Standard tests, NAFEMS

Results.

Problem. The NAFEMS problems are standard tests used to compare finite element programs. LE1 measures a stress concentration in an elliptic membrane, FV12 the natural frequencies of a free thin plate and FV32 those of a tapered membrane cantilever.

Reference document. The reference values are the target values published by NAFEMS. The Standard NAFEMS Benchmarks (1990) is used for LE1, and Selected Benchmarks for Natural Frequency Analysis (1987) for FV12 and FV32.

Numerical model. LE1 is a quarter model solved in plane stress, and the stress at point D is read at the corner of the element. In the FV12 plate the in-plane translations and the in-plane rotation are held at every node. The FV32 cantilever is held along its root edge and only in-plane vibration is solved.

NAFEMS LE1, elliptic membrane#

Published source. NAFEMS, The Standard NAFEMS Benchmarks (1990), LE1

Note. The stress is read at the corner of the element touching point D. Because the corner value is extrapolated from inside the element, on the finer meshes it stays 1.5 to 2.5% above the target. An independent four-node element solution gives the same values within 1% on the same meshes. Since the model shows section forces, the $N_{yy}$ row is the same corner value multiplied by the thickness and is read in the shell detail window of the element at D.

NAFEMS FV12, free thin square plate#

Parameters. mesh = 32×32

Published source. NAFEMS, Selected Benchmarks for Natural Frequency Analysis (1987)

Note. As the plate is free, the first three modes are rigid body motions with zero frequency. The comparison starts at the fourth mode, and modes 7 and 8 are a pair with the same frequency.

NAFEMS FV32, cantilevered tapered membrane#

Parameters. mesh = 32×16

Published source. NAFEMS, Selected Benchmarks for Natural Frequency Analysis (1987)