped at one end and compressed at the other end in the axial direction by an imposed displacement of 0.00425. This problem can be modeled with an eight of a cylinder (half in the longitudinal direction and a fourth in the circumferential direction). The figure below display the meshes with Q4.S.MITC.E4. Boundary conditions are symmetry along both longitudinal edges and along one circumferential edge, the other circumferential edge being clamped. Figure 21. Cylinder with square cutouts: Meshes with Q4.S.MITC.E4 elements. 1/8 of cylinder is modeled. Figure 22. Cylinder with square cutouts: Boundary conditions and local node coordinate systems.

The test is run with Q4.S.MITC.E4, Q8.S.MITC, and Q9.S.MITC shell elements, comparing the cutout tip displacement-load function against the reported solution by Almroth and Holmesand later by Knight and Rankin. The comparison is made against a very fine mesh of Q4.S.MITC.E4 elements, since the STAGS reference solution (mesh-3) is too coarse. The Q8.S.MITC and Q9.S.MITC meshes have the same number of elements (18x32) as the Q4.S.MITC.E4. To reproduce results similar to those from STAGS, a 9x16 Q9.S.MITC elements mesh is adequate. The graphs below plot the cutout tip out of plane displacement versus the relative reaction force P/P0, with

P 0 = 1.2 π E t 2

and E=1·107 and T=0.014. Figure 23. Cylinder with square cutouts: Load-displacement graph (Q4 mesh). Figure 24. Cylinder with square cutouts: Load-displacement graph (Q8 mesh). Figure 25. Cylinder with square cutouts: Load-displacement graph (Q9 mesh). Figure 26. Cylinder with square cutouts: Stress σzz (Q4 mesh).

 B. 0. Almroth and A. M. C. Holmes; Buckling of Shells; International Journal Solids and Structures, Vol 8, pp 1057-1071, 1972.

 N. F. Knight and C. C. Rankin: STAGS Example Problems Manual; NASA/CR-2006-214281, 2006.