# SS-V: 5070 Pinched Hemispherical Shell

Test No. VNL08Find displacements of a hemispherical shell loaded with inward and outward concentrated forces.

## Definition

**Properties****Value**- Modulus of Elasticity
- 6.825e+7 psi
- Poisson's Ratio
- 0.3

## Results

Symmetry conditions were simulated via sliding boundary conditions applied at faces coinciding with symmetry planes (Figure 2). Concentrated forces were applied in points of outer face of the sphere (Figure 3). In order to eliminate rigid body motion along Z-axis a point on the top of the sphere was constrained in Z-direction (Figure 4).

In Figure 5 and Figure 6 true deformations of the shell at load P = 100 lbf are shown.

Load [lbf] | Ref Solution *, Uy at Point A [in] | SimSolid, Displacement Ux at Point A [in] | % Difference |
---|---|---|---|

40 | -3.280 | -3.148 | -4.02% |

60 | -4.360 | -4.120 | -5.50 |

100 | -5.950 | -5.482 | -7.87 |

Load [lbf] | Ref Solution *, Uy at Point B [in] | SimSolid, Displacement Ux at Point B [in] | % Difference |
---|---|---|---|

40 | -2.330 | -2.268 | -2.66% |

60 | -2.830 | -2.725 | -3.71% |

100 | -3.430 | -3.255 | -5.10% |

* Ref Solution is a thin shell model

^{1}Test 3DNLG-9 from NAFEMS Publication R0024 “A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3-D Beams and Shells (SUMMARY).”