Transient Thermal Loading of a Viscoelastic Slab

Description

A viscoelastic slab is subjected to a temperature loading on its outside faces. The slab is very long in the Z-dir and has a thickness of 2 in.

A typical away-from-boundaries region of dimensions 0.1in. x 1in. x 1in. (half slab thickness due to symmetry) is modeled as shown in the figure. Investigate the response of the slab corresponding to different time values.



File Name

Browse to drive letter:\Users\Public\Public Documents\SOLIDWORKS\SOLIDWORKS version\samples\Simulation Examples\Verification\Nonlinear_Thermal.SLDPRT and open the file.

Study Types

Transient thermal and nonlinear static with thermal effects.

Mesh Type

Solid mesh.

Meshing Parameters

Use a Global Size of 0.1".

Material Model

Viscoelastic

Modeling Hints

The half-thickness of the slab (H/2 = 1 in) is modeled. First a transient thermal analysis is performed, where at the end of 6 sec the slab reaches its thermal equilibrium condition. A nonlinear analysis is performed with temperatures at any time obtained by interpolation from the thermal study.

Material Properties

Modulus of elasticity = 10,000 psi, Poisson's ratio = 0.4833, Coefficient of thermal expansion = 1e-5/ºF, Shear relaxation modulus = 0.901, Shear relaxation time = 0.9899 sec, Glassy transition temperature = 70 ºF, First constant for WLF equation = 4.92, Second constant for WLF equation = 215, Mass density = 386.22 lb/in3, Thermal conductivity = 1/ sec in ºF, Specific heat = 0.0025892 / lb ºF.

Restraints and Loads

Uniform temperature T0 = 100 ºF is applied at the outer face as shown in the figure. X-axis is sec, Y-axis is ºF.

All the faces are restrained in the Z- dir, the top and bottom faces are restrained in the Y-dir, and symmetry conditions are applied to the face of symmetry.

Results

  • Transient thermal analysis: Temperature distribution at time t =1 sec.

      Theory (ºF) SOLIDWORKS Simulation(ºF)
    x = 0.0 in 89.2 88.88
    x = 0.2 in 89.5 89.42
    x = 0.5 in 92.2 92.14
    x = 0.7 in 95.0 94.95
    x = 0.9 in 98.2 98.26
  • Nonlinear analysis: SY: Y Normal stress distribution at different time steps. X-axis is parametric distance in inches, Y-axis is stress in psi.
Time t = 0.007 sec
Time t = 1.21 sec
Time t = 6.0 sec

References

  1. Carslaw, H.S. and Yeager, J.C., Conduction of Heat in Solids, Clarendon Press, Oxford, 1959.
  2. Williams, M.L., Landel, R.F., Ferry, J.D., Journal of American Chemical Society, V77, pp. 3701, 1955.