3.2.2 Steady-state dynamic analysis for two-dimensional elements

Product: ABAQUS/Standard

Elements tested

CPE3 CPE3H CPE4 CPE4H CPE4I CPE4IH CPE4R CPE4RH CPE6 CPE6H CPE6M CPE6MH CPE8 CPE8H CPE8R CPE8RH CPS3 CPS4 CPS4I CPS4R CPS6 CPS6M CPS8 CPS8R

Features tested

Direct-solution and subspace-based steady-state dynamic analysis of two-dimensional elements with damping.

Problem description

The model consists of a square structure that is fixed at edge and has a forced harmonic pressure applied at edge . Material damping is provided in the form of mass and stiffness proportional damping.

Material:

Young's modulus = 20 GPa, Poisson's ratio = 0, density = 8000 kg/m³.

Boundary conditions:

= = 0 at end .

Damping:

= 5.36, = 7.46 × 10^–5.

Forcing function:

(steady-state harmonic)

F =

= 30,000 N/m on edge

= Hz

f = 10 to 15 Hz

Reference solution

The results are confirmed by comparing them to a mode-based steady-state dynamic analysis using CPS4 elements.

Results and discussion

	Peak displacement	Peak stress	Frequency
	(mm)	(N/mm²)	(Hz)
Reference solution	16.90	0.478	12.18
3-node elements	17.55	0.481	12.07
6-node elements	16.46	0.539	12.47
6-node modified elements	16.85	0.536	12.37
4-node elements	16.92	0.478	12.17
8-node elements	16.45	0.540	12.47