structuralIC
Set initial conditions for a transient structural model
Domain-specific structural workflow is not recommended. New features might not be compatible with this workflow. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.
Syntax
Description
structuralIC(
sets initial displacement and velocity for the entire geometry.structuralmodel
,"Displacement",u0
,"Velocity",v0
)
structuralIC(___
sets initial displacement and velocity for a particular geometry region using the
arguments from the previous syntax.RegionType
,RegionID
)
structuralIC(
sets initial displacement and velocity using the solution
structuralmodel
,Sresults
)Sresults
from a previous structural analysis on the same
geometry. If Sresults
is obtained by solving a transient
structural problem, then structuralIC
uses the solution
Sresults
for the last time-step.
structuralIC(
uses the solution structuralmodel
,Sresults
,iT
)Sresults
for the time-step
iT
from a previous structural analysis on the same
geometry.
returns a handle to the structural initial conditions object.struct_ic
= structuralIC(___)
Examples
Specify Initial Velocity
Specify initial velocity values for the entire geometry and for a particular face.
Create a transient dynamic model for a 3-D problem.
structuralmodel = createpde("structural","transient-solid");
Create a geometry and include it into the model. Plot the geometry.
gm = multicuboid(0.06,0.005,0.01); structuralmodel.Geometry = gm; pdegplot(structuralmodel,"FaceLabels","on","FaceAlpha",0.5) view(50,20)
Specify the zero initial velocity on the entire geometry. When you specify only the initial velocity or initial displacement, structuralIC
assumes that the omitted parameter is zero. For example, here the initial displacement is also zero.
structuralIC(structuralmodel,"Velocity",[0;0;0])
ans = GeometricStructuralICs with properties: RegionType: 'Cell' RegionID: 1 InitialDisplacement: [] InitialVelocity: [3x1 double]
Update the initial velocity on face 2 to model impulsive excitation.
structuralIC(structuralmodel,"Face",2,"Velocity",[0;60;0])
ans = GeometricStructuralICs with properties: RegionType: 'Face' RegionID: 2 InitialDisplacement: [] InitialVelocity: [3x1 double]
Specify Nonconstant Initial Displacement by Using Function Handle
Specify initial z-displacement to be dependent on the coordinates x and y.
Create a transient dynamic model for a 3-D problem.
structuralmodel = createpde("structural","transient-solid");
Create the geometry and include it into the model. Plot the geometry.
gm = multicuboid(0.06,0.005,0.01); structuralmodel.Geometry = gm; pdegplot(structuralmodel,"FaceLabels","on","FaceAlpha",0.5) view(50,20)
Specify the zero initial displacement on the entire geometry.
structuralIC(structuralmodel,"Displacement",[0;0;0])
ans = GeometricStructuralICs with properties: RegionType: 'Cell' RegionID: 1 InitialDisplacement: [3x1 double] InitialVelocity: []
Now change the initial displacement in the z-direction on face 2 to a function of the coordinates x and y:
Write the following function file. Save it to a location on your MATLAB® path.
function uinit = initdisp(location)
M = length(location.x);
uinit = zeros(3,M);
uinit(3,:) = location.x.^2 + location.y.^2;
Pass the initial displacement to your structural model.
structuralIC(structuralmodel,"Face",2,"Displacement",@initdisp)
ans = GeometricStructuralICs with properties: RegionType: 'Face' RegionID: 2 InitialDisplacement: @initdisp InitialVelocity: []
Use Static Solution as Initial Condition
Use a static solution as an initial condition for a dynamic structural model.
Create a static model.
staticmodel = createpde("structural","static-solid");
Create the geometry and include it in the model. Plot the geometry.
gm = multicuboid(0.06,0.005,0.01); staticmodel.Geometry = gm; pdegplot(staticmodel,"FaceLabels","on","FaceAlpha",0.5) view(50,20)
Specify Young's modulus, Poisson's ratio, and the mass density.
structuralProperties(staticmodel,"YoungsModulus",210E9, ... "PoissonsRatio",0.3,... "MassDensity",7800);
Apply the boundary condition and static load.
structuralBC(staticmodel,"Face",5,"Constraint","fixed"); structuralBoundaryLoad(staticmodel,"Face",3, ... "SurfaceTraction", ... [0;1E6;0]);
Generate a mesh and solve the model.
generateMesh(staticmodel,"Hmax",0.02);
Rstatic = solve(staticmodel);
Create a dynamic model and assign geometry.
dynamicmodel = createpde("structural","transient-solid"); gm = multicuboid(0.06,0.005,0.01); dynamicmodel.Geometry = gm;
Apply the boundary condition.
structuralBC(dynamicmodel,"Face",5,"Constraint","fixed");
Generate a mesh.
generateMesh(dynamicmodel,"Hmax",0.02);
Specify the initial condition using the static solution.
structuralIC(dynamicmodel,Rstatic)
ans = NodalStructuralICs with properties: InitialDisplacement: [189x3 double] InitialVelocity: [189x3 double]
Input Arguments
structuralmodel
— Transient structural model
StructuralModel
object
Transient structural model, specified as a
StructuralModel
object. The model contains the
geometry, mesh, structural properties of the material, body loads, boundary
loads, boundary conditions, and initial conditions.
Example: structuralmodel =
createpde("structural","transient-solid")
u0
— Initial displacement
numeric vector | function handle
Initial displacement, specified as a numeric vector or function handle. A numeric vector must contain two elements for a 2-D model and three elements for a 3-D model. The elements represent the components of initial displacement.
Use a function handle to specify spatially varying initial displacement. The function must return a two-row matrix for a 2-D model and a three-row matrix for a 3-D model. Each column of the matrix corresponds to the initial displacement at the coordinates provided by the solver. For details, see More About.
Example: structuralIC(structuralmodel,"Face",[2,5],"Displacement",[0;0;0.01])
Data Types: double
| function_handle
v0
— Initial velocity
numeric vector | function handle
Initial velocity, specified as a numeric vector or function handle. A numeric vector must contain two elements for a 2-D model and three elements for a 3-D model. The elements represent the components of initial velocity.
Use a function handle to specify spatially varying initial velocity. The function must return a two-row matrix for a 2-D model and a three-row matrix for a 3-D model. Each column of the matrix corresponds to the initial velocity at the coordinates provided by the solver. For details, see More About.
Example: structuralIC(structuralmodel,"Face",[2,5],"Displacement",[0;0;0.01],"Velocity",[0;60;0])
Data Types: double
| function_handle
RegionType
— Geometric region type
"Face"
| "Edge"
| "Vertex"
| "Cell"
Geometric region type, specified as "Face"
,
"Edge"
, "Vertex"
, or
"Cell"
.
When you apply multiple initial condition assignments, the solver uses these precedence rules for determining the initial condition.
For multiple assignments to the same geometric region, the solver uses the last applied setting.
For separate assignments to a geometric region and the boundaries of that region, the solver uses the specified assignment on the region and chooses the assignment on the boundary as follows. The solver gives an
"Edge"
assignment precedence over a"Face"
assignment, even if you specify a"Face"
assignment after an"Edge"
assignment. The precedence levels are"Vertex"
(highest precedence),"Edge"
,"Face"
,"Cell"
(lowest precedence).For an assignment made with the
results
object, the solver uses that assignment instead of all previous assignments.
Example: structuralIC(structuralmodel,"Face",[2,5],"Displacement",[0;0;0.01],"Velocity",[0;60;0])
Data Types: char
RegionID
— Geometric region ID
vector of positive integers
Geometric region ID, specified as a vector of positive integers. Find the
region IDs by using pdegplot
.
Example: structuralIC(structuralmodel,"Face",[2,5],"Displacement",[0;0;0.01],"Velocity",[0;60;0])
Data Types: double
Sresults
— Structural model solution
StaticStructuralResults
object | TransientStructuralResults
object
Structural model solution, specified as a
StaticStructuralResults
or
TransientStructuralResults
object. Create
Sresults
by using solve
.
iT
— Time index
positive integer
Time index, specified as a positive integer.
Example: structuralIC(structuralmodel,Sresults,21)
Data Types: double
Output Arguments
struct_ic
— Handle to initial conditions
GeometricStructuralICs
object | NodalStructuralICs
object
Handle to initial conditions, returned as a
GeometricStructuralICs
or
NodalStructuralICs
object. See GeometricStructuralICs Properties and NodalStructuralICs Properties.
structuralIC
associates the structural initial
condition with the geometric region in the case of a geometric assignment,
or the nodes in the case of a results-based assignment.
More About
Specifying Nonconstant Parameters of a Structural Model
Use a function handle to specify the following structural parameters when they depend on space and, depending of the type of structural analysis, either time or frequency:
Surface traction on the boundary
Pressure normal to the boundary
Concentrated force at a vertex
Distributed spring stiffness for each translational direction used to model elastic foundation
Enforced displacement and its components
Initial displacement and velocity (can depend on space only)
For example, use function handles to specify the pressure load, x-component of the enforced displacement, and the initial displacement for this model.
structuralBoundaryLoad(model,"Face",12, ... "Pressure",@myfunPressure) structuralBC(model,"Face",2, ... "XDisplacement",@myfunBC) structuralIC(model,"Face",12, ... "Displacement",@myfunIC)
For all parameters, except the initial displacement and velocity, the function must be of the form:
function structuralVal = myfun(location,state)
For the initial displacement and velocity the function must be of the form:
function structuralVal = myfun(location)
The solver computes and populates the data in the location
and
state
structure arrays and passes this data to your function. You can
define your function so that its output depends on this data. You can use any names instead
of location
and state
, but the function must have
exactly two arguments (or one argument if the function specifies the initial displacement or
initial velocity).
location
— A structure containing these fields:location.x
— The x-coordinate of the point or pointslocation.y
— The y-coordinate of the point or pointslocation.z
— For a 3-D or an axisymmetric geometry, the z-coordinate of the point or pointslocation.r
— For an axisymmetric geometry, the r-coordinate of the point or points
Furthermore, for boundary conditions, the solver passes these data in the
location
structure:location.nx
— x-component of the normal vector at the evaluation point or pointslocation.ny
— y-component of the normal vector at the evaluation point or pointslocation.nz
— For a 3-D or an axisymmetric geometry, z-component of the normal vector at the evaluation point or pointslocation.nr
— For an axisymmetric geometry, r-component of the normal vector at the evaluation point or points
state
— A structure containing these fields for dynamic structural problems:state.time
contains the time at evaluation points.state.frequency
contains the frequency at evaluation points.
state.time
andstate.frequency
are scalars.
Boundary constraints and loads get these data from the solver:
location.x
,location.y
,location.z
,location.r
location.nx
,location.ny
,location.nz
,location.nr
state.time
orstate.frequency
(depending of the type of structural analysis)
Initial conditions get these data from the solver:
location.x
,location.y
,location.z
,location.r
Subdomain ID
If a parameter represents a vector value, such as surface traction, spring stiffness, force, or displacement, your function must return a two-row matrix for a 2-D model and a three-row matrix for a 3-D model. Each column of the matrix corresponds to the parameter value (a vector) at the boundary coordinates provided by the solver.
If a parameter represents a scalar value, such as pressure or a displacement component, your function must return a row vector where each element corresponds to the parameter value (a scalar) at the boundary coordinates provided by the solver.
If boundary conditions depend on state.time
or
state.frequency
, ensure that your function returns a matrix of
NaN
of the correct size when state.frequency
or
state.time
are NaN
. Solvers check whether a
problem is nonlinear or time dependent by passing NaN
state values and
looking for returned NaN
values.
Additional Arguments in Functions for Nonconstant Structural Parameters
To use additional arguments in your function, wrap your function (that takes additional arguments) with an anonymous function that takes only the location
and state
arguments. For example:
structuralVal = ... @(location,state) myfunWithAdditionalArgs(location,state,arg1,arg2...) structuralBC(model,"Face",2,"XDisplacement",structuralVal) structuralVal = ... @(location) myfunWithAdditionalArgs(location,arg1,arg2...) structuralIC(model,"Face",2,"Displacement",structuralVal)
Version History
Introduced in R2018a
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