A hemispherical shell is subjected to point loads at the lower two edges. The shell is 0.04 inches thick and the radius is 10.0 inches. The modulus of elasticity is 6.825x107 and Poisson's Ratio 0.30.

The top of the sphere is open at a vertical elevation of 9.511 inches. The elevation of the opening corresponds to a Phi angle of 72 degrees when measured from the vertical axis Z.

Determine the displacement at the point of application of loads at joints 1 and 74.

A quarter of the hemispherical shell is used as a model. The model consists of 8 x 8 mesh of shell elements with the horizontal mesh of 11.25 degrees and the vertical mesh of 9 degrees.

The boundary conditions are prescribed for the symmetry. The joints along the edge from joint 1 to 9 are restrained for translation in the Global Y-direction and for rotations about Global X and Z-directions. Similarly, the joints along the edge from joint 74 to 82 are restrained for translation in the Global X-direction and for rotations about the Global Y and Z-directions. Joint 38 at the lower center of the free edge is restrained to prevent unstable solution.

The geometry, material and section property data of the shell is:

Modulus of Elasticity = 68,250,000 psi

Poisson's Ratio = 0.30

Shear Modulus = 26,250,000 psi

Shell Thickness = 0.04 inch

Radius of the Hemisphere = 10 inch

The displacement reported is at the point of application of the load and in the direction of the load. The comparison between LARSA, Reference [1] and Reference[2] is excellent. Reference [1] suggests a value of 0.094 for comparison of the results with the theoretical lower bound of 0.0924.

Tested Features

Sources

LARSA 4D
MacNeal, R.H. and Harder, R.C., "A Proposed Standard Set of Problems to Test Finite Element Accuracy," Finite Elements Analysis and Design 1 (1985), pp. 3-20, North-Holland.
Computers & Structures Inc., "SAP90 Structural Analysis Verification Manual", October, 1990, 18-1.

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