Cyclic Thermal Loading of Two Bar Assembly - Shakedown Approach

Determine the cyclic variation of stresses and strains for a two-bar assembly loaded axially by a constant mechanical load and a cyclic thermal load of ± 100 °C.

A mechanical load (P) = 15 N is applied to the rigid bar. A cyclic thermal load is applied to Bar 1 as shown.

File Name

Open drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\NAFEMS_NL2A.SLDASM.

Study Type

Nonlinear static with large strain and large displacement formulations

Mesh Type

Solid mesh

Mesh Size

Use standard mesh with a global element size of 0.577 mm.

Material Properties

Bar 1 and Bar 2

Model Type: Plasticity - von Mises

Material Property Value
Elasticity modulus (E) 10000 MPa
Poisson's ratio (ν) 0
Yield stress (σy) 10 MPa
Tangent modulus 1000 MPa
Coefficient of thermal expansion 1 x 10-5 /K
Hardening factor 1

Rigid Bar

  • Elastic Modulus (E) = 1 x 108 MPa
  • Poisson's ratio (ν) = 0
The rigid bar is assigned stiffer material properties to simulate the behavior of a rigid body.

Results

Plot the cyclic variation of stress component SX for Bar 1.

X-axis shows half cycles (pseudo time in sec) and Y-axis shows stress in MPa.

Plot the cyclic variation of stress component SX for Bar 2.

X-axis shows half cycles (pseudo time in sec) and Y-axis shows stress in MPa.

Obtain the strain component at selected cycles.

Half-Cycle Mechanical Strain (x10-4)

(Total Strain - Thermal Strain)

Bar 1 Bar 2
Reference SOLIDWORKS Simulation Reference SOLIDWORKS Simulation
0 7.500 7.598 7.500 7.402
2 8.264 8.395 18.264 18.675
4 13.797 14.095 23.797 24.285
6 17.500 17.815 27.500 27.975
8 19.980 20.275 29.980 30.415
10 21.639 21.895 31.639 32.015

Reference

NAFEMS Publication R0026, The International Association for the Engineering Analysis Community, “Selected Benchmarks for Material Non-Linearity”, 1993.