OS-V: 0270 Torsional Creep of Circular Shaft

This benchmark illustrates the structural response of a power law creeping material in a geometrical configuration subjected to pure torsion. OptiStruct examines strain at the edge of the shaft.

The model examines the torsional creep in circular shaft with 2 variations:

Relaxation at constant twist
Forward creep at steady twist rate

Relaxation at Constant Twist

Twist is applied to the shaft and remains constant from 0 to 100s. Total strain and creep strains then analyzed.

Benchmark Model

Four 20-noded brick elements, plus one 16-noded wedge are used. All nodes on lower face are fixed in X, Y, Z.

X, Y displacements given at all nodes of front face using cylindrical system: 0.002 mm
Rotation is given at mid-side nodes: 0.001 radians

Uniform twist of 0.01 radians/unit length is held constant in time from 0 to 100s.

Twist is instantaneously applied to the shaft and then maintained constant. The initial response is elastic and subsequently the structure response with a progressive accumulation of creep strain. Stress reduces (relaxes) slowly till 100s due to creep.

Material Properties: Value
Young's modulus: 10 GPa
Poisson's ratio: 0.3
Creep law equation: ${\dot{ε}}_{e q} = 1000 σ^{5}_{e q}$

Where,

${\dot{ε}}_{e q}$: Equivalent creep strain rate
$σ_{e q}$: Equivalent stress (Mises)

Nonlinear Static Analysis Results

An implicit visco-elastic solution method was used. Displacement, total strain and creep strain results are analyzed at the edge of the shaft at 100s.

	OptiStruct	NAFEMS	Normalized Target Value
Total Strain (*10^-3)	5.46	5.77	0.95
Creep Strain (*10^-3)	4.85	4.77	1.01

Comparison of strain plots.

Model Files

必要なモデルファイルのダウンロードについては、モデルファイルへのアクセスを参照してください。

The model file used in this example includes:

Torsional_Creep_Relaxation_at_constant_twist.fem

Forward Creep at Steady Twist Rate

A steadily increasing twist is applied at constant rate to the shaft.

The stresses increase from zero to steady value. The loads, which cause this steady-state behavior are referred as “primary” loads.

This model is the same as used in Relaxation at Constant Twist; except the boundary conditions.

Benchmark Model

Four 20-noded brick elements, plus one 16-noded wedge are used. All nodes on lower face are fixed in X, Y, Z.

X, Y displacements given at all nodes of front face using cylindrical system: 0.004 mm/unit time
Rotation is given at mid-side nodes: 0.002 radians/unit time

Uniform twist of 0.02 radians/unit time is steadily increating with time from 0 to 1.5 applied using table curve.

Material Properties: Value
Young's modulus: 10 GPa
Poisson's ratio: 0.3
Creep law equation: ${\dot{ε}}_{e q} = 1000 σ^{5}_{e q}$

Where,

${\dot{ε}}_{e q}$: Equivalent creep strain rate
$σ_{e q}$: Equivalent stress (Mises)

Nonlinear Static Analysis Results

An implicit visco-elastic solution method was used. Displacement, total strain and creep strain results are analyzed at the edge of the shaft at 1.5s.

	OptiStruct	NAFEMS	Normalized Target Value
Total Strain (*10^-2)	1.62	1.7321	0.94
Creep Strain (*10^-2)	1.27	1.1693	1.094

Comparison of strain plots.

Model Files

必要なモデルファイルのダウンロードについては、モデルファイルへのアクセスを参照してください。

The model file used in this example includes:

Torsional_forward_creep_at_steady_twist_rate.fem

Reference

NAFEMS R0026 - Selected Benchmarks for Material Non-Linearity- Volume 1