dynamics_truss_elements Module

Two-node, axial-only planar and spatial truss elements. Each node carries only translational degrees of freedom. The global stiffness of a member of length L and unit direction n is

$$K = \frac{E A}{L}\begin{bmatrix}-n\\n\end{bmatrix} \begin{bmatrix}-n^T & n^T\end{bmatrix}.$$

The inherited mass matrix uses consistent linear interpolation, giving rhoAL/6 times [[2I,I],[I,2I]]. Neither element resists bending or has nodal rotational degrees of freedom.

Contents

Interfaces

truss_element_2d truss_element_3d

Derived Types

truss_element_2d truss_element_3d

Interfaces

public interface truss_element_2d

• private pure function t2d_init(mat, area, nd1, nd2) result(rst)

  Initializes a [[truss_element_2d]].

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(material),	intent(in)			::	mat	The elastic material and density.
  real(kind=real64),	intent(in)			::	area	The cross-sectional area.
  class(node),	intent(in)			::	nd1	The first and second truss nodes.
  class(node),	intent(in)			::	nd2	The first and second truss nodes.

  Return Value type(truss_element_2d)

  The initialized planar truss element.

public interface truss_element_3d

• private pure function t3d_init(mat, area, nd1, nd2) result(rst)

  Initializes a [[truss_element_3d]].

  Arguments

  Type	Intent	Optional	Attributes		Name
  class(material),	intent(in)			::	mat	The elastic material and density.
  real(kind=real64),	intent(in)			::	area	The cross-sectional area.
  class(node),	intent(in)			::	nd1	The first and second truss nodes.
  class(node),	intent(in)			::	nd2	The first and second truss nodes.

  Return Value type(truss_element_3d)

  The initialized spatial truss element.

Derived Types

type, public, extends(line_element) ::  truss_element_2d

Defines a pin-jointed 2D bar with x and y translations per node. Use the parent mass_matrix and the global axial stiffness override.

Components

Type	Visibility	Attributes		Name		Initial
real(kind=real64),	public		::	area			The element cross-sectional area.
type(material),	public		::	material			The material.
type(node),	public		::	node_1			The node at natural coordinate s = -1.
type(node),	public		::	node_2			The node at natural coordinate s = 1.

Constructor

private pure function t2d_init (mat, area, nd1, nd2)

Initializes a [[truss_element_2d]].

Type-Bound Procedures

procedure , public :: constitutive_matrix => t2d_constitutive_matrix Function
procedure , public :: evaluate_shape_function => t2d_shape_function Function
procedure , public :: external_force_vector => le_ext_force_vector Function
procedure , public :: get_dimensionality => t2d_dimensionality Function
procedure , public :: get_dof_per_node => t2d_dof_per_node Function
procedure , public :: get_node => t2d_get_node Function
procedure , public :: get_node_count => t2d_node_count Function
procedure , public :: get_node_natural_coordinates => le_get_node_natural_coordinates Function
procedure , public :: get_terminal_nodes => t2d_terminal_nodes Subroutine
procedure , public :: jacobian => t2d_jacobian Function
procedure , public :: length => le_length Function
procedure , public :: mass_matrix => le_mass_matrix Function
procedure , public :: rotation_matrix => t2d_rotation_matrix Function
procedure , public :: shape_function_matrix => t2d_shape_matrix Function
procedure , public :: stiffness_matrix => t2d_stiffness_matrix Function
procedure , public :: strain => le_strain Function
procedure , public :: strain_displacement_matrix => t2d_strain_matrix Function
procedure , public :: stress => le_stress Function

type, public, extends(line_element) ::  truss_element_3d

Defines a pin-jointed 3D bar with three translations per node. The local transverse axes are arbitrary; only the longitudinal direction influences axial strain and stiffness.

Components

Type	Visibility	Attributes		Name		Initial
real(kind=real64),	public		::	area			The element cross-sectional area.
type(material),	public		::	material			The material.
type(node),	public		::	node_1			The node at natural coordinate s = -1.
type(node),	public		::	node_2			The node at natural coordinate s = 1.

Constructor

private pure function t3d_init (mat, area, nd1, nd2)

Initializes a [[truss_element_3d]].

Type-Bound Procedures

procedure , public :: constitutive_matrix => t3d_constitutive_matrix Function
procedure , public :: evaluate_shape_function => t3d_shape_function Function
procedure , public :: external_force_vector => le_ext_force_vector Function
procedure , public :: get_dimensionality => t3d_dimensionality Function
procedure , public :: get_dof_per_node => t3d_dof_per_node Function
procedure , public :: get_node => t3d_get_node Function
procedure , public :: get_node_count => t3d_node_count Function
procedure , public :: get_node_natural_coordinates => le_get_node_natural_coordinates Function
procedure , public :: get_terminal_nodes => t3d_terminal_nodes Subroutine
procedure , public :: jacobian => t3d_jacobian Function
procedure , public :: length => le_length Function
procedure , public :: mass_matrix => le_mass_matrix Function
procedure , public :: rotation_matrix => t3d_rotation_matrix Function
procedure , public :: shape_function_matrix => t3d_shape_matrix Function
procedure , public :: stiffness_matrix => t3d_stiffness_matrix Function
procedure , public :: strain => le_strain Function
procedure , public :: strain_displacement_matrix => t3d_strain_matrix Function
procedure , public :: stress => le_stress Function