4.4.7 FV32: Cantilevered tapered membrane

Product: ABAQUS/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:

along the y-axis. 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
NAFEMS44.623130.03162.70246.05379.90391.44
CPS444.782 (0.36)130.63 (0.46)162.59 (–0.07)246.79 (0.30)379.14 (–0.20)389.83 (–0.41)
CPS4I44.524 (–0.23)129.55 (–0.09)162.55 (–0.09)244.13 (–0.78)374.46 (–1.43)389.60 (–0.47)
CPS844.636 (0.04)130.14 (0.08)162.72 (0.01)246.63 (0.24)382.02 (0.56)391.55 (0.03)
CPS8R44.629 (0.02)130.11 (0.06)162.70 (0.00)246.42 (0.15)381.32 (0.37)391.51 (0.02)
CPS644.624 (0.00)130.04 (0.00)162.70 (0.00)246.09 (0.02)379.99 (0.02)391.45 (0.02)
CPS6M44.637 (0.03)129.88 (–0.12)162.67 (–0.02)245.29 (–0.31)377.64 (–0.59)390.98 (–0.12)

Input files

nfv32f4f.inp

CPS4 elements.

nfv32i4f.inp

CPS4I elements.

nfv32f8c.inp

CPS8 elements.

nfv32r8c.inp

CPS8R elements.

nfv32f6c.inp

CPS6 elements.

nfv32m6c.inp

CPS6M elements.