Shell07 – Hemispherical Shell Structure with Static Loads✔!

Problem Description

In this example a hemispherical shell structure is analyzed for the effects of four 2 kip edge point loads alternating in sign at 90° intervals around the equator of the hemisphere. The deflections at the locations where the point loads are applied, in the direction of the point loads, are compared with published independent results.
The geometry, properties and loading are as suggested in MacNeal and Harder 1985. The 0.04 foot thick hemispherical shell has a 10 foot radius. A hole is introduced at the top of the hemisphere, as shown in the figure on the following page, to avoid triangular elements at the top of the hemisphere.
The top and bottom edges of the hemisphere are free. As suggested in MacNeal and Harder 1985, only a quarter of the hemispherical shell structure is modeled. Symmetrical boundary conditions are imposed on the side edges of the quarter hemisphere. An 8x8 mesh is used for the quarter hemispherical shell structure.
To properly apply the symmetrical boundary conditions the local axes of each joint are rotated such that local axis 1 is in the same direction as a vector defined from the center point of the hemisphere to the point under consideration. In other words, local axis 1 is in the direction of a radial line to the point considered. Local axis 2 is horizontal and tangent to the hemispherical surface.
With the joint local axes as described in the previous paragraph, the symmetry conditions are applied as follows. Joints 1, 10, 19, 28, 37, 46, 55, 64, and 73 are restrained in the U2 and R3 degrees of freedom. Joints 9, 18, 27, 36, 45, 54, 63, 72 and 81 are also restrained in the U2 and R3 degrees of freedom. In addition, a single vertical restraint is applied at the center of the bottom edge, at joint 5, to maintain stability of the structure.

Tested Features

•  Three-dimensional analysis using shell elements
•  Joint local axes
•  Joint force loads

Result Comparison

App

Object Link: https://openbrim.org/objide1y1molg6evkpujh1ua.project

Library

Object Link: https://openbrim.org/objideemebdi1o5jygiddys7wyq.libobj