fegeometry

Geometry object for finite element analysis

Since R2023a

Description

An fegeometry object contains a geometry for use in a finite element analysis with an femodel object.

Creation

Syntax

gm = fegeometry(geometry)

gm = fegeometry(geometry,MaxRelativeDeviation=d)

gm = fegeometry(nodes,elements)

gm = fegeometry(nodes,elements,ElementIDToRegionID)

Description

gm = fegeometry(geometry) creates an fegeometry object that you can use in a finite element analysis with an femodel object. Alternatively, you can assign a geometry directly to the Geometry property of femodel, for example, femodel.Geometry = geometry.

gm = fegeometry(geometry,MaxRelativeDeviation=d) controls the accuracy of the geometry import from a STEP file by specifying the relative sag.

gm = fegeometry(nodes,elements) creates an fegeometry object from a mesh defined by nodes and elements.

gm = fegeometry(nodes,elements,ElementIDToRegionID) creates a multidomain geometry. ElementIDToRegionID specifies the domain IDs for each element of the mesh.

Input Arguments

geometry — Geometry description

string scalar | character vector | decomposed geometry matrix | handle to a geometry function | triangulation object | delaunayTriangulation object | DiscreteGeometry object | AnalyticGeometry object

Geometry description, specified as one of these values:

• String scalar or character vector that contains a path to an STL or STEP file. The path must end with the file extension ".stl", ".STL", ".stp", ".STP", ".step", ".STEP", or any combination of uppercase and lowercase letters in this extension.

• Decomposed geometry matrix or a handle to a geometry function. For details about a decomposed geometry matrix, see decsg. A geometry function must return the same result for the same input arguments in every function call. Thus, it must not contain functions and expressions designed to return a variety of results, such as random number generators.

• triangulation object. The fegeometry function accepts both surface triangulation and triangulation with tetrahedra for 3-D geometries. For a 3-D geometry created from surface triangulation, the Mesh property remains empty. For a 2-D geometry or a 3-D geometry created from triangulation with tetrahedra, fegeometry uses triangulation points and connectivity list to specify a linear mesh. If the Mesh property is empty or your task requires a more accurate quadratic mesh or a finer linear mesh, use the generateMesh function.

• delaunayTriangulation object. The fegeometry function uses triangulation points to specify a mesh. If your task requires a more accurate quadratic mesh, use the generateMesh function.

• DiscreteGeometry object.

• AnalyticGeometry object.

d — Relative sag

1 (default) | number in the range [0.1, 10]

Relative sag for importing a STEP geometry, specified as a number in the range [0.1, 10]. A relative sag is the ratio between the local absolute sag and the local mesh edge length. The absolute sag is the maximal gap between the mesh and the geometry.

Example: gm = fegeometry("AngleBlock.step",MaxRelativeDeviation=5)

Data Types: double

nodes — Mesh nodes

Nnodes-by-2 numeric matrix | Nnodes-by-3 numeric matrix

Mesh nodes, specified as an Nnodes-by-2 or Nnodes-by-3 matrix for a 2-D or 3-D geometry, respectively. Nnodes is the number of nodes in the mesh. Each row of the matrix contains x-, y-, and, if applicable, z- coordinates of one node.

Data Types: double

elements — Mesh elements

Nelements-by-3 integer matrix | Nelements-by-4 integer matrix | Nelements-by-6 integer matrix | Nelements-by-10 integer matrix

Mesh elements, specified as an integer matrix with Nelements rows and 3, 4, 6, or 10 columns, where Nelements is the number of elements in the mesh.

• Linear planar mesh or linear mesh on the geometry surface has size Nelements-by-3. Each row of elements contains the indices of the triangle corner nodes for a surface element. In this case, the resulting geometry does not contain a full mesh. Create the mesh using the generateMesh function.

• Linear elements have size Nelements-by-4. Each row of elements contains the indices of the tetrahedral corner nodes for an element.

• Quadratic planar mesh or quadratic mesh on the geometry surface has size Nelements-by-6. Each row of elements contains the indices of the triangle corner nodes and edge centers for a surface element. In this case, the resulting geometry does not contain a full mesh. Create the mesh using the generateMesh function.

• Quadratic elements have size Nelements-by-10. Each row of elements contains the indices of the tetrahedral corner nodes and the tetrahedral edge midpoint nodes for an element.

For details on node numbering for linear and quadratic elements, see Mesh Data.

Data Types: double

ElementIDToRegionID — Domain information for each mesh element

vector of positive integers

Domain information for each mesh element, specified as a vector of positive integers. Each mesh element is an ID of a geometric region for an element of the mesh. The length of this vector equals the number of elements in the mesh.

Data Types: double

Properties

NumCells — Number of geometry cells

nonnegative integer

This property is read-only.

Number of geometry cells, returned as a nonnegative integer.

Data Types: double

NumFaces — Number of geometry faces

positive integer

This property is read-only.

Number of geometry faces, returned as a positive integer.

Data Types: double

NumEdges — Number of geometry edges

nonnegative integer

This property is read-only.

Number of geometry edges, returned as a nonnegative integer.

Data Types: double

NumVertices — Number of geometry vertices

nonnegative integer

This property is read-only.

Number of geometry vertices, returned as a nonnegative integer.

Data Types: double

Vertices — Coordinates of geometry vertices

N-by-2 numeric matrix | N-by-3 numeric matrix

This property is read-only.

Coordinates of geometry vertices, returned as an N-by-2 or N-by-3 numeric matrix for a 2-D or 3-D geometry, respectively. Here, N is the number of vertices.

Data Types: double

Mesh — Mesh for solution

FEMesh object

Mesh for solution, specified as an FEMesh object. See FEMesh Properties for details.

Object Functions

addCell	Combine two geometries by adding one inside a cell of another
addFace	Fill void regions in 2-D and split cells in 3-D geometry
addVertex	Add vertex on geometry boundary
addVoid	Create void regions inside 3-D geometry
cellEdges	Find edges belonging to boundaries of specified cells
cellFaces	Find faces belonging to specified cells
extrude	Vertically extrude 2-D geometry or specified faces of 3-D geometry
faceEdges	Find edges belonging to specified faces
facesAttachedToEdges	Find faces attached to specified edges
generateMesh	Create triangular or tetrahedral mesh
mergeCells	Merge geometry cells
nearestEdge	Find edges nearest to specified point
nearestFace	Find faces nearest to specified point
pdegplot	Plot PDE geometry
pdemesh	Plot PDE mesh
rotate	Rotate geometry
scale	Scale geometry
translate	Translate geometry
triangulation	Create triangulation object from fegeometry

Examples

fegeometry Object from DiscreteGeometry Object

Create an fegeometry object from a DiscreteGeometry object by assigning it to an femodel object for a finite element analysis.

Create and plot a 3-D geometry consisting of three nested cuboids of the same height.

gm = multicuboid([2 3 5],[4 6 10],3);
pdegplot(gm,CellLabels="on",FaceAlpha=0.3)

Create an femodel object for solving a static structural problem and assign the geometry to the model.

model = femodel(AnalysisType="structuralStatic", ...
                Geometry=gm);
model.Geometry

ans = 
  fegeometry with properties:

       NumFaces: 18
       NumEdges: 36
    NumVertices: 24
       NumCells: 3
       Vertices: [24x3 double]
           Mesh: []

fegeometry Object from STL File

Create an fegeometry object from an STL file representing a forearm link, and use it for a finite element analysis with an femodel object.

Create an femodel object for solving a static structural problem, and assign the geometry to the model.

model = femodel(AnalysisType="structuralStatic", ...
                Geometry="ForearmLink.stl");
model.Geometry

ans = 
  fegeometry with properties:

       NumFaces: 147
       NumEdges: 329
    NumVertices: 213
       NumCells: 1
       Vertices: [213x3 double]
           Mesh: []

Plot the geometry.

pdegplot(model,FaceAlpha=0.3)

fegeometry Object from Function Handle

Create an fegeometry object from a function handle.

gm = fegeometry(@cardg)

gm = 
  fegeometry with properties:

       NumFaces: 1
       NumEdges: 4
    NumVertices: 4
       NumCells: 0
       Vertices: [4x2 double]
           Mesh: []

Plot the geometry with the edge labels.

pdegplot(gm,EdgeLabels="on");

fegeometry Object from Geometry Description Matrix

Create an fegeometry object from a geometry description matrix.

g = [3 4 0 1 1 0 0 0 1.0 1.0];
sf = 'S1'; 
ns = 'S1';
gm = fegeometry(decsg(g',sf,ns'))

gm = 
  fegeometry with properties:

       NumFaces: 1
       NumEdges: 4
    NumVertices: 4
       NumCells: 0
       Vertices: [4x2 double]
           Mesh: []

Plot the geometry with the edge labels.

pdegplot(gm,EdgeLabels="on");
xlim([-0.1 1.1])
ylim([-0.1 1.1])

fegeometry Object from triangulation Object

Create an fegeometry object from a 2-D triangulation object.

Define the points in a 2-D triangulation.

P = [2.5 8.0;
     6.5 8.0;
     2.5 5.0;
     6.5 5.0;
     1.0 6.5;
     8.0 6.5];

Define the triangulation connectivity list.

T = [5 3 1;
     3 2 1;
     3 4 2;
     4 6 2];

Create the triangulation representation.

TR = triangulation(T,P)

TR = 
  triangulation with properties:

              Points: [6x2 double]
    ConnectivityList: [4x3 double]

Create an fegeometry object from the triangulation object TR.

gm = fegeometry(TR)

gm = 
  fegeometry with properties:

       NumFaces: 1
       NumEdges: 6
    NumVertices: 6
       NumCells: 0
       Vertices: [6x3 double]
           Mesh: [1x1 FEMesh]

The created geometry includes a linear mesh.

gm.Mesh

ans = 
  FEMesh with properties:

             Nodes: [2x6 double]
          Elements: [3x4 double]
    MaxElementSize: 5
    MinElementSize: 2.1213
     MeshGradation: []
    GeometricOrder: 'linear'

To create a more accurate quadratic mesh, use generateMesh.

gm = generateMesh(gm);
gm.Mesh

ans = 
  FEMesh with properties:

             Nodes: [2x871 double]
          Elements: [6x408 double]
    MaxElementSize: 0.3046
    MinElementSize: 0.1523
     MeshGradation: 1.5000
    GeometricOrder: 'quadratic'

Version History

Introduced in R2023a

R2023b: Create geometry from triangulation and delaunayTriangulation objects

You can use triangulation, specified as a triangulation or delaunayTriangulation object, to create an fegeometry object.