Steady-state dynamic analysis for two-dimensional elements

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

Elements tested
Features tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/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 $A D$ and has a forced harmonic pressure applied at edge $B C$ . 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:

$u_{x}$ = $u_{y}$ = 0 at end $A D$ .

Damping

$α$ = 5.36, $β$ = 7.46 × 10⁻⁵.

Forcing function

(steady-state harmonic)

F = $F_{0} \sin (ω t)$

$F_{0}$ = 30,000 N/m on edge $B C$

$ω$ = $2 π f$ 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

Input files

pssdce3sf.inp: CPE3 elements.
pssdce3sh.inp: CPE3H elements.
pssdce4sf.inp: CPE4 elements.
pssdce4sh.inp: CPE4H elements.
pssdce4si.inp: CPE4I elements.
pssdce4sj.inp: CPE4IH elements.
pssdce4sr.inp: CPE4R elements.
pssdce4sy.inp: CPE4RH elements.
pssdce6sf.inp: CPE6 elements.
pssdce6sh.inp: CPE6H elements.
pssdce6sk.inp: CPE6M elements.
pssdce6sl.inp: CPE6MH elements.
pssdce8sf.inp: CPE8 elements.
pssdce8sh.inp: CPE8H elements.
pssdce8sr.inp: CPE8R elements.
pssdce8sy.inp: CPE8RH elements.
pssdcs3sf.inp: CPS3 elements.
pssdcs4sf.inp: CPS4 elements.
pssdcs4si.inp: CPS4I elements.
pssdcs4sr.inp: CPS4R elements.
pssdcs6sf.inp: CPS6 elements.
pssdcs6sk.inp: CPS6M elements.
pssdcs8sf.inp: CPS8 elements.
pssdcs8sr.inp: CPS8R elements.
pssdmcs4sf.inp: Reference mode-based steady-state dynamic analysis.