# OS-V: 0030 Radial Point Load on a Hemisphere

Test No. LE3 The model is a hemispherical shell subjected to concentrated radial loads at its free edges. It examines the performance of the three-dimensional shell to model local bending behavior under conditions where the deformations are primarily due to bending.

## Benchmark Model

4-node, first order CQUAD4 elements are benchmarked in LE3. The hemisphere is 10m in radius and 0.04m in radial thickness. Two pairs of identical loads, 4000N, are applied at the free edge of the hemisphere, and are at right angles to each other. One pair of the loads is directed inwards (toward the center) of the hemisphere, while the second pair is directed outward from the center, producing deformation of compression in one direction and elongation in another. Since both the geometry and loads are symmetrical, only a quarter of the hemisphere is modeled. Symmetric boundary constraints are applied on edges AE and CE. The z-translation at point E is fixed, and all displacements on edge AC are free. The test also requires the mesh of the hemisphere to have equally spaced nodes on edges AC, CE, EA, BG, DG, and FG. The target is x-translation at point A, with a target value of 0.185m.

The material properties for the hemisphere are:
Material Properties
Value
E
68.25 GPa
$\upsilon$
0.3

## Linear Static Analysis Results

All results are normalized with the target values of x translation at point A.
Element Type Mesh Configuration nacx nce x nea
CQUAD4 4 x 4 x 4 8 x 8 x 8 16 x 16 x 16 32 x 32 x 32 64 x 64 x 64
0.9865 1.0200 1.0076 1.0032 1.0016

## Model Files

Refer to Access the Model Files to download the required model file(s).

The model files used in this problem include:
• LE3.fem.zip

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis