Generic mesh operations, and simple mesh definitions. More...

Namespaces
namespace	Hex8
	Simple meshes of 8-noded hexahedral elements in 3d (ElementType::Hex8).

namespace	Quad4
	Simple meshes of 4-noded quadrilateral elements in 2d (ElementType::Quad4).

namespace	Tri3
	Simple meshes of and mesh operations for triangular elements of type ElementType::Tri3.

Classes
class	ManualStitch
	Stitch two mesh objects, specifying overlapping nodes by hand. More...

class	RegularBase
	CRTP base class for regular meshes. More...

class	RegularBase2d
	CRTP base class for regular meshes in 2d. More...

class	RegularBase3d
	CRTP base class for regular meshes in 3d. More...

class	Renumber
	Renumber indices to lowest possible index. More...

class	Reorder
	Reorder to lowest possible index, in specific order. More...

class	Stitch
	Stitch mesh objects, automatically searching for overlapping nodes. More...

class	Vstack
	Vertically stack meshes. More...

Enumerations
enum class	ElementType { Unknown , Quad4 , Hex8 , Tri3 }
	Enumerator for element-types. More...

Functions
template<class D >
std::vector< std::vector< size_t > >	nodaltyings (const D &dofs)
	List nodal tyings based on DOF-numbers per node.

template<class S , class T >
ElementType	defaultElementType (const S &coor, const T &conn)
	Extract the element type based on the connectivity.

array_type::tensor< size_t, 2 >	dofs (size_t nnode, size_t ndim)
	List with DOF-numbers in sequential order.

template<class T >
T	renumber (const T &dofs)
	Renumber to lowest possible index (see GooseFEM::Mesh::Renumber).

template<class S , class T >
array_type::tensor< size_t, 2 >	overlapping (const S &coor_a, const T &coor_b, double rtol=1e-5, double atol=1e-8)
	Find overlapping nodes.

template<class E >
array_type::tensor< size_t, 1 >	coordination (const E &conn)
	Number of elements connected to each node.

template<class E >
std::vector< std::vector< size_t > >	elem2node (const E &conn, bool sorted=true)
	Elements connected to each node.

template<class E , class D >
std::vector< std::vector< size_t > >	elem2node (const E &conn, const D &dofs, bool sorted=true)
	Elements connected to each node.

template<class D >
std::vector< std::vector< size_t > >	node2dof (const D &dofs, bool sorted=true)
	Nodes connected to each DOF.

template<class C , class E >
array_type::tensor< double, 2 >	edgesize (const C &coor, const E &conn, ElementType type)
	Return size of each element edge.

template<class C , class E >
array_type::tensor< double, 2 >	edgesize (const C &coor, const E &conn)
	Return size of each element edge.

template<class C , class E >
array_type::tensor< double, 2 >	centers (const C &coor, const E &conn, ElementType type)
	Coordinates of the center of each element.

template<class C , class E >
array_type::tensor< double, 2 >	centers (const C &coor, const E &conn)
	Coordinates of the center of each element.

template<class T , class C , class E >
array_type::tensor< size_t, 1 >	elemmap2nodemap (const T &elem_map, const C &coor, const E &conn, ElementType type)
	Convert an element-map to a node-map.

template<class T , class C , class E >
array_type::tensor< size_t, 1 >	elemmap2nodemap (const T &elem_map, const C &coor, const E &conn)
	Convert an element-map to a node-map.

template<class C , class E >
array_type::tensor< double, 2 >	nodal_mass (const C &coor, const E &conn, ElementType type)
	Compute the mass of each node in the mesh.

template<class C , class E >
array_type::tensor< double, 2 >	nodal_mass (const C &coor, const E &conn)
	Compute the mass of each node in the mesh.

template<class C , class E >
array_type::tensor< double, 1 >	center_of_gravity (const C &coor, const E &conn, ElementType type)
	Compute the center of gravity of a mesh.

template<class C , class E >
array_type::tensor< double, 1 >	center_of_gravity (const C &coor, const E &conn)
	Compute the center of gravity of a mesh.

Detailed Description

Generic mesh operations, and simple mesh definitions.

Enumeration Type Documentation

◆ ElementType

enum class GooseFEM::Mesh::ElementType

strong

Enumerator for element-types.

Enumerator
Unknown	Unknown element-type.
Quad4	Quadrilateral: 4-noded element in 2-d.
Hex8	Hexahedron: 8-noded element in 3-d.
Tri3	Triangle: 3-noded element in 2-d.

Definition at line 31 of file Mesh.h.

Function Documentation

◆ center_of_gravity() [1/2]

template<class C , class E >

array_type::tensor< double, 1 > GooseFEM::Mesh::center_of_gravity	(	const C &	coor,
		const E &	conn )

inline

Compute the center of gravity of a mesh.

Template Parameters

C	e.g. `array_type::tensor<double, 2>`
E	e.g. `array_type::tensor<size_t, 2>`

Parameters

coor	Nodal coordinates `[nnode, ndim]`.
conn	Connectivity `[nelem, nne]`.

Returns: Center of gravity [ndim].

Definition at line 2826 of file Mesh.h.

◆ center_of_gravity() [2/2]

template<class C , class E >

array_type::tensor< double, 1 > GooseFEM::Mesh::center_of_gravity	(	const C &	coor,
		const E &	conn,
		ElementType	type )

inline

Compute the center of gravity of a mesh.

Template Parameters

C	e.g. `array_type::tensor<double, 2>`
E	e.g. `array_type::tensor<size_t, 2>`

Parameters

coor	Nodal coordinates `[nnode, ndim]`.
conn	Connectivity `[nelem, nne]`.
type	ElementType.

Returns: Center of gravity [ndim].

Definition at line 2809 of file Mesh.h.

◆ centers() [1/2]

template<class C , class E >

array_type::tensor< double, 2 > GooseFEM::Mesh::centers	(	const C &	coor,
		const E &	conn )

inline

Coordinates of the center of each element.

The element-type is automatically determined, see defaultElementType().

Parameters

coor	Nodal coordinates.
conn	Connectivity.

Returns: Center of each element.

Definition at line 2656 of file Mesh.h.

◆ centers() [2/2]

template<class C , class E >

array_type::tensor< double, 2 > GooseFEM::Mesh::centers	(	const C &	coor,
		const E &	conn,
		ElementType	type )

inline

Coordinates of the center of each element.

Parameters

coor	Nodal coordinates.
conn	Connectivity.
type	ElementType.

Returns: Center of each element.

Definition at line 2626 of file Mesh.h.

◆ coordination()

template<class E >

array_type::tensor< size_t, 1 > GooseFEM::Mesh::coordination ( const E & conn )

inline

Number of elements connected to each node.

Parameters

conn	Connectivity [nelem, nne].

Returns: Coordination per node.

Definition at line 2463 of file Mesh.h.

◆ defaultElementType()

template<class S , class T >

ElementType GooseFEM::Mesh::defaultElementType	(	const S &	coor,
		const T &	conn )

inline

Extract the element type based on the connectivity.

Parameters

coor	Nodal coordinates [nnode, ndim].
conn	Connectivity [nelem, nne].

Returns: ElementType().

Definition at line 46 of file Mesh.h.

◆ dofs()

array_type::tensor< size_t, 2 > GooseFEM::Mesh::dofs	(	size_t	nnode,
		size_t	ndim )

inline

List with DOF-numbers in sequential order.

The output is a sequential list of DOF-numbers for each vector-component of each node. For example for 3 nodes in 2 dimensions the output is

\( \begin{bmatrix} 0 & 1 \\ 2 & 3 \\ 4 & 5 \end{bmatrix} \)

Parameters

nnode	Number of nodes.
ndim	Number of dimensions.

Returns: DOF-numbers.

Definition at line 93 of file Mesh.h.

◆ edgesize() [1/2]

template<class C , class E >

array_type::tensor< double, 2 > GooseFEM::Mesh::edgesize	(	const C &	coor,
		const E &	conn )

inline

Return size of each element edge.

The element-type is automatically determined, see defaultElementType().

Parameters

coor	Nodal coordinates.
conn	Connectivity.

Returns: Edge-sizes per element.

Definition at line 2612 of file Mesh.h.

◆ edgesize() [2/2]

template<class C , class E >

array_type::tensor< double, 2 > GooseFEM::Mesh::edgesize	(	const C &	coor,
		const E &	conn,
		ElementType	type )

inline

Return size of each element edge.

Parameters

coor	Nodal coordinates.
conn	Connectivity.
type	ElementType.

Returns: Edge-sizes per element.

Definition at line 2571 of file Mesh.h.

◆ elem2node() [1/2]

template<class E >

std::vector< std::vector< size_t > > GooseFEM::Mesh::elem2node	(	const E &	conn,
		bool	sorted = true )

inline

Elements connected to each node.

Parameters

conn	Connectivity [nelem, nne].
sorted	If `true` the list of elements for each node is sorted.

Returns: Elements per node [nnode, ...].

Definition at line 2486 of file Mesh.h.

◆ elem2node() [2/2]

template<class E , class D >

std::vector< std::vector< size_t > > GooseFEM::Mesh::elem2node	(	const E &	conn,
		const D &	dofs,
		bool	sorted = true )

inline

Elements connected to each node.

Parameters

conn	Connectivity [nelem, nne].
sorted	If `true` the list of elements for each node is sorted.

Returns: Elements per node [nnode, ...].

Parameters

dofs	DOFs per node, allowing accounting for periodicity [nnode, ndim].

Definition at line 2517 of file Mesh.h.

◆ elemmap2nodemap() [1/2]

template<class T , class C , class E >

array_type::tensor< size_t, 1 > GooseFEM::Mesh::elemmap2nodemap	(	const T &	elem_map,
		const C &	coor,
		const E &	conn )

inline

Convert an element-map to a node-map.

The element-type is automatically determined, see defaultElementType().

Parameters

elem_map	Element-map such that `new_elvar = elvar[elem_map]`.
coor	Nodal coordinates.
conn	Connectivity.

Returns: Node-map such that new_nodevar = nodevar[node_map]

Definition at line 2712 of file Mesh.h.

◆ elemmap2nodemap() [2/2]

template<class T , class C , class E >

array_type::tensor< size_t, 1 > GooseFEM::Mesh::elemmap2nodemap	(	const T &	elem_map,
		const C &	coor,
		const E &	conn,
		ElementType	type )

inline

Convert an element-map to a node-map.

Parameters

elem_map	Element-map such that `new_elvar = elvar[elem_map]`.
coor	Nodal coordinates.
conn	Connectivity.
type	ElementType.

Returns: Node-map such that new_nodevar = nodevar[node_map]

Definition at line 2672 of file Mesh.h.

◆ nodal_mass() [1/2]

template<class C , class E >

array_type::tensor< double, 2 > GooseFEM::Mesh::nodal_mass	(	const C &	coor,
		const E &	conn )

inline

Compute the mass of each node in the mesh.

If nodes are not part of the connectivity the mass is set to zero, such that the center of gravity is simply::

 average(coor, GooseFEM.Mesh.nodal_mass(coor, conn), axis=0);

Template Parameters

C	e.g. `array_type::tensor<double, 2>`
E	e.g. `array_type::tensor<size_t, 2>`

Parameters

coor	Nodal coordinates `[nnode, ndim]`.
conn	Connectivity `[nelem, nne]`.

Returns: Center of gravity [ndim].

Definition at line 2768 of file Mesh.h.

◆ nodal_mass() [2/2]

template<class C , class E >

array_type::tensor< double, 2 > GooseFEM::Mesh::nodal_mass	(	const C &	coor,
		const E &	conn,
		ElementType	type )

inline

Compute the mass of each node in the mesh.

If nodes are not part of the connectivity the mass is set to zero, such that the center of gravity is simply::

 average(coor, GooseFEM.Mesh.nodal_mass(coor, conn, type), axis=0);

Template Parameters

C	e.g. `array_type::tensor<double, 2>`
E	e.g. `array_type::tensor<size_t, 2>`

Parameters

coor	Nodal coordinates `[nnode, ndim]`.
conn	Connectivity `[nelem, nne]`.
type	ElementType.

Returns: Center of gravity [ndim].

Definition at line 2732 of file Mesh.h.

◆ nodaltyings()

template<class D >

std::vector< std::vector< size_t > > GooseFEM::Mesh::nodaltyings ( const D & dofs )

inline

List nodal tyings based on DOF-numbers per node.

Parameters

dofs	DOFs per node [nnode, ndim].

Returns: Nodes to which the nodes is connected (sorted) [nnode, ...]

Definition at line 2840 of file Mesh.h.

◆ node2dof()

template<class D >

std::vector< std::vector< size_t > > GooseFEM::Mesh::node2dof	(	const D &	dofs,
		bool	sorted = true )

inline

Nodes connected to each DOF.

Parameters

dofs	DOFs per node [nnode, ndim].
sorted	If `true` the list of nodes for each DOF is sorted.

Returns: Nodes per DOF [ndof, ...].

Definition at line 2557 of file Mesh.h.

◆ overlapping()

template<class S , class T >

array_type::tensor< size_t, 2 > GooseFEM::Mesh::overlapping	(	const S &	coor_a,
		const T &	coor_b,
		double	rtol = 1e-5,
		double	atol = 1e-8 )

inline

Find overlapping nodes.

The output has the following structure:

 [
     [nodes_from_mesh_a],
     [nodes_from_mesh_b],
 ]

Parameters

coor_a	Nodal coordinates of mesh "a" [nnode, ndim].
coor_b	Nodal coordinates of mesh "b" [nnode, ndim].
rtol	Relative tolerance for position match.
atol	Absolute tolerance for position match.

Returns: Overlapping nodes.

Definition at line 1716 of file Mesh.h.

◆ renumber()

template<class T >

T GooseFEM::Mesh::renumber ( const T & dofs )

inline

Renumber to lowest possible index (see GooseFEM::Mesh::Renumber).

Parameters

dofs	DOF-numbers [nnode, ndim].

Returns: Renumbered DOF-numbers.

Definition at line 172 of file Mesh.h.

Namespaces

Classes

Enumerations

Functions

Detailed Description

Enumeration Type Documentation

◆ ElementType

Function Documentation

◆ center_of_gravity() [1/2]

◆ center_of_gravity() [2/2]

◆ centers() [1/2]

◆ centers() [2/2]

◆ coordination()

◆ defaultElementType()

◆ dofs()

◆ edgesize() [1/2]

◆ edgesize() [2/2]

◆ elem2node() [1/2]

◆ elem2node() [2/2]

◆ elemmap2nodemap() [1/2]

◆ elemmap2nodemap() [2/2]

◆ nodal_mass() [1/2]

◆ nodal_mass() [2/2]

◆ nodaltyings()

◆ node2dof()

◆ overlapping()

◆ renumber()