FV32: Cantilevered tapered membrane

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

ProductsAbaqus/Standard

Elements tested

CPS4

CPS4I

CPS8

CPS8R

CPS6

CPS6M

Problem description



Model:

Plate thickness = 0.05 m.

Material:

Young's modulus = 200 GPa, Poisson's ratio = 0.3, density = 8000 kg/m3.

Boundary conditions:

ux=uy=0 along the y-axis. uz=0 at all nodes.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test FV32 from NAFEMS publication TNSB, Rev. 3, “The Standard NAFEMS Benchmarks,” October 1990.

Mode shapes predicted by Abaqus (for element type CPS4)



Results and discussion

The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

 Mode
123456
NAFEMS 44.623 130.03 162.70 246.05 379.90 391.44
CPS4 44.782 (0.36) 130.63 (0.46) 162.59 (−0.07) 246.79 (0.30) 379.14 (−0.20) 389.83 (−0.41)
CPS4I 44.524 (−0.23) 129.55 (−0.09) 162.55 (−0.09) 244.13 (−0.78) 374.46 (−1.43) 389.60 (−0.47)
CPS8 44.636 (0.04) 130.14 (0.08) 162.72 (0.01) 246.63 (0.24) 382.02 (0.56) 391.55 (0.03)
CPS8R 44.629 (0.02) 130.11 (0.06) 162.70 (0.00) 246.42 (0.15) 381.32 (0.37) 391.51 (0.02)
CPS6 44.624 (0.00) 130.04 (0.00) 162.70 (0.00) 246.09 (0.02) 379.99 (0.02) 391.45 (0.02)
CPS6M 44.637 (0.03) 129.88 (−0.12) 162.67 (−0.02) 245.29 (−0.31) 377.64 (−0.59) 390.98 (−0.12)