beam_element_3d Derived Type
type, public, extends(line_element) :: beam_element_3d
Defines a three-dimensional Bernoulli-Euler beam element.
The local x-axis runs from node 1 to node 2. The orientation point defines the local z-axis; the local y-axis completes the right-handed element coordinate system.
Components
| Type | Visibility | Attributes | Name | Initial | |||
|---|---|---|---|---|---|---|---|
| real(kind=real64), | public | :: | Ixx |
The beam moment of inertia about the element x-axis. |
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| real(kind=real64), | public | :: | Iyy |
The beam moment of inertia about the element y-axis. |
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| real(kind=real64), | public | :: | Iyz |
The cross-sectional product of inertia. |
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| real(kind=real64), | public | :: | Izz |
The beam moment of inertia about the element z-axis. |
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| real(kind=real64), | public | :: | area |
The element cross-sectional area. |
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| type(material), | public | :: | material |
The material. |
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| type(node), | public | :: | node_1 |
The first node of the element (s = -1). |
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| type(node), | public | :: | node_2 |
The second node of the element (s = 1). |
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| type(point), | public | :: | orientation_point |
A point used to determine the orientation of the beam in 3D space. The orientation point is measured relative to the first node in the element. Specifically, the element z axis is assumed to be defined by the location of this point relative to the location of node 1. |
Constructor
public interface beam_element_3d
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private pure function b3d_init(mat, area, ixx, iyy, izz, iyz, nd1, nd2, orient) result(rst)
Constructs a new [[beam_element_3d]] object.
Arguments
Type Intent Optional Attributes Name class(material), intent(in) :: mat The material.
real(kind=real64), intent(in) :: area The cross-sectional area.
real(kind=real64), intent(in) :: ixx The moment of inertia about the element's x-axis (torsional).
real(kind=real64), intent(in) :: iyy The moment of inertia about the element's y-axis.
real(kind=real64), intent(in) :: izz The moment of inertia about the element's z-axis.
real(kind=real64), intent(in) :: iyz The cross-sectional product of inertia.
class(node), intent(in) :: nd1 The first node.
class(node), intent(in) :: nd2 The second node.
class(point), intent(in) :: orient An orientation node that locates the direction of the element z-axis. The orientation point is measured relative to the first node in the element. Specifically, the element z-axis is assumed to be defined by the location of this point relative to the location of node 1.
Return Value type(beam_element_3d)
The new [[beam_element_3d]] object.
Type-Bound Procedures
procedure, public :: bending_moment => b3d_bending_moment
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private pure function b3d_bending_moment(this, displacement, s) result(rst)
Computes the local moment vector at the specified natural coordinate. The result is ordered as [torsional, y-axis, z-axis] moments.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam element.
real(kind=real64), intent(in), dimension(:) :: displacement The element displacement vector in the global coordinate system.
real(kind=real64), intent(in), dimension(:) :: s The natural coordinate at which to evaluate the moments.
Return Value real(kind=real64), (3)
The local moment vector.
procedure, public :: constitutive_matrix => b3d_constitutive_matrix
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private pure function b3d_constitutive_matrix(this) result(rst)
Computes the constitutive matrix for the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
Return Value real(kind=real64), allocatable, dimension(:,:)
The resulting matrix.
procedure, public :: evaluate_shape_function => b3d_shape_function
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private pure function b3d_shape_function(this, i, s) result(rst)
Evaluates the i-th shape function at natural coordinate s.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d 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 coordinate 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 => le_ext_force_vector
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private pure function le_ext_force_vector(this, q, rule) result(rst)
Computes the external force vector for the element.
Arguments
Type Intent Optional Attributes Name class(line_element), intent(in) :: this The line_element object.
real(kind=real64), intent(in), dimension(:) :: q The surface traction or body-force vector.
integer(kind=int32), intent(in), optional :: rule The optional numerical integration rule.
Return Value real(kind=real64), allocatable, dimension(:)
The resulting vector.
procedure, public :: get_dimensionality => b3d_dimensionality
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private pure function b3d_dimensionality(this) result(rst)
Gets the dimensionality of the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
Return Value integer(kind=int32)
The dimensionality.
procedure, public :: get_dof_per_node => b3d_dof_per_node
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private pure function b3d_dof_per_node(this) result(rst)
Gets the number of degrees of freedom per node.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
Return Value integer(kind=int32)
The number of DOF per node.
procedure, public :: get_node => b3d_get_node
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private pure function b3d_get_node(this, i) result(rst)
Gets the requested node from the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
integer(kind=int32), intent(in) :: i The local index of the node to retrieve.
Return Value type(node)
The requested node.
procedure, public :: get_node_count => b3d_get_node_count
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private pure function b3d_get_node_count(this) result(rst)
Gets the number of nodes for the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
Return Value integer(kind=int32)
The number of nodes.
procedure, public :: get_node_natural_coordinates => le_get_node_natural_coordinates
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private pure function le_get_node_natural_coordinates(this, i) result(rst)
Returns the natural coordinate of a terminal node.
Arguments
Type Intent Optional Attributes Name class(line_element), intent(in) :: this The line_element object.
integer(kind=int32), intent(in) :: i The local node index.
Return Value real(kind=real64), allocatable, dimension(:)
The natural coordinate of the node.
procedure, public :: get_terminal_nodes => b3d_terminal_nodes
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private pure subroutine b3d_terminal_nodes(this, i1, i2)
Gets the terminal node numbers for the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
integer(kind=int32), intent(out) :: i1 The index of the node at the head of the element.
integer(kind=int32), intent(out) :: i2 The index of the node at the tail of the element.
procedure, public :: jacobian => b3d_jacobian
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private pure function b3d_jacobian(this, s) result(rst)
Computes the Jacobian matrix for a 3D beam element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
real(kind=real64), intent(in), dimension(:) :: s The value of the natural coordinate at which to evaluate the matrix.
Return Value real(kind=real64), allocatable, dimension(:,:)
The Jacobian matrix.
procedure, public :: length => le_length
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private pure function le_length(this) result(rst)
Computes the length of the line_element.
Arguments
Type Intent Optional Attributes Name class(line_element), intent(in) :: this The line_element object.
Return Value real(kind=real64)
The length of the line element.
procedure, public :: mass_matrix => b3d_mass_matrix
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private pure function b3d_mass_matrix(this, rule) result(rst)
Computes the consistent mass matrix for the element. Translational and bending terms scale with , and the torsional terms scale with .
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
integer(kind=int32), intent(in), optional :: rule The integration rule. This argument is unused and is present for interface compatibility; the mass matrix is computed in closed form.
Return Value real(kind=real64), allocatable, dimension(:,:)
The resulting matrix.
procedure, public :: rotation_matrix => b3d_rotation_matrix
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private pure function b3d_rotation_matrix(this) result(rst)
Computes the rotation matrix for the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
Return Value real(kind=real64), allocatable, dimension(:,:)
The resulting 12-by-12 rotation matrix.
procedure, public :: shape_function_matrix => b3d_shape_function_matrix_3d
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private pure function b3d_shape_function_matrix_3d(this, s) result(rst)
Computes the shape function matrix for a beam element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
real(kind=real64), intent(in), dimension(:) :: s The value of the natural coordinate at which to evaluate the shape functions.
Return Value real(kind=real64), allocatable, dimension(:,:)
The shape function matrix.
procedure, public :: shear_force => b3d_shear_force
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private pure function b3d_shear_force(this, displacement, s) result(rst)
Computes the local shear force vector at the specified natural coordinate. The result is ordered as [y-axis, z-axis] forces.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam element.
real(kind=real64), intent(in), dimension(:) :: displacement The element displacement vector in the global coordinate system.
real(kind=real64), intent(in), dimension(:) :: s The natural coordinate at which to evaluate the shear forces.
Return Value real(kind=real64), (2)
The local shear force vector.
procedure, public :: stiffness_matrix => b3d_stiffness_matrix
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private pure function b3d_stiffness_matrix(this, rule) result(rst)
Computes the stiffness matrix for the element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
integer(kind=int32), intent(in), optional :: rule The integration rule. The rule must be one of the following:
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MECH_ONE_POINT_INTEGRATION_RULE
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MECH_TWO_POINT_INTEGRATION_RULE
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MECH_THREE_POINT_INTEGRATION_RULE
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MECH_FOUR_POINT_INTEGRATION_RULE
The default integration rule is MECH_TWO_POINT_INTEGRATION_RULE.
Return Value real(kind=real64), allocatable, dimension(:,:)
The resulting matrix.
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procedure, public :: strain => le_strain
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private pure function le_strain(this, displacement, s) result(rst)
Computes the line-element strain from global element displacements at the specified natural coordinate.
Arguments
Type Intent Optional Attributes Name class(line_element), intent(in) :: this The line_element object.
real(kind=real64), intent(in), dimension(:) :: displacement The element displacement vector in the global 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 in the element coordinate system.
procedure, public :: strain_displacement_matrix => b3d_strain_disp_matrix_3d
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private pure function b3d_strain_disp_matrix_3d(this, s) result(rst)
Computes the strain-displacement matrix for a 3D beam element.
Arguments
Type Intent Optional Attributes Name class(beam_element_3d), intent(in) :: this The beam_element_3d object.
real(kind=real64), intent(in), dimension(:) :: s The value of the natural coordinate at which to evaluate the matrix.
Return Value real(kind=real64), allocatable, dimension(:,:)
The strain-displacement matrix.
procedure, public :: stress => le_stress
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private pure function le_stress(this, displacement, s) result(rst)
Computes the line-element stress result from global element displacements at the specified natural coordinate.
Arguments
Type Intent Optional Attributes Name class(line_element), intent(in) :: this The line_element object.
real(kind=real64), intent(in), dimension(:) :: displacement The element displacement vector in the global 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 in the element coordinate system.