SolidDisplacementCondition
SolidDisplacementCondition[pred,vars,pars]
represents a prescribed displacement on a solid boundary for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
SolidDisplacementCondition[pred,vars,pars,lkeys]
represents a prescribed displacement with local parameters specified in pars[lkey].
Details
- SolidDisplacementCondition specifies a boundary condition for SolidMechanicsPDEComponent.
- SolidDisplacementCondition is typically used to prescribe the displacement of a boundary of a solid. Common examples include a beam that has a face displaced from its original position.
- SolidDisplacementCondition constrains the movement of a solid with dependent variables
, 
and 
, independent variables 
and time variable 
. - Stationary variables vars are vars={{u[x1,…,xn],v[x1,…,xn],…},{x1,…,xn}}.
- Time-dependent variables vars are vars={{u[t,x1,…,xn],v[t,x1,…,xn],…},t,{x1,…,xn}}.
- Frequency-dependent variables vars are vars={{u[x1,…,xn],v[x1,…,xn],…},ω,{x1,…,xn}}.
- Model parameters pars are specified as for SolidMechanicsPDEComponent.
- SolidDisplacementCondition implements constraints
, 
and 
with 
the prescribed displacement. - The following model parameters pars can be given:
-
parameter default symbol "Displacement" {0,0,0} 
- To leave direction
unconstrained, None can be specified for that displacement. - The default behavior of SolidDisplacementCondition is a SolidFixedCondition.
- The fixed constraint SolidDisplacementCondition models
, 
and 
. - A prescribed displacement condition boundary can be used with:
-
analysis type applicable Transient Yes Frequency Response Yes Eigenfrequency No Stationary Yes - SolidDisplacementCondition can only be used with an eigenfrequency analysis if the prescribed component is 0 or None.
- SolidDisplacementCondition evaluates to a DirichletCondition.
- The boundary predicate pred can be specified as in DirichletCondition.
Examples
open all close allBasic Examples (3)
Create a zero displacement condition on 
, 
and 
:
SolidDisplacementCondition[x == 0, {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"Displacement" -> {0, 0, 0}|>]Create a zero displacement condition on 
and 
:
SolidDisplacementCondition[x == 0, {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"Displacement" -> {0, 0, None}|>]Create a displacement condition of 1 unit on 
and hold 
fixed:
SolidDisplacementCondition[x == 0, {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"Displacement" -> {1, None, 0}|>]Scope (2)
Create a time-dependent displacement condition:
SolidDisplacementCondition[x == 0, {{u[t, x, y, z], v[t, x, y, z], w[t, x, y, z]}, t, {x, y, z}}, <|"Displacement" -> {Sin[t], 0, None}|>]Create a parametric displacement condition:
SolidDisplacementCondition[x == 0, {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <|"Displacement" -> {None, a, 0}|>]Applications (1)
Set up variables, parameters and a beam of 1 meter length and 1/10 meter height and width:
vars = {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}};
pars = <|"PoissonRatio" -> 0.3, "YoungModulus" -> 2.1 * 10 ^ 9|>;
beam = \!\(\*Graphics3DBox[«5»]\);The beam is held fixed at the left. Prescribe 0 displacement in the 
and 
directions and a displacement of 1/10 meter in the negative 
direction:
displacement = NDSolveValue[{SolidMechanicsPDEComponent[vars, pars] == {0, 0, 0}, SolidFixedCondition[x == 0, vars, pars], SolidDisplacementCondition[x == 1, vars, pars, <|"Displacement" -> {0, 0, -1 / 10}|>]}, {u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}∈beam];Visualize the deformed beam in blue and note that at the right end the prescribed displacement relative to the original beam is satisfied:
VectorDisplacementPlot3D[displacement, {x, y, z}∈beam, VectorSizes -> Full, Rule[...]]Prescribe a displacement of 1/10 meter in the negative 
direction and keep the other directions unconstrained:
displacement = NDSolveValue[{SolidMechanicsPDEComponent[vars, pars] == {0, 0, 0}, SolidFixedCondition[x == 0, vars, pars], SolidDisplacementCondition[x == 1, vars, pars, <|"Displacement" -> {None, None, -1 / 10}|>]}, {u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}∈beam];Visualize the deformed beam in blue and note that at the right end the prescribed displacement relative to the original beam is satisfied:
VectorDisplacementPlot3D[displacement, {x, y, z}∈beam, VectorSizes -> Full, Rule[...]]Properties & Relations (2)
SolidDisplacementCondition evaluates to DirichletCondition:
SolidDisplacementCondition[x == 0, {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}}, <||>, <|"Displacement" -> {a, b, c}|>]SolidFixedCondition is a special case of SolidDisplacementCondition. Set up variables and parameters:
vars = {{u[x, y, z], v[x, y, z], w[x, y, z]}, {x, y, z}};SolidFixedCondition[x == 0, vars, <||>]This is the same as a displacement condition with 0 displacement:
SolidDisplacementCondition[x == 0, vars, <||>, <|"Displacement" -> {0, 0, 0}|>]Text
Wolfram Research (2021), SolidDisplacementCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/SolidDisplacementCondition.html.
CMS
Wolfram Language. 2021. "SolidDisplacementCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SolidDisplacementCondition.html.
APA
Wolfram Language. (2021). SolidDisplacementCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SolidDisplacementCondition.html