discrete_element – DYNAMICS

type, public, abstract, extends(element) :: discrete_element

Defines a discrete (lumped-parameter) element. Discrete elements have no spatial extent; therefore, the stiffness, mass, and damping matrices default to zero and are overridden only where the element contributes to the system. The inherited material is unused.

Variables

material

Type-Bound Procedures

constitutive_matrix damping_matrix evaluate_shape_function external_force_vector get_dimensionality get_dof_per_node get_node get_node_count get_node_natural_coordinates jacobian mass_matrix shape_function_matrix stiffness_matrix strain strain_displacement_matrix stress

Components

Type	Visibility	Attributes		Name		Initial
type(material),	public		::	material			The material.

Type-Bound Procedures

procedure(element_const_matrix_function), public, deferred, pass :: constitutive_matrix

pure function element_const_matrix_function(this) result(rst) Prototype

Defines the signature of a routine for returning a matrix associated with the element.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.

Return Value real(kind=real64), allocatable, dimension(:,:)

The resulting matrix.

procedure, public :: damping_matrix => de_damping_matrix

private pure function de_damping_matrix(this) result(rst)

Returns the element damping matrix. The default implementation returns a zero-valued matrix.

Arguments

Type	Intent	Optional	Attributes		Name
class(discrete_element),	intent(in)			::	this	The discrete_element object.

Return Value real(kind=real64), allocatable, dimension(:,:)

The N-by-N damping matrix, where N is the total number of element degrees of freedom.

procedure(element_shape_function), public, deferred, pass :: evaluate_shape_function

pure function element_shape_function(this, i, s) result(rst) Prototype

Defines the signature of a routine for computing the value of the i-th element shape function at natural coordinate.

Arguments

Type	Intent	Attributes		Name
class(element),	intent(in)		::	this	The element object.
integer(kind=int32),	intent(in)		::	i	The index of the shape function to evaluate.
real(kind=real64),	intent(in),	dimension(:)	::	s	The value of the natural coordinates at which to evaluate the shape function.

Return Value real(kind=real64)

The value of the i-th shape function at s.

procedure, public :: external_force_vector => de_ext_force_vector

private pure function de_ext_force_vector(this, q, rule) result(rst)

Returns the element external force vector. Discrete elements do not support distributed loads; therefore, a zero-valued vector is returned. Concentrated loads should be applied directly to the global force vector.

Arguments

Type	Intent	Optional	Attributes		Name
class(discrete_element),	intent(in)			::	this	The discrete_element object.
real(kind=real64),	intent(in),		dimension(:)	::	q	The distributed load vector. This argument is unused and is present for interface compatibility.
integer(kind=int32),	intent(in),	optional		::	rule	The integration rule. This argument is unused and is present for interface compatibility.

Return Value real(kind=real64), allocatable, dimension(:)

The N-element force vector, where N is the total number of element degrees of freedom.

procedure(element_query), public, deferred, pass :: get_dimensionality

pure function element_query(this) result(rst) Prototype

Defines the signature of a function performing a query on an integer-valued property of a element type.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.

Return Value integer(kind=int32)

The resulting value.

procedure(element_query), public, deferred, pass :: get_dof_per_node

pure function element_query(this) result(rst) Prototype

Defines the signature of a function performing a query on an integer-valued property of a element type.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.

Return Value integer(kind=int32)

The resulting value.

procedure(element_get_node), public, deferred, pass :: get_node

pure function element_get_node(this, i) result(rst) Prototype

Defines the signature of a function for retrieving the requested node from the element.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.
integer(kind=int32),	intent(in)			::	i	The local index of the node to retrieve.

Return Value type(node)

The node.

procedure(element_query), public, deferred, pass :: get_node_count

pure function element_query(this) result(rst) Prototype

Defines the signature of a function performing a query on an integer-valued property of a element type.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.

Return Value integer(kind=int32)

The resulting value.

procedure, public :: get_node_natural_coordinates => de_get_node_natural_coordinates

private pure function de_get_node_natural_coordinates(this, i) result(rst)

Returns the natural coordinate of the requested node. A single-node element has its node at s = 0; a two-node element has its nodes at s = -1 and s = 1, respectively.

Arguments

Type	Intent	Optional	Attributes		Name
class(discrete_element),	intent(in)			::	this	The discrete_element object.
integer(kind=int32),	intent(in)			::	i	The local index of the node.

Return Value real(kind=real64), allocatable, dimension(:)

The natural coordinate of the node.

procedure, public :: jacobian => de_jacobian

private pure function de_jacobian(this, s) result(rst)

Returns the element Jacobian. Discrete elements have no spatial extent; therefore, a unit 1-by-1 Jacobian is returned.

Arguments

Type	Intent	Optional	Attributes		Name
class(discrete_element),	intent(in)			::	this	The discrete_element object.
real(kind=real64),	intent(in),		dimension(:)	::	s	The natural coordinates at which to evaluate the Jacobian. This argument is unused and is present for interface compatibility.

Return Value real(kind=real64), allocatable, dimension(:,:)

The 1-by-1 Jacobian matrix.

procedure, public :: mass_matrix => de_mass_matrix

private pure function de_mass_matrix(this, rule) result(rst)

Returns the element mass matrix. The default implementation returns a zero-valued matrix.

Arguments

Type	Intent	Optional	Attributes		Name
class(discrete_element),	intent(in)			::	this	The discrete_element object.
integer(kind=int32),	intent(in),	optional		::	rule	The integration rule. This argument is unused and is present for interface compatibility.

Return Value real(kind=real64), allocatable, dimension(:,:)

The N-by-N mass matrix, where N is the total number of element degrees of freedom.

procedure(element_matrix_function), public, deferred, pass :: shape_function_matrix

pure function element_matrix_function(this, s) result(rst) Prototype

Defines the signature of a routine for returning a matrix associated with the element.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.
real(kind=real64),	intent(in),		dimension(:)	::	s	The value of the natural coordinates at which the matrix should be evaluated.

Return Value real(kind=real64), allocatable, dimension(:,:)

The resulting matrix.

procedure, public :: stiffness_matrix => de_stiffness_matrix

private pure function de_stiffness_matrix(this, rule) result(rst)

Returns the element stiffness matrix. The default implementation returns a zero-valued matrix.

Arguments

Type	Intent	Optional	Attributes		Name
class(discrete_element),	intent(in)			::	this	The discrete_element object.
integer(kind=int32),	intent(in),	optional		::	rule	The integration rule. This argument is unused and is present for interface compatibility.

Return Value real(kind=real64), allocatable, dimension(:,:)

The N-by-N stiffness matrix, where N is the total number of element degrees of freedom.

procedure, public :: strain => e_strain

private pure function e_strain(this, displacement, s) result(rst)

Computes the element strain at the specified natural coordinate. The strain is $\boldsymbol{\varepsilon}=B\boldsymbol{u}_e.$

Arguments

Type	Intent	Attributes		Name
class(element),	intent(in)		::	this	The element object.
real(kind=real64),	intent(in),	dimension(:)	::	displacement	The element displacement vector in the element coordinate system.
real(kind=real64),	intent(in),	dimension(:)	::	s	The natural coordinates at which to evaluate the strain.

Return Value real(kind=real64), allocatable, dimension(:)

The resulting strain vector.

procedure(element_matrix_function), public, deferred, pass :: strain_displacement_matrix

pure function element_matrix_function(this, s) result(rst) Prototype

Defines the signature of a routine for returning a matrix associated with the element.

Arguments

Type	Intent	Optional	Attributes		Name
class(element),	intent(in)			::	this	The element object.
real(kind=real64),	intent(in),		dimension(:)	::	s	The value of the natural coordinates at which the matrix should be evaluated.

Return Value real(kind=real64), allocatable, dimension(:,:)

The resulting matrix.

procedure, public :: stress => e_stress

private pure function e_stress(this, displacement, s) result(rst)

Computes the element stress result at the specified natural coordinate. The stress result is $\boldsymbol{\sigma}=D B\boldsymbol{u}_e.$

Arguments

Type	Intent	Attributes		Name
class(element),	intent(in)		::	this	The element object.
real(kind=real64),	intent(in),	dimension(:)	::	displacement	The element displacement vector in the element coordinate system.
real(kind=real64),	intent(in),	dimension(:)	::	s	The natural coordinates at which to evaluate the stress.

Return Value real(kind=real64), allocatable, dimension(:)

The resulting stress vector.

discrete_element Derived Type

Contents

Variables

Type-Bound Procedures

type, public, abstract, extends(element) :: discrete_element

Contents

Variables

Type-Bound Procedures

Components

Type-Bound Procedures

procedure(element_const_matrix_function), public, deferred, pass :: constitutive_matrix

pure function element_const_matrix_function(this) result(rst) Prototype

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure, public :: damping_matrix => de_damping_matrix

private pure function de_damping_matrix(this) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure(element_shape_function), public, deferred, pass :: evaluate_shape_function

pure function element_shape_function(this, i, s) result(rst) Prototype

Arguments

Return Value real(kind=real64)

procedure, public :: external_force_vector => de_ext_force_vector

private pure function de_ext_force_vector(this, q, rule) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

procedure(element_query), public, deferred, pass :: get_dimensionality

pure function element_query(this) result(rst) Prototype

Arguments

Return Value integer(kind=int32)

procedure(element_query), public, deferred, pass :: get_dof_per_node

pure function element_query(this) result(rst) Prototype

Arguments

Return Value integer(kind=int32)

procedure(element_get_node), public, deferred, pass :: get_node

pure function element_get_node(this, i) result(rst) Prototype

Arguments

Return Value type(node)

procedure(element_query), public, deferred, pass :: get_node_count

pure function element_query(this) result(rst) Prototype

Arguments

Return Value integer(kind=int32)

procedure, public :: get_node_natural_coordinates => de_get_node_natural_coordinates

private pure function de_get_node_natural_coordinates(this, i) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

procedure, public :: jacobian => de_jacobian

private pure function de_jacobian(this, s) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure, public :: mass_matrix => de_mass_matrix

private pure function de_mass_matrix(this, rule) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure(element_matrix_function), public, deferred, pass :: shape_function_matrix

pure function element_matrix_function(this, s) result(rst) Prototype

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure, public :: stiffness_matrix => de_stiffness_matrix

private pure function de_stiffness_matrix(this, rule) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure, public :: strain => e_strain

private pure function e_strain(this, displacement, s) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)

procedure(element_matrix_function), public, deferred, pass :: strain_displacement_matrix

pure function element_matrix_function(this, s) result(rst) Prototype

Arguments

Return Value real(kind=real64), allocatable, dimension(:,:)

procedure, public :: stress => e_stress

private pure function e_stress(this, displacement, s) result(rst)

Arguments

Return Value real(kind=real64), allocatable, dimension(:)