Static stress 01: elliptic membrane under uniform pressure

An elliptical membrane of constant thickness of 0.1 m with a uniform outward pressure of -10 MPa is analyzed for tangential edge stress.

Case Description

Steel material properties were used.

Geometry

• Thickness = 100 mm
• Equation of smaller curve: (Y/2)2 + Z2 = 1
• Equation of larger curve: (Y/3.25)2 + (Z/2.75)2 = 1

Study Type

• Static Stress

Mesh Parameters

• Mesh Type = Solid (Tetrahedral)
• Element Order = Parabolic
• Mesh Size = 150 mm, absolute
• Adaptive Mesh Refinement: None

Material Properties

• Modulus of elasticity = 210 X 103 MPa
• Poisson's ratio (v) = 0.3

Constraints

• X direction only fixed at points A, B, and C (vertices on back face of the solid model)
• Y direction only fixed at left (AB) face
• Z direction only fixed at bottom (CD) face

Load

• Pressure = -10 Mpa

Comparison of Results

Tangential Edge Stress (σzz) at D (MPa) - Maximum value along 100 mm long edge of the solid element corresponding to point D of the benchmark shell element model.

Reference

NAFEMS Publication Test No. LE1, The International Association for the Engineering Analysis Community, "NAFEMS Background To Benchmarks", G.A.O Davies, R.T. Fenner, R.W. Lewis, June, 1992.