Structural analysis and line elements

Functions
double	c_beam_element_2d_length (const c_beam_element_2d *elem)
	Compute the length of a 2D beam element.
void	c_beam_element_2d_stiffness_matrix (const c_beam_element_2d *elem, int rule, double *k, int ldk)
	Compute the 6-by-6 stiffness matrix of a 2D beam element.
void	c_beam_element_2d_mass_matrix (const c_beam_element_2d *elem, int rule, double *m, int ldm)
	Compute the 6-by-6 mass matrix of a 2D beam element.
void	c_beam_element_2d_rotation_matrix (const c_beam_element_2d *elem, double *r, int ldr)
	Compute the 6-by-6 rotation matrix of a 2D beam element.
void	c_beam_element_2d_strain (const c_beam_element_2d *elem, const double displacement[6], double s, double strain[2])
	Compute the strain in a 2D beam element at a natural coordinate.
void	c_beam_element_2d_stress (const c_beam_element_2d *elem, const double displacement[6], double s, double stress[2])
	Compute the stress in a 2D beam element at a natural coordinate.
double	c_beam_element_2d_shear_force (const c_beam_element_2d *elem, const double displacement[6], double s)
	Compute the local shear force in a 2D beam element at a natural coordinate.
double	c_beam_element_2d_bending_moment (const c_beam_element_2d *elem, const double displacement[6], double s)
	Compute the local bending moment in a 2D beam element at a natural coordinate.
void	c_beam_element_2d_external_force_vector (const c_beam_element_2d *elem, const double q[2], int rule, double f[6])
	Compute the equivalent nodal force vector for a distributed load on a 2D beam element.
double	c_beam_element_3d_length (const c_beam_element_3d *elem)
	Compute the length of a 3D beam element.
void	c_beam_element_3d_stiffness_matrix (const c_beam_element_3d *elem, int rule, double *k, int ldk)
	Compute the 12-by-12 stiffness matrix of a 3D beam element.
void	c_beam_element_3d_mass_matrix (const c_beam_element_3d *elem, int rule, double *m, int ldm)
	Compute the 12-by-12 mass matrix of a 3D beam element.
void	c_beam_element_3d_rotation_matrix (const c_beam_element_3d *elem, double *r, int ldr)
	Compute the 12-by-12 rotation matrix of a 3D beam element.
void	c_beam_element_3d_strain (const c_beam_element_3d *elem, const double displacement[12], double s, double strain[4])
	Compute the strain in a 3D beam element at a natural coordinate.
void	c_beam_element_3d_stress (const c_beam_element_3d *elem, const double displacement[12], double s, double stress[4])
	Compute the stress in a 3D beam element at a natural coordinate.
void	c_beam_element_3d_shear_force (const c_beam_element_3d *elem, const double displacement[12], double s, double force[2])
	Compute the local shear-force vector in a 3D beam element at a natural coordinate.
void	c_beam_element_3d_bending_moment (const c_beam_element_3d *elem, const double displacement[12], double s, double moment[3])
	Compute the local moment vector in a 3D beam element at a natural coordinate.
void	c_beam_element_3d_external_force_vector (const c_beam_element_3d *elem, const double q[4], int rule, double f[12])
	Compute the equivalent nodal force vector for a distributed load on a 3D beam element.
void	c_assemble_static_system_beam_2d (int gdof, int n, const c_beam_element_2d *elements, int nn, const c_node *nodes, int rule, double *k, int ldk)
	Assemble a dense global stiffness matrix from 2D beam elements.
void	c_assemble_dynamic_system_beam_2d (int gdof, int n, const c_beam_element_2d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
	Assemble dense global mass and stiffness matrices from 2D beam elements.
void	c_assemble_static_system_beam_3d (int gdof, int n, const c_beam_element_3d *elements, int nn, const c_node *nodes, int rule, double *k, int ldk)
	Assemble a dense global stiffness matrix from 3D beam elements.
void	c_assemble_dynamic_system_beam_3d (int gdof, int n, const c_beam_element_3d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
	Assemble dense global mass and stiffness matrices from 3D beam elements.
void	c_apply_boundary_conditions_mtx (int n, int nbc, int *gdof, const double *x, int ldx, double *rst, int ldr)
	Apply boundary conditions to a dense matrix by removing the constrained rows and columns.
void	c_apply_boundary_conditions_vec (int n, int nbc, int *gdof, const double *x, double *rst)
	Apply boundary conditions to a dense vector by removing the constrained entries.
void	c_restore_constrained_values_dense (int nred, int nbc, int *gdof, const double *x, double *rst)
	Restore the constrained degrees of freedom removed by c_apply_boundary_conditions_vec.
void	c_apply_displacement_constraint_dense (int dof, double val, int n, double *k, int ldk, double *f)
	Apply a displacement constraint to a single degree of freedom.
void	c_solve_static_system_dense (int n, const double *k, int ldk, const double *f, double *u)
	Solve the static system K*u = f for a dense stiffness matrix.
double	c_truss_element_2d_length (const c_truss_element_2d *elem)
	Compute the length of a 2D truss element.
void	c_truss_element_2d_stiffness_matrix (const c_truss_element_2d *elem, double *k, int ldk)
	Compute the 4-by-4 global stiffness matrix of a 2D truss element.
void	c_truss_element_2d_mass_matrix (const c_truss_element_2d *elem, int rule, double *m, int ldm)
	Compute the 4-by-4 consistent mass matrix of a 2D truss element.
void	c_truss_element_2d_rotation_matrix (const c_truss_element_2d *elem, double *r, int ldr)
	Compute the 4-by-4 rotation matrix of a 2D truss element.
double	c_truss_element_2d_strain (const c_truss_element_2d *elem, const double displacement[4])
	Compute the axial strain in a 2D truss element.
double	c_truss_element_2d_axial_force (const c_truss_element_2d *elem, const double displacement[4])
	Compute the axial force (positive in tension) in a 2D truss element.
void	c_truss_element_2d_external_force_vector (const c_truss_element_2d *elem, const double q[2], int rule, double f[4])
	Compute the equivalent nodal force vector for a distributed load on a 2D truss element.
double	c_truss_element_3d_length (const c_truss_element_3d *elem)
	Compute the length of a 3D truss element.
void	c_truss_element_3d_stiffness_matrix (const c_truss_element_3d *elem, double *k, int ldk)
	Compute the 6-by-6 global stiffness matrix of a 3D truss element.
void	c_truss_element_3d_mass_matrix (const c_truss_element_3d *elem, int rule, double *m, int ldm)
	Compute the 6-by-6 consistent mass matrix of a 3D truss element.
void	c_truss_element_3d_rotation_matrix (const c_truss_element_3d *elem, double *r, int ldr)
	Compute the 6-by-6 rotation matrix of a 3D truss element.
double	c_truss_element_3d_strain (const c_truss_element_3d *elem, const double displacement[6])
	Compute the axial strain in a 3D truss element.
double	c_truss_element_3d_axial_force (const c_truss_element_3d *elem, const double displacement[6])
	Compute the axial force (positive in tension) in a 3D truss element.
void	c_truss_element_3d_external_force_vector (const c_truss_element_3d *elem, const double q[3], int rule, double f[6])
	Compute the equivalent nodal force vector for a distributed load on a 3D truss element.
void	c_assemble_static_system_truss_2d (int gdof, int n, const c_truss_element_2d *elements, int nn, const c_node *nodes, double *k, int ldk)
	Assemble a dense global stiffness matrix from 2D truss elements.
void	c_assemble_dynamic_system_truss_2d (int gdof, int n, const c_truss_element_2d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
	Assemble dense global mass and stiffness matrices from 2D truss elements.
void	c_assemble_static_system_truss_3d (int gdof, int n, const c_truss_element_3d *elements, int nn, const c_node *nodes, double *k, int ldk)
	Assemble a dense global stiffness matrix from 3D truss elements.
void	c_assemble_dynamic_system_truss_3d (int gdof, int n, const c_truss_element_3d *elements, int nn, const c_node *nodes, int rule, double *m, int ldm, double *k, int ldk)
	Assemble dense global mass and stiffness matrices from 3D truss elements.
void	c_spring_element_2d_stiffness_matrix (const c_spring_element_2d *elem, double *k, int ldk)
	Compute the 4-by-4 global stiffness matrix of a 2D spring element.
double	c_spring_element_2d_force (const c_spring_element_2d *elem, const double displacement[4])
	Compute the spring force (positive in tension) in a 2D spring element.
void	c_spring_element_3d_stiffness_matrix (const c_spring_element_3d *elem, double *k, int ldk)
	Compute the 6-by-6 global stiffness matrix of a 3D spring element.
double	c_spring_element_3d_force (const c_spring_element_3d *elem, const double displacement[6])
	Compute the spring force (positive in tension) in a 3D spring element.
void	c_damper_element_2d_damping_matrix (const c_damper_element_2d *elem, double *c, int ldc)
	Compute the 4-by-4 global damping matrix of a 2D damper element.
double	c_damper_element_2d_force (const c_damper_element_2d *elem, const double velocity[4])
	Compute the damper force (positive in tension) in a 2D damper element.
void	c_damper_element_3d_damping_matrix (const c_damper_element_3d *elem, double *c, int ldc)
	Compute the 6-by-6 global damping matrix of a 3D damper element.
double	c_damper_element_3d_force (const c_damper_element_3d *elem, const double velocity[6])
	Compute the damper force (positive in tension) in a 3D damper element.
void	c_mass_element_2d_mass_matrix (const c_mass_element_2d *elem, double *m, int ldm)
	Compute the 2-by-2 mass matrix of a 2D point mass element.
void	c_mass_element_3d_mass_matrix (const c_mass_element_3d *elem, double *m, int ldm)
	Compute the 3-by-3 mass matrix of a 3D point mass element.
void	c_assemble_discrete_system_2d (int gdof, int nm, const c_mass_element_2d *masses, int nd, const c_damper_element_2d *dampers, int ns, const c_spring_element_2d *springs, int nn, const c_node *nodes, double *m, int ldm, double *c, int ldc, double *k, int ldk)
	Assemble dense global mass, damping, and stiffness matrices for a 2D system composed of discrete elements.
void	c_assemble_discrete_system_3d (int gdof, int nm, const c_mass_element_3d *masses, int nd, const c_damper_element_3d *dampers, int ns, const c_spring_element_3d *springs, int nn, const c_node *nodes, double *m, int ldm, double *c, int ldc, double *k, int ldk)
	Assemble dense global mass, damping, and stiffness matrices for a 3D system composed of discrete elements.

Detailed Description

Function Documentation

c_beam_element_2d_length()

double c_beam_element_2d_length

(

const c_beam_element_2d *

elem

)

Compute the length of a 2D beam element.

Parameters

elem	Beam element.

Returns

Element length.

c_beam_element_2d_stiffness_matrix()

void c_beam_element_2d_stiffness_matrix	(	const c_beam_element_2d *	elem,
		int	rule,
		double *	k,
		int	ldk
	)

Compute the 6-by-6 stiffness matrix of a 2D beam element.

Parameters

elem	Beam element.
rule	Integration rule, or zero to use the default rule.
k	Output stiffness matrix.
ldk	Leading dimension of k.

c_beam_element_2d_mass_matrix()

void c_beam_element_2d_mass_matrix	(	const c_beam_element_2d *	elem,
		int	rule,
		double *	m,
		int	ldm
	)

Compute the 6-by-6 mass matrix of a 2D beam element.

Parameters

elem	Beam element.
rule	Integration rule, or zero to use the default rule.
m	Output mass matrix.
ldm	Leading dimension of m.

c_beam_element_2d_rotation_matrix()

void c_beam_element_2d_rotation_matrix	(	const c_beam_element_2d *	elem,
		double *	r,
		int	ldr
	)

Compute the 6-by-6 rotation matrix of a 2D beam element.

Parameters

elem	Beam element.
r	Output rotation matrix.
ldr	Leading dimension of r.

c_beam_element_2d_strain()

void c_beam_element_2d_strain	(	const c_beam_element_2d *	elem,
		const double	displacement[6],
		double	s,
		double	strain[2]
	)

Compute the strain in a 2D beam element at a natural coordinate.

Parameters

elem	Beam element.
displacement	6-element element displacement vector.
s	Natural coordinate in [-1, 1].
strain	Output 2-element strain vector.

c_beam_element_2d_stress()

void c_beam_element_2d_stress	(	const c_beam_element_2d *	elem,
		const double	displacement[6],
		double	s,
		double	stress[2]
	)

Compute the stress in a 2D beam element at a natural coordinate.

Parameters

elem	Beam element.
displacement	6-element element displacement vector.
s	Natural coordinate in [-1, 1].
stress	Output 2-element stress vector.

c_beam_element_2d_shear_force()

double c_beam_element_2d_shear_force	(	const c_beam_element_2d *	elem,
		const double	displacement[6],
		double	s
	)

Compute the local shear force in a 2D beam element at a natural coordinate.

Parameters

elem	Beam element.
displacement	6-element element displacement vector.
s	Natural coordinate in [-1, 1].

Returns

Local shear force.

c_beam_element_2d_bending_moment()

double c_beam_element_2d_bending_moment	(	const c_beam_element_2d *	elem,
		const double	displacement[6],
		double	s
	)

Compute the local bending moment in a 2D beam element at a natural coordinate.

Parameters

elem	Beam element.
displacement	6-element element displacement vector.
s	Natural coordinate in [-1, 1].

Returns

Local bending moment.

c_beam_element_2d_external_force_vector()

void c_beam_element_2d_external_force_vector	(	const c_beam_element_2d *	elem,
		const double	q[2],
		int	rule,
		double	f[6]
	)

Compute the equivalent nodal force vector for a distributed load on a 2D beam element.

Parameters

elem	Beam element.
q	2-element distributed load vector, [qx, qy].
rule	Integration rule, or zero to use the default rule.
f	Output 6-element nodal force vector.

c_beam_element_3d_length()

double c_beam_element_3d_length

(

const c_beam_element_3d *

elem

)

Compute the length of a 3D beam element.

Parameters

elem	Beam element.

Returns

Element length.

c_beam_element_3d_stiffness_matrix()

void c_beam_element_3d_stiffness_matrix	(	const c_beam_element_3d *	elem,
		int	rule,
		double *	k,
		int	ldk
	)

Compute the 12-by-12 stiffness matrix of a 3D beam element.

Parameters

elem	Beam element.
rule	Integration rule, or zero to use the default rule.
k	Output stiffness matrix.
ldk	Leading dimension of k.

c_beam_element_3d_mass_matrix()

void c_beam_element_3d_mass_matrix	(	const c_beam_element_3d *	elem,
		int	rule,
		double *	m,
		int	ldm
	)

Compute the 12-by-12 mass matrix of a 3D beam element.

Parameters

elem	Beam element.
rule	Integration rule, or zero to use the default rule.
m	Output mass matrix.
ldm	Leading dimension of m.

c_beam_element_3d_rotation_matrix()

void c_beam_element_3d_rotation_matrix	(	const c_beam_element_3d *	elem,
		double *	r,
		int	ldr
	)

Compute the 12-by-12 rotation matrix of a 3D beam element.

Parameters

elem	Beam element.
r	Output rotation matrix.
ldr	Leading dimension of r.

c_beam_element_3d_strain()

void c_beam_element_3d_strain	(	const c_beam_element_3d *	elem,
		const double	displacement[12],
		double	s,
		double	strain[4]
	)

Compute the strain in a 3D beam element at a natural coordinate.

Parameters

elem	Beam element.
displacement	12-element element displacement vector.
s	Natural coordinate in [-1, 1].
strain	Output 4-element strain vector.

c_beam_element_3d_stress()

void c_beam_element_3d_stress	(	const c_beam_element_3d *	elem,
		const double	displacement[12],
		double	s,
		double	stress[4]
	)

Compute the stress in a 3D beam element at a natural coordinate.

Parameters

elem	Beam element.
displacement	12-element element displacement vector.
s	Natural coordinate in [-1, 1].
stress	Output 4-element stress vector.

c_beam_element_3d_shear_force()

void c_beam_element_3d_shear_force	(	const c_beam_element_3d *	elem,
		const double	displacement[12],
		double	s,
		double	force[2]
	)

Compute the local shear-force vector in a 3D beam element at a natural coordinate.

The output is ordered [y-axis, z-axis].

Parameters

elem	Beam element.
displacement	12-element element displacement vector.
s	Natural coordinate in [-1, 1].
force	Output 2-element local shear-force vector.

c_beam_element_3d_bending_moment()

void c_beam_element_3d_bending_moment	(	const c_beam_element_3d *	elem,
		const double	displacement[12],
		double	s,
		double	moment[3]
	)

Compute the local moment vector in a 3D beam element at a natural coordinate.

The output is ordered [torsional, y-axis, z-axis].

Parameters

elem	Beam element.
displacement	12-element element displacement vector.
s	Natural coordinate in [-1, 1].
moment	Output 3-element local moment vector.

c_beam_element_3d_external_force_vector()

void c_beam_element_3d_external_force_vector	(	const c_beam_element_3d *	elem,
		const double	q[4],
		int	rule,
		double	f[12]
	)

Compute the equivalent nodal force vector for a distributed load on a 3D beam element.

Parameters

elem	Beam element.
q	4-element distributed load vector, [qx, qy, qz, qtheta].
rule	Integration rule, or zero to use the default rule.
f	Output 12-element nodal force vector.

c_assemble_static_system_beam_2d()

void c_assemble_static_system_beam_2d	(	int	gdof,
		int	n,
		const c_beam_element_2d *	elements,
		int	nn,
		const c_node *	nodes,
		int	rule,
		double *	k,
		int	ldk
	)

Assemble a dense global stiffness matrix from 2D beam elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Beam elements.
nn	Node count.
nodes	Global node list.
rule	Integration rule, or zero to use the default rule.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_dynamic_system_beam_2d()

void c_assemble_dynamic_system_beam_2d	(	int	gdof,
		int	n,
		const c_beam_element_2d *	elements,
		int	nn,
		const c_node *	nodes,
		int	rule,
		double *	m,
		int	ldm,
		double *	k,
		int	ldk
	)

Assemble dense global mass and stiffness matrices from 2D beam elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Beam elements.
nn	Node count.
nodes	Global node list.
rule	Integration rule, or zero to use the default rule.
m	Output gdof-by-gdof mass matrix.
ldm	Leading dimension of m.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_static_system_beam_3d()

void c_assemble_static_system_beam_3d	(	int	gdof,
		int	n,
		const c_beam_element_3d *	elements,
		int	nn,
		const c_node *	nodes,
		int	rule,
		double *	k,
		int	ldk
	)

Assemble a dense global stiffness matrix from 3D beam elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Beam elements.
nn	Node count.
nodes	Global node list.
rule	Integration rule, or zero to use the default rule.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_dynamic_system_beam_3d()

void c_assemble_dynamic_system_beam_3d	(	int	gdof,
		int	n,
		const c_beam_element_3d *	elements,
		int	nn,
		const c_node *	nodes,
		int	rule,
		double *	m,
		int	ldm,
		double *	k,
		int	ldk
	)

Assemble dense global mass and stiffness matrices from 3D beam elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Beam elements.
nn	Node count.
nodes	Global node list.
rule	Integration rule, or zero to use the default rule.
m	Output gdof-by-gdof mass matrix.
ldm	Leading dimension of m.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_apply_boundary_conditions_mtx()

void c_apply_boundary_conditions_mtx	(	int	n,
		int	nbc,
		int *	gdof,
		const double *	x,
		int	ldx,
		double *	rst,
		int	ldr
	)

Apply boundary conditions to a dense matrix by removing the constrained rows and columns.

Parameters

n	Matrix order.
nbc	Number of constrained degrees of freedom.
gdof	Constrained degree-of-freedom indices; sorted in place.
x	n-by-n matrix to constrain.
ldx	Leading dimension of x.
rst	Output (n - nbc)-by-(n - nbc) constrained matrix.
ldr	Leading dimension of rst.

c_apply_boundary_conditions_vec()

void c_apply_boundary_conditions_vec	(	int	n,
		int	nbc,
		int *	gdof,
		const double *	x,
		double *	rst
	)

Apply boundary conditions to a dense vector by removing the constrained entries.

Parameters

n	Vector length.
nbc	Number of constrained degrees of freedom.
gdof	Constrained degree-of-freedom indices; sorted in place.
x	n-element vector to constrain.
rst	Output (n - nbc)-element constrained vector.

c_restore_constrained_values_dense()

void c_restore_constrained_values_dense	(	int	nred,
		int	nbc,
		int *	gdof,
		const double *	x,
		double *	rst
	)

Restore the constrained degrees of freedom removed by c_apply_boundary_conditions_vec.

Parameters

nred	Length of the reduced vector.
nbc	Number of constrained degrees of freedom.
gdof	Constrained degree-of-freedom indices; sorted in place.
x	nred-element reduced vector.
rst	Output (nred + nbc)-element restored vector.

c_apply_displacement_constraint_dense()

void c_apply_displacement_constraint_dense	(	int	dof,
		double	val,
		int	n,
		double *	k,
		int	ldk,
		double *	f
	)

Apply a displacement constraint to a single degree of freedom.

Parameters

dof	Global degree-of-freedom index (one-based).
val	Prescribed displacement value.
n	Matrix order.
k	n-by-n stiffness matrix, updated in place.
ldk	Leading dimension of k.
f	n-element external force vector, updated in place.

c_solve_static_system_dense()

void c_solve_static_system_dense	(	int	n,
		const double *	k,
		int	ldk,
		const double *	f,
		double *	u
	)

Solve the static system K*u = f for a dense stiffness matrix.

Parameters

n	Matrix order.
k	n-by-n stiffness matrix.
ldk	Leading dimension of k.
f	n-element external force vector.
u	Output n-element solution vector.

c_truss_element_2d_length()

double c_truss_element_2d_length

(

const c_truss_element_2d *

elem

)

Compute the length of a 2D truss element.

Parameters

elem	Truss element.

Returns

Element length.

c_truss_element_2d_stiffness_matrix()

void c_truss_element_2d_stiffness_matrix	(	const c_truss_element_2d *	elem,
		double *	k,
		int	ldk
	)

Compute the 4-by-4 global stiffness matrix of a 2D truss element.

Parameters

elem	Truss element.
k	Output stiffness matrix.
ldk	Leading dimension of k.

c_truss_element_2d_mass_matrix()

void c_truss_element_2d_mass_matrix	(	const c_truss_element_2d *	elem,
		int	rule,
		double *	m,
		int	ldm
	)

Compute the 4-by-4 consistent mass matrix of a 2D truss element.

Parameters

elem	Truss element.
rule	Integration rule, or zero to use the default rule.
m	Output mass matrix.
ldm	Leading dimension of m.

c_truss_element_2d_rotation_matrix()

void c_truss_element_2d_rotation_matrix	(	const c_truss_element_2d *	elem,
		double *	r,
		int	ldr
	)

Compute the 4-by-4 rotation matrix of a 2D truss element.

Parameters

elem	Truss element.
r	Output rotation matrix.
ldr	Leading dimension of r.

c_truss_element_2d_strain()

double c_truss_element_2d_strain	(	const c_truss_element_2d *	elem,
		const double	displacement[4]
	)

Compute the axial strain in a 2D truss element.

Parameters

elem	Truss element.
displacement	4-element global element displacement vector.

Returns

Axial strain.

c_truss_element_2d_axial_force()

double c_truss_element_2d_axial_force	(	const c_truss_element_2d *	elem,
		const double	displacement[4]
	)

Compute the axial force (positive in tension) in a 2D truss element.

Parameters

elem	Truss element.
displacement	4-element global element displacement vector.

Returns

Axial force.

c_truss_element_2d_external_force_vector()

void c_truss_element_2d_external_force_vector	(	const c_truss_element_2d *	elem,
		const double	q[2],
		int	rule,
		double	f[4]
	)

Compute the equivalent nodal force vector for a distributed load on a 2D truss element.

Parameters

elem	Truss element.
q	2-element distributed load vector in the element coordinate system.
rule	Integration rule, or zero to use the default rule.
f	Output 4-element nodal force vector.

c_truss_element_3d_length()

double c_truss_element_3d_length

(

const c_truss_element_3d *

elem

)

Compute the length of a 3D truss element.

Parameters

elem	Truss element.

Returns

Element length.

c_truss_element_3d_stiffness_matrix()

void c_truss_element_3d_stiffness_matrix	(	const c_truss_element_3d *	elem,
		double *	k,
		int	ldk
	)

Compute the 6-by-6 global stiffness matrix of a 3D truss element.

Parameters

elem	Truss element.
k	Output stiffness matrix.
ldk	Leading dimension of k.

c_truss_element_3d_mass_matrix()

void c_truss_element_3d_mass_matrix	(	const c_truss_element_3d *	elem,
		int	rule,
		double *	m,
		int	ldm
	)

Compute the 6-by-6 consistent mass matrix of a 3D truss element.

Parameters

elem	Truss element.
rule	Integration rule, or zero to use the default rule.
m	Output mass matrix.
ldm	Leading dimension of m.

c_truss_element_3d_rotation_matrix()

void c_truss_element_3d_rotation_matrix	(	const c_truss_element_3d *	elem,
		double *	r,
		int	ldr
	)

Compute the 6-by-6 rotation matrix of a 3D truss element.

Parameters

elem	Truss element.
r	Output rotation matrix.
ldr	Leading dimension of r.

c_truss_element_3d_strain()

double c_truss_element_3d_strain	(	const c_truss_element_3d *	elem,
		const double	displacement[6]
	)

Compute the axial strain in a 3D truss element.

Parameters

elem	Truss element.
displacement	6-element global element displacement vector.

Returns

Axial strain.

c_truss_element_3d_axial_force()

double c_truss_element_3d_axial_force	(	const c_truss_element_3d *	elem,
		const double	displacement[6]
	)

Compute the axial force (positive in tension) in a 3D truss element.

Parameters

elem	Truss element.
displacement	6-element global element displacement vector.

Returns

Axial force.

c_truss_element_3d_external_force_vector()

void c_truss_element_3d_external_force_vector	(	const c_truss_element_3d *	elem,
		const double	q[3],
		int	rule,
		double	f[6]
	)

Compute the equivalent nodal force vector for a distributed load on a 3D truss element.

Parameters

elem	Truss element.
q	3-element distributed load vector in the element coordinate system.
rule	Integration rule, or zero to use the default rule.
f	Output 6-element nodal force vector.

c_assemble_static_system_truss_2d()

void c_assemble_static_system_truss_2d	(	int	gdof,
		int	n,
		const c_truss_element_2d *	elements,
		int	nn,
		const c_node *	nodes,
		double *	k,
		int	ldk
	)

Assemble a dense global stiffness matrix from 2D truss elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Truss elements.
nn	Node count.
nodes	Global node list.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_dynamic_system_truss_2d()

void c_assemble_dynamic_system_truss_2d	(	int	gdof,
		int	n,
		const c_truss_element_2d *	elements,
		int	nn,
		const c_node *	nodes,
		int	rule,
		double *	m,
		int	ldm,
		double *	k,
		int	ldk
	)

Assemble dense global mass and stiffness matrices from 2D truss elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Truss elements.
nn	Node count.
nodes	Global node list.
rule	Integration rule, or zero to use the default rule.
m	Output gdof-by-gdof mass matrix.
ldm	Leading dimension of m.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_static_system_truss_3d()

void c_assemble_static_system_truss_3d	(	int	gdof,
		int	n,
		const c_truss_element_3d *	elements,
		int	nn,
		const c_node *	nodes,
		double *	k,
		int	ldk
	)

Assemble a dense global stiffness matrix from 3D truss elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Truss elements.
nn	Node count.
nodes	Global node list.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_dynamic_system_truss_3d()

void c_assemble_dynamic_system_truss_3d	(	int	gdof,
		int	n,
		const c_truss_element_3d *	elements,
		int	nn,
		const c_node *	nodes,
		int	rule,
		double *	m,
		int	ldm,
		double *	k,
		int	ldk
	)

Assemble dense global mass and stiffness matrices from 3D truss elements.

Parameters

gdof	Total number of global degrees of freedom.
n	Element count.
elements	Truss elements.
nn	Node count.
nodes	Global node list.
rule	Integration rule, or zero to use the default rule.
m	Output gdof-by-gdof mass matrix.
ldm	Leading dimension of m.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_spring_element_2d_stiffness_matrix()

void c_spring_element_2d_stiffness_matrix	(	const c_spring_element_2d *	elem,
		double *	k,
		int	ldk
	)

Compute the 4-by-4 global stiffness matrix of a 2D spring element.

Parameters

elem	Spring element.
k	Output stiffness matrix.
ldk	Leading dimension of k.

c_spring_element_2d_force()

double c_spring_element_2d_force	(	const c_spring_element_2d *	elem,
		const double	displacement[4]
	)

Compute the spring force (positive in tension) in a 2D spring element.

Parameters

elem	Spring element.
displacement	4-element global element displacement vector.

Returns

Spring force.

c_spring_element_3d_stiffness_matrix()

void c_spring_element_3d_stiffness_matrix	(	const c_spring_element_3d *	elem,
		double *	k,
		int	ldk
	)

Compute the 6-by-6 global stiffness matrix of a 3D spring element.

Parameters

elem	Spring element.
k	Output stiffness matrix.
ldk	Leading dimension of k.

c_spring_element_3d_force()

double c_spring_element_3d_force	(	const c_spring_element_3d *	elem,
		const double	displacement[6]
	)

Compute the spring force (positive in tension) in a 3D spring element.

Parameters

elem	Spring element.
displacement	6-element global element displacement vector.

Returns

Spring force.

c_damper_element_2d_damping_matrix()

void c_damper_element_2d_damping_matrix	(	const c_damper_element_2d *	elem,
		double *	c,
		int	ldc
	)

Compute the 4-by-4 global damping matrix of a 2D damper element.

Parameters

elem	Damper element.
c	Output damping matrix.
ldc	Leading dimension of c.

c_damper_element_2d_force()

double c_damper_element_2d_force	(	const c_damper_element_2d *	elem,
		const double	velocity[4]
	)

Compute the damper force (positive in tension) in a 2D damper element.

Parameters

elem	Damper element.
velocity	4-element global element velocity vector.

Returns

Damper force.

c_damper_element_3d_damping_matrix()

void c_damper_element_3d_damping_matrix	(	const c_damper_element_3d *	elem,
		double *	c,
		int	ldc
	)

Compute the 6-by-6 global damping matrix of a 3D damper element.

Parameters

elem	Damper element.
c	Output damping matrix.
ldc	Leading dimension of c.

c_damper_element_3d_force()

double c_damper_element_3d_force	(	const c_damper_element_3d *	elem,
		const double	velocity[6]
	)

Compute the damper force (positive in tension) in a 3D damper element.

Parameters

elem	Damper element.
velocity	6-element global element velocity vector.

Returns

Damper force.

c_mass_element_2d_mass_matrix()

void c_mass_element_2d_mass_matrix	(	const c_mass_element_2d *	elem,
		double *	m,
		int	ldm
	)

Compute the 2-by-2 mass matrix of a 2D point mass element.

Parameters

elem	Mass element.
m	Output mass matrix.
ldm	Leading dimension of m.

c_mass_element_3d_mass_matrix()

void c_mass_element_3d_mass_matrix	(	const c_mass_element_3d *	elem,
		double *	m,
		int	ldm
	)

Compute the 3-by-3 mass matrix of a 3D point mass element.

Parameters

elem	Mass element.
m	Output mass matrix.
ldm	Leading dimension of m.

c_assemble_discrete_system_2d()

void c_assemble_discrete_system_2d	(	int	gdof,
		int	nm,
		const c_mass_element_2d *	masses,
		int	nd,
		const c_damper_element_2d *	dampers,
		int	ns,
		const c_spring_element_2d *	springs,
		int	nn,
		const c_node *	nodes,
		double *	m,
		int	ldm,
		double *	c,
		int	ldc,
		double *	k,
		int	ldk
	)

Assemble dense global mass, damping, and stiffness matrices for a 2D system composed of discrete elements.

Any element count may be zero, in which case the corresponding array pointer may be NULL.

Parameters

gdof	Total number of global degrees of freedom.
nm	Mass element count.
masses	Mass elements.
nd	Damper element count.
dampers	Damper elements.
ns	Spring element count.
springs	Spring elements.
nn	Node count.
nodes	Global node list.
m	Output gdof-by-gdof mass matrix.
ldm	Leading dimension of m.
c	Output gdof-by-gdof damping matrix.
ldc	Leading dimension of c.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.

c_assemble_discrete_system_3d()

void c_assemble_discrete_system_3d	(	int	gdof,
		int	nm,
		const c_mass_element_3d *	masses,
		int	nd,
		const c_damper_element_3d *	dampers,
		int	ns,
		const c_spring_element_3d *	springs,
		int	nn,
		const c_node *	nodes,
		double *	m,
		int	ldm,
		double *	c,
		int	ldc,
		double *	k,
		int	ldk
	)

Assemble dense global mass, damping, and stiffness matrices for a 3D system composed of discrete elements.

Any element count may be zero, in which case the corresponding array pointer may be NULL.

Parameters

gdof	Total number of global degrees of freedom.
nm	Mass element count.
masses	Mass elements.
nd	Damper element count.
dampers	Damper elements.
ns	Spring element count.
springs	Spring elements.
nn	Node count.
nodes	Global node list.
m	Output gdof-by-gdof mass matrix.
ldm	Leading dimension of m.
c	Output gdof-by-gdof damping matrix.
ldc	Leading dimension of c.
k	Output gdof-by-gdof stiffness matrix.
ldk	Leading dimension of k.