beam_element_2d Derived Type

type, public, extends(line_element) :: beam_element_2d

Defines a two-dimensional Bernoulli-Euler beam element.


Contents

Variables

Type-Bound Procedures


Components

Type Visibility Attributes Name Initial
real(kind=real64), public :: area

The element cross-sectional area.
type(material), public :: material

The material.
real(kind=real64), public :: moment_of_inertia

The beam moment of inertia (second moment of area).
type(node), public :: node_1

The first node of the element (s = -1).
type(node), public :: node_2

The second node of the element (s = 1).

Type-Bound Procedures

procedure, public :: constitutive_matrix => b2d_constitutive_matrix

  • private pure function b2d_constitutive_matrix(this) result(rst)

    Computes the constitutive matrix for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.

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

    The resulting matrix.

procedure, public :: evaluate_shape_function => b2d_shape_function

  • private pure function b2d_shape_function(this, i, s) result(rst)

    Evaluates the i-th shape function at natural coordinate s.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d 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

  • private pure function le_ext_force_vector(this, q, rule) result(rst)

    Computes the mass matrix for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(line_element), intent(in) :: this

    The line_element object.
    real(kind=real64), intent(in), dimension(:) :: q

    The surface traction forces vector or body force vector.
    For instance, a 2D problem this vector would look like [qx, qy]**T.
    integer(kind=int32), intent(in), optional :: rule

    The integration rule. The rule must be one of the following:

    • DYN_ONE_POINT_INTEGRATION_RULE

    • DYN_TWO_POINT_INTEGRATION_RULE

    • DYN_THREE_POINT_INTEGRATION_RULE

    • DYN_FOUR_POINT_INTEGRATION_RULE

    The default integration rule is DYN_TWO_POINT_INTEGRATION_RULE.

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

    The resulting vector.

procedure, public :: get_dimensionality => b2d_dimensionality

  • private pure function b2d_dimensionality(this) result(rst)

    Gets the dimensionality of the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.

    Return Value integer(kind=int32)

    The dimensionality.

procedure, public :: get_dof_per_node => b2d_dof_per_node

  • private pure function b2d_dof_per_node(this) result(rst)

    Gets the number of degrees of freedom per node.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.

    Return Value integer(kind=int32)

    The number of DOF per node.

procedure, public :: get_node => b2d_get_node

  • private pure function b2d_get_node(this, i) result(rst)

    Gets the requested node from the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d 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 => b2d_get_node_count

  • private pure function b2d_get_node_count(this) result(rst)

    Gets the number of nodes for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.

    Return Value integer(kind=int32)

    The number of nodes.

procedure, public :: get_terminal_nodes => b2d_terminal_nodes

  • private pure subroutine b2d_terminal_nodes(this, i1, i2)

    Gets the terminal node numbers for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d 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 => b2d_jacobian

  • private pure function b2d_jacobian(this, s) result(rst)

    Computes the Jacobian matrix for a 2D beam element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d 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

  • private pure function le_length(this) result(rst)

    Computes the length of the line_element.

    Arguments

    Type IntentOptional 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 => b2d_mass_matrix

  • private pure function b2d_mass_matrix(this, rule) result(rst)

    Computes the mass matrix for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.
    integer(kind=int32), intent(in), optional :: rule

    The integration rule. The rule must be one of the following:

    • MECH_ONE_POINT_INTEGRATION_RULE

    • MECH_TWO_POINT_INTEGRATION_RULE

    • MECH_THREE_POINT_INTEGRATION_RULE

    • 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.

procedure, public :: rotation_matrix => b2d_rotation_matrix

  • private pure function b2d_rotation_matrix(this) result(rst)

    Computes the rotation matrix for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.

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

    The resulting 6-by-6 rotation matrix.

procedure, public :: shape_function_matrix => b2d_shape_function_matrix_2d

  • private pure function b2d_shape_function_matrix_2d(this, s) result(rst)

    Computes the shape function matrix for a beam element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d 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 :: stiffness_matrix => b2d_stiffness_matrix

  • private pure function b2d_stiffness_matrix(this, rule) result(rst)

    Computes the stiffness matrix for the element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d object.
    integer(kind=int32), intent(in), optional :: rule

    The integration rule. The rule must be one of the following:

    • MECH_ONE_POINT_INTEGRATION_RULE

    • MECH_TWO_POINT_INTEGRATION_RULE

    • MECH_THREE_POINT_INTEGRATION_RULE

    • 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.

procedure, public :: strain_displacement_matrix => b2d_strain_disp_matrix_2d

  • private pure function b2d_strain_disp_matrix_2d(this, s) result(rst)

    Computes the strain-displacement matrix for a 2D beam element.

    Arguments

    Type IntentOptional Attributes Name
    class(beam_element_2d), intent(in) :: this

    The beam_element_2d 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.