Structural-thermal analysis allows you to perform thermal-stress, plastic heat, and viscoelastic heat analyses. In dynamic analyses, you can also include the piezocaloric effect. Applications of the latter include thermoelastic damping in metals and MEMS devices such as resonator beams.
The following related topics are available:
- 2.6.1. Elements Used in a Structural-Thermal Analysis
- 2.6.2. Performing a Structural-Thermal Analysis
- 2.6.3. Example: Thermoelastic Damping in a Silicon Beam
- 2.6.4. Example: Thermoplastic Heating of a Thick-Walled Sphere
- 2.6.5. Example: Viscoelastic Heating of a Rubber Cylinder
- 2.6.6. Other Structural-Thermal Analysis Examples
The program includes a variety of elements that you can use to perform a coupled structural-thermal analysis. Table 2.22: Elements Used in Structural-Thermal Analyses summarizes them. For detailed descriptions of the elements and their characteristics (degrees of freedom, KEYOPT options, inputs and outputs, etc.), see the Element Reference.
For a coupled structural-thermal analysis, you need to select the UX, UY, UZ, and TEMP element degrees of freedom. For SOLID5 or SOLID98, set KEYOPT(1) to 0. For PLANE13 set KEYOPT(1) to 4. For PLANE222, PLANE223, SOLID225, SOLID226, SOLID227, or LINK228, set KEYOPT(1) to 11.
The structural-thermal KEYOPT settings also make large-deflection, stress-stiffening effects, and prestress effects available (NLGEOM and PSTRES). See the Structural Analysis Guide and Structures with Geometric Nonlinearities in the Theory Reference for more information about those capabilities.)
To include piezocaloric effects in dynamic analyses (transient and harmonic), use PLANE222, PLANE223, SOLID225, SOLID226,SOLID227, or LINK228.
Table 2.22: Elements Used in Structural-Thermal Analyses
| Elements | Effects | Analysis Types |
|---|---|---|
|
SOLID5 - 8-Node Coupled-Field Hexahedral PLANE13 - 4-Node Coupled-Field Quadrilateral SOLID98 - 10-Node Coupled-Field Tetrahedral |
Thermoelastic (Thermal Stress) |
Static Full Transient |
|
PLANE222 - 4-Node Coupled-Field Quadrilateral PLANE223 - 8-Node Coupled-Field Quadrilateral SOLID225 - 8-Node Coupled-Field Hexahedral SOLID226 - 20-Node Coupled-Field Hexahedral SOLID227 - 10-Node Coupled-Field Tetrahedral LINK228 - Coupled-Field Line |
Thermoelastic (Thermal Stress and Piezocaloric) Thermoplastic Thermoviscoelastic |
Static Full Harmonic Full Transient |
To perform a structural-thermal analysis you need to do the following:
Select a coupled-field element that is appropriate for the analysis (Table 2.22: Elements Used in Structural-Thermal Analyses). Use KEYOPT (1) to select the UX, UY, UZ, and TEMP element degrees of freedom.
Specify structural material properties:
If the material is isotropic or orthotropic, input Young's moduli (EX, EY, EZ), Poisson's ratios (PRXY, PRYZ, PRXZ, or NUXY, NUYZ, NUXZ), and shear moduli (GXY, GYZ, and GXZ) (MP).
If the material is anisotropic, input the elastic-stiffness matrix (TB,ANEL).
If using PLANE222, PLANE223, SOLID225, SOLID226, SOLID227, or LINK228 you can also specify structural nonlinear material models. See the Structural Material Properties table in those element descriptions for details.
Specify thermal material properties:
Specify coefficients of thermal expansion (ALPX, ALPY, ALPZ), thermal strains (THSX, THSY, THSZ), or the instantaneous coefficients of thermal expansion (CTEX, CTEY, CTEZ) (MP).
Specify the reference temperature for the thermal strain calculations (TREF or MP,REFT).
Apply structural and thermal loads and boundary conditions.
Structural loads and boundary conditions include displacement (UX, UY, UZ), force (F), pressure (PRES), and force density (FORC).
Thermal loads and boundary conditions include temperature (TEMP), heat flow rate (HEAT), convection (CONV), heat flux (HFLUX), radiation (RDSF), and heat generation (HGEN).
Specify analysis type and solve:
Analysis type can be static, full transient, or full harmonic. See Table 2.22: Elements Used in Structural-Thermal Analyses for more details.
To prevent unwanted oscillation of temperature outside of the physically meaningful range in a transient analysis that includes PLANE223, SOLID226, or SOLID227 elements, it is recommended that you create the elements without midside nodes and set the specific heat matrix option to diagonalized (KEYOPT(10) = 1).
The following only apply to the PLANE222, PLANE223, SOLID225, SOLID226, SOLID227, and LINK228 elements:
If you perform a static or full transient analysis, you can use KEYOPT(2) to select a strong (matrix) or weak (load vector) structural-thermal coupling. Strong coupling produces an unsymmetric matrix. In a linear analysis, a strong coupled response is achieved after one iteration. Weak coupling produces a symmetric matrix and requires at least two iterations to achieve a coupled response.
Note: For full harmonic analysis with these elements, strong structural-thermal coupling only applies.
These elements support a piezocaloric effect calculation in dynamic analyses. (For more information, see Thermoelasticity.)
Note the following about the inputs for a piezocaloric effect calculation:
Elastic coefficients are interpreted as isothermal coefficients, not adiabatic coefficients.
Specific heat is assumed to be at constant pressure (or constant stress), and it is automatically converted to specific heat at constant volume (or constant strain).
Specify the temperature offset from absolute zero to zero (TOFFST). The offset is added to the specified temperature (TREF) to obtain the absolute reference temperature.
All thermal material properties and loads must have the same energy units. For the SI system, both energy and heat units are in Joules. For the U. S. Customary system, energy units are in-lbf or ft-lbf and heat units are in BTUs. British heat units (BTUs) must be converted to energy units of in-lbf or ft-lbf (1BTU = 9.338e3 in-lbf = 778.17 ft-lbf).
Table 2.23: Units for Thermal Quantities
Thermal Quantity Units Thermal Conductivity energy/length-temperature-time Specific Heat energy/mass-temperature Heat Flux energy/length2-time Volumetric Heat Source energy/length3-time Heat Transfer Coefficient energy/length2-temperature-time
In a structural-thermal analysis with structural nonlinearities using elements PLANE222, PLANE223, SOLID225, SOLID226, SOLID227, or LINK228, you should use weak (load vector) coupling between the structural and thermal degrees of freedom (KEYOPT(2) = 1) and suppress the thermoelastic damping in a transient analysis (KEYOPT(9) = 1). When using the SOLID226 element, you should also select the uniform reduced integration option (KEYOPT(6) = 1). These options will be automatically set if ETCONTROL is active.
PLANE222, PLANE223, SOLID225, SOLID226, SOLID227, and LINK228 also support the calculation of thermoplastic and thermoviscoelastic effects in static or transient analyses. To activate these effects, specify a fraction of plastic work converted to heat or a fraction of viscoelastic loss converted to heat (MP,QRATE). For more information, see Thermoplasticity and Thermoviscoelasticity.
Post-process structural and thermal results:
Structural results include displacements (U), total strain (EPTO), elastic strain (EPEL), thermal strain (EPTH), stress (S), plastic heat generation rate (PHEAT), viscoelastic heat generation rate (VHEAT), and total strain energy (UT).
Thermal results include temperature (TEMP), thermal gradient (TG), and thermal flux (TF).
To activate the enhanced strain formulation in PLANE222 and SOLID225, set KEYOPT(6) = 2.
In this example, a harmonic analysis is performed to calculate the effect of thermoelastic damping in a thin silicon beam vibrating transversely. The thermoelastic damping, or "internal friction," arising from the irreversible heat flow across the temperature gradients induced by the strain field in vibrating reeds has been predicted and investigated by C. Zener in "Internal Friction in Solids" published in Physical Review, Vol. 52, (1937), p.230 and Vol. 53, (1938), p.90.
The following topics are available:
A thin silicon clamped-clamped beam of length L = 300 µm and width W = 5 µm vibrates transversely under a uniform pressure P = 0.1 MPa applied in the -Y direction. The beam temperature in equilibrium is T0 = 27 °C.
Table 2.24: Material Properties
| Material Property | Value (μMKSV) |
|---|---|
| Young's Modulus | 1.3 x 105 MPa |
| Poisson's Ratio | 0.28 |
| Density | 2.23 x 10-15 kg/(µm)3 |
| Thermal Conductivity | 9.0 x 107 pW/(µm*K) |
| Specific Heat | 6.99 x 1014 pJ/(kg*K) |
| Thermal Expansion Coefficient | 7.8 x 10-6 1/K |
The beam finite element model is built using the plane stress thermoelastic analysis options on the PLANE223 coupled-field element. A structural-thermal harmonic analysis is performed in the frequency range between 10 kHz and 10 MHz that spans the first six resonant modes of the beam.
The thermoelastic damping Q-1 is calculated using the equation given in Thermoelasticity. The following figure compares the numerical results with Zener's analytical expression for the thermoelastic damping in transversely vibrating reeds.
The following figure shows the beam temperature distribution for a frequency of 5 MHz.
/title, Thermoelastic Damping in a Silicon Beam, uMKSV system of units /com, /com, Reference for the analytical solution: /com, C. Zener, "Internal Friction in Solids," /com, Phys. Rev., Vol. 53, (1938), p. 90 /com, /nopr ! ! Material constants for silicon [100] ! E=1.3e5 ! Young's modulus, MPa nu=0.28 ! Poisson's ratio k=90e6 ! Thermal conductivity, pW/(um*K) rho=2330e-18 ! Density, kg/(um)**3 Cp=699e12 ! Heat capacity, pJ/(kg*K) alp=7.8e-6 ! Thermal expansion, 1/K ! ! Dimensions L=300 ! Length, um W=5 ! Width, um ! ! Loads ! t0=27 ! Reference temperature, C Toff=273 ! Offset temperature, K P=0.1 ! Pressure, MPa ! ! Analysis parameters ! fmin=0.1e6 ! Start frequency, Hz fmax=10e6 ! End frequency, Hz nsbs=100 ! Number of substeps ! ! Build finite element model ! /PREP7 mp,EX,1,E mp,PRXY,1,NU mp,DENS,1,rho mp,ALPX,1,ALP mp,KXX,1,k mp,C,1,Cp et,1,PLANE223,11 ! Thermoelastic plane stress rect,,L,,W esize,W/2 amesh,1 nsel,s,loc,x,0 ! Clamp beam ends nsel,a,loc,x,L d,all,UX,0 nsel,r,loc,y,0 d,all,UY,0 nsel,all Tref,t0 ! Set reference temperature Toffst,Toff ! Set offset temperature fini /com, /com, == Perform thermoelastic harmonic analysis /com, /solu antyp,harmic ! Harmonic analysis outres,all,all ! Write all solution items to the database harfrq,fmin,fmax ! Specify frequency range nsubs,nsbs ! Set number of substeps nsel,s,loc,y,W sf,all,pres,P ! Apply pressure load nsel,all kbc,1 ! Stepped loading solve fini ! ! Prepare for Zener's analytical solution ! delta=E*alp**2*(t0+Toff)/(rho*Cp) pi=acos(-1) tau=rho*Cp*W**2/(k*pi**2) f_Qmin=1/(2*pi*tau) /com, /com, Frequency of minimum Q-factor: f_Qmin=%f_Qmin% /com, f_0=0.986 f_1=0.012 f_2=0.0016 tau0=tau tau1=tau/9 tau2=tau/25 ! *dim,freq,table,nsbs *dim,Q,table,nsbs,2 ! ! Post-process solution ! /post1 df=(fmax-fmin)/nsbs f=fmin+df *do,i,1,nsbs set,,,,0,f ! Read real solution at frequency f etab,w_r,nmisc,4 ! Store real part of total strain energy set,,,,1,f ! Read imaginary solution at frequency f etab,w_i,nmisc,4 ! Store imag part of total strain energy (losses) ssum ! Sum up element energies *get,Wr,ssum,,item,w_r *get,Wi,ssum,,item,w_i Qansys=Wr/Wi ! Numerical quality factor om=2*pi*f omt0=om*tau0 omt1=om*tau1 omt2=om*tau2 Q1=delta*f_0*omt0/(1+omt0**2) Q1=Q1+delta*f_1*omt1/(1+omt1**2) Q1=Q1+delta*f_2*omt2/(1+omt2**2) Qzener=1/Q1 ! Analytical quality factor /com, /com, Q-factor at f=%f%: /com, ANSYS: Q=%Qansys% Zener: Q=%Qzener% /com, freq(i)=f Q(i,1)=1/Qansys Q(i,2)=1/Qzener f=f+df *enddo ! ! Plot computed and analytical damping factors ! /axlab,x,Frequency f (Hz) /axlab,y,Thermoelastic Damping 1/Q /gcol,1,1/Qansys /gcol,2,1/Qzener *vplot,freq(1),Q(1,1),2 ! ! Plot temperature change due to thermoelastic damping ! set,,,1,1,5e6 ! Read imag solution at f=5MHz plnsol,temp
In this example, a transient analysis is performed to calculate thermally induced expansion of a thick-walled sphere. The thermoplasticity-induced transient heat conduction has been studied by J. C. Simo and C. Miehe in “Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation” published in Computer Methods in Applied Mechanics and Engineering, Vol. 98, (1992), pp. 41-104.
The following topics are available:
A thick-walled sphere with initial inner radius A = 10 mm is subjected to a constant internal pressure PA = 187.5 MPa. At the outer radius B = 20 mm, a constant temperature boundary condition TB = 626.333 K is applied. Initial temperature is the same as the homogeneous reference temperature, Tref = 293 K.
Table 2.25: Material Properties
| Material Property | Value |
|---|---|
| Bulk Modulus | 166670 MPa |
| Shear Modulus | 76920 MPa |
| Yield Stress (Flow Stress) | 300 MPa |
| Tangent Modulus (Hardening Modulus) | 700 MPa |
| Density | 7.8 x 10-9 N*s2/(mm)4 |
| Thermal Expansion Coefficient | 1.0 x 10-6 K-1 |
| Thermal Conductivity | 45 N/(s*K) |
| Specific Heat | 4.6 x 108 (mm)2/(s2K) |
| Dissipation Factor | 0.9 |
| Yield Stress Softening | 0.003 K-1 |
The 2D axisymmetric sphere is modelled using the 2D coupled field element, PLANE222. The structural-thermal coupling option and mixed u-P element formulation are used. Thermoelastic damping is suppressed in the transient analysis. A structural-thermal transient analysis, including large-deflection effects, is performed for time = 0 to 7 seconds.
The time-history evolution of temperature and radial displacement on the inner surface of the sphere is calculated and plotted in the following figures.
/title, 2D thermal induced blow-up of a thick-walled sphere /com, /com, Reference: /com, J. C. Simo and C. Miehe, “Associative coupled thermoplasticity /com, at finite strains: Formulation, numerical analysis and implementation” /com, Computer Methods in Applied Mechanics and Engineering vol. 98 (1992) 41-104 /com, /prep7 /nopr A=10 ! inner radius, mm B=20 ! outer radius, mm K=166670 ! bulk modulus, N/mm^2 G=76920 ! shear modulus, N/mm^2 E=(9*K*G)/(3*K+G) ! Young's modulus, N/mm^2 nu=(3*K-2*G)/(2*(3*K+G)) ! Poisson's ratio rho=7.8E-9 ! density, N*s^2/mm^4 alpha=1.E-6 ! expansion coefficient, K^(-1) k=45 ! conductivity, N/(s*K) c=4.6E8 ! specific heat, mm^2/(s^2 K) q=0.9 ! Taylor-Quinney coefficient (fraction of plastic work converted to heat) PA=187.5 ! internal pressure, N/mm^2 Tref=293 ! reference temperature, K TB=626.333 ! boundary temperature, K y0=300 ! yield stress at Tref, N/mm^2 h0=700 ! hardening modulus, N/mm^2 w0=0.003 ! yield stress softening, N/mm^2 T1=100 T2=200 T3=300 y1=y0*(1-w0*T1) y2=y0*(1-w0*T2) y3=y0*(1-w0*T3) y4=y0*(1-w0*(TB-Tref)) et,1,222,11 ! PLANE222 with structural-thermal coupling keyo,1,3,1 ! axisymmetric keyo,1,9,1 ! thermoelastic damping suppressed keyo,1,11,1 ! mixed u-p mp,ex,1,E mp,nuxy,1,nu mp,dens,1,rho mp,alpx,1,alpha mp,kxx,1,k mp,c,1,c mp,qrate,1,0.9 tb,biso,1,,2 tbtemp,Tref tbdata,1,y0,h0 tbtemp,T1+Tref tbdata,1,y1,h0 tbtemp,T2+Tref tbdata,1,y2,h0 tbtemp,T3+Tref tbdata,1,y3,h0 tbtemp,TB tbdata,1,y4,h0 cyl4,0,0,A,0,B,90 type,1 mat,1 mshape,0,2D mshkey,1 esize,1 amesh,all arsym,y,all,,,,0 nummrg,kp nummrg,node csys,2 nsel,s,loc,x,A sf,all,pres,PA nsel,s,loc,x,B d,all,temp,TB alls csys,0 nsel,s,loc,x,0 d,all,ux nsel,s,loc,y,0 d,all,uy alls tref,Tref ic,all,temp,Tref finish /solu anty,trans nlgeom,on ! large deflection time,7 nsub,50,50,50 outres,all,all solve fini /post26 nsel,s,loc,x,A nsel,r,loc,y,0 nd=ndnext(0) nsol,2,nd,temp filldata,3,,,,-1 filldata,4,,,,293.0 prod,5,3,4 add,6,2,5 nsol,7,nd,u,x,ux prvar,6 prvar,7 /grid,1 /axlab,x,Time [s] /xrange,0,7.0 /gropt,divx,14 /axlab,y,Temperature Increase [K] /yrange,0,350 /gropt,divy,14 plvar,6 /axlab,y,Displacement [mm] /yrange,0,5.0 /gropt,divy,20 plvar,7 alls finish
In this example, a transient analysis is performed to determine the temperature rise due to viscoelastic heating in a rubber cylinder compressed between steel fixtures as described in:
| A. R. Johnson and T.-K. Chen. “Approximating thermoviscoelastic heating of largely strained solid rubber components”. Computer Methods in Applied Mechanics and Engineering. Vol. 194. 313-325. 2005. |
The following topics are available:
Following is a 2D diagram of the rubber cylinder, compressed between two steel fixtures, with a steel disk at the center. The rubber cylinder has a radius of 0.0282 m and a height of 0.05 m. The steel disk has a radius of 0.0141 m and a height of 0.0025 m. The fixture-rubber interface is considered frictionless, and the internal steel disk is bonded to the rubber.
The hyperelastic behavior of the rubber cylinder is modeled using the Neo-Hookean model, and its viscous behavior is described using Prony series terms.
Table 2.26: Material Properties
| Material Property | Value |
|---|---|
| Rubber | |
| Neo-Hookean Hyperelasticity (TB,HYPER,,,,NEO): | |
| Initial Bulk Modulus | 2*1000 x 106 Pa |
| Initial Shear Modulus | 2*1.155 x 106 Pa |
| Prony Series (TB,PRONY,,,,SHEAR): | |
| Relative Shear Modulus | 0.3 |
| Characteristic Relaxation Time (Shear Modulus) | 0.1 s |
| Other: | |
| Density | 1000 kg/m3 |
| Thermal Conductivity | 0.20934 J/(°C*m*s) |
| Specific Heat | 2093.4 J/(kg*°C) |
| Thermal Expansion Coefficient | 80 x 106 °C-1 |
| Steel | |
| Elastic Modulus | 206.8 x 109 Pa |
| Poisson Ratio | 0.3 |
| Density | 7849 kg/m3 |
| Thermal Conductivity | 45.83379 J/(°C*m*s) |
| Specific Heat | 460 J/(kg*°C) |
| Thermal Expansion Coefficient | 12 x 10-6 °C-1 |
The rubber-to-air and rubber-to-fixture film coefficients are 5.44284 J/(ºC*m2*s) and 20934 J/(ºC*m2*s), respectively.
The axisymmetric structural-thermal analysis option of the PLANE223 element is used to create a half-symmetry finite element model of the rubber cylinder and the internal steel disk, as shown in this figure:
Thermoelastic damping is turned off (KEYOPT(9) = 1) to restrict the source of heat to viscoelastic effects. Diagonalized specific heat is turned on (KEYOPT(10) = 1). A mixed u-P formulation (KEYOPT(11) = 1) is active for the rubber elements.
The top end of the cylinder is subjected to the prescribed axial displacement (in meters):
uy(t) = (-0.0045) – (0.003sin(2π*6.5*t))
The dependence of the axial displacement uy on time t is defined using a TABLE array parameter input on this command:
D,,UY,%tabname% |
A transient analysis is performed for 20 seconds with a 0.005 s time step. Geometric nonlinearities are included (NLGEOM,ON).
The deformation of the cylinder with respect to the undeformed mesh is shown in Figure 2.62: Deformation of the Cylinder . The corresponding temperature distribution resulting from the viscoelastic heating of the cylinder after 20 s of cyclic loading is shown in Figure 2.63: Temperature Distribution in the Cylinder and Disk. Temperature as a function of time is shown in Figure 2.64: Temperature Evolution at Selected Locations at some selected locations (points A, B, C, and D in Figure 2.63: Temperature Distribution in the Cylinder and Disk).
/title, Viscoelastic heating of a rubber cylinder
/nopr
pi=acos(-1)
seltol,1e-7
! CASE 2:
behavior=1 ! 0: Plane-stress 1: Axisymmetric 2: Plane-strain
coupling=0 ! 0: Strong coupling 1: Weak coupling
! Rubber
Conductivity_rubber=0.20934 ! J/C.m.s
Density_rubber=1000 ! kg/m^3
SpecificHeat_rubber=2093.4 ! J/kg.C
ThermalExpansion_rubber=80e-6 ! 1/C
Go=2*1.155e6 ! Initial shear modulus in Pa
gr=0.3 ! Relative shear modulus (unitless)
Ko=2*1000e6 ! Initial bulk modulus in Pa
tauG=0.1 ! Characteristic relaxation time (shear modulus) in s
! Steel
Conductivity_steel=45.83379 ! J/C.m.s
Density_steel=7849 ! kg/m^3
SpecificHeat_steel=460 ! J/kg.C
ThermalExpansion_steel=12e-6 ! 1/C
ElasticModulus_steel=206.8e9 ! Pa
PoissonRatio_steel=0.3
!
h_RubberAir=5.44284 ! J/C.m^2.s
h_RubberSteel=20934 ! J/C.m^2.s
/prep7
et,1,223 ! Coupled-field element
keyopt,1,1,11 ! ux,uy,temp degrees of freedom
keyopt,1,2,coupling ! Coupling method between displacement and temperature degrees of freedom
keyopt,1,3,behavior ! Set element behavior
keyopt,1,9,1 ! TED off
keyopt,1,10,1 ! Diagonalized specific heat
keyopt,1,11,1 ! Mixed u-p
!
et,2,223 ! Coupled-field element
keyopt,2,1,11 ! ux,uy,temp degrees of freedom
keyopt,2,2,coupling ! Coupling method between displacement and temperature degrees of freedom
keyopt,2,3,behavior ! Set element behavior
keyopt,2,9,1 ! TED off
keyopt,2,10,1 ! Diagonalized specific heat
!
tb,hyper,1,1,1,neo ! Neo-Hookean
tbdata,1,Go,2/Ko ! Initial Shear Modulus, incompressibility
tb,prony,1,1,1,shear ! Viscoelastic part
tbdata,1,gr,tauG ! Shear relaxation
mp,dens,1,Density_rubber
mp,kxx,1,Conductivity_rubber
mp,C,1,SpecificHeat_rubber
mp,alpx,1,ThermalExpansion_rubber
mp,qrate,1,1 ! Transfer viscoelastic heating
!
mp,EX,2,ElasticModulus_steel
mp,nuxy,2,PoissonRatio_steel
mp,dens,2,Density_steel
mp,Kxx,2,Conductivity_steel
mp,C,2,SpecificHeat_steel
mp,alpx,2,ThermalExpansion_steel
!
tunif,0.
!
! Model
r_Rubber=0.0282 ! m
h_Rubber=0.05/2 ! m, half symmetry
r_Steel=0.0141 ! m
h_Steel=0.0025/2 ! m, half symmetry
rect,,r_Rubber,,h_Rubber
rect,,r_Steel,,h_Steel
aovlap,all
esize,h_Steel/2
mat,1
type,1
amesh,4
!
mat,2,
type,2
amesh,3
!
nsel,s,loc,y,0.
d,all,uy,0.
allsel,all
nsel,s,loc,y,h_Rubber
sf,all,conv,h_RubberSteel,0. ! Rubber to fixture
alls
!
nsel,s,loc,x,r_Rubber
sf,all,conv,h_RubberAir,0. ! Rubber to air
alls
finish
!
/solu
antype,trans
nlgeom,on
outres,all,all
kbc,0
deltim,5e-3,1e-5,5e-3
nsel,s,loc,y,h_Rubber
d,all,uy,-0.0045
nsel,all
time,0.05
solve
!
nsel,s,loc,y,h_Rubber
*dim,displacement,TABLE,(20-0.05)/0.005+2,1,1,TIME
displacement(1,0,1) = 0.
displacement(1,1,1) = 0.
ii=2
*do,tt,0.05,20,0.005
! Time values
displacement(ii,0,1) = tt
! Displacement values
displacement(ii,1,1) = -0.0045-0.003*sin(2*pi*6.5*tt)
ii=ii+1
*enddo
d,all,uy,%displacement%
allsel,all
time,20
solve
fini
/post1
pldisp ! Deformed shape
plnsol,temp ! Temperature distribution
fini
/post26
numvar,200
ndA=node(0,h_Rubber/3,0)
ndB=node(0,h_Steel,0)
ndC=node(0.015939,0,0)
ndD=node(5*r_Rubber/6,0,0)
nsol,2,ndA,temp,,A
nsol,3,ndB,temp,,B
nsol,4,ndC,temp,,C
nsol,5,ndD,temp,,D
/axlab,x, Time (s)
/axlab,y, Temperature increase (deg C)
/yrange,0,6
plvar,2,3,4,5
nprint,50
prvar,2,3,4,5
fini
For other structural-thermal analysis examples, see the Mechanical APDL Verification Manual:
and this more comprehensive example: