beamel3d Class Reference

#include <beamel3d.h>

Public Member Functions
void	beam_transf_matrix (matrix &tmat, double &dl, vector &vec, vector &x, vector &y, vector &z, long eid)
	beamel3d (void)
void	bf_matrix (matrix &n, double s, double dl, double gy, double gz)
void	bf_matrix_transl (matrix &n, double xi, double l, double gy, double gz)
void	define_meaning (long eid)
void	geom_matrix (matrix &n, double s, double dl, double gy, double gz)
void	initstr_matrix (long eid, long ri, long ci, matrix &ism)
void	internal_forces (long lcid, long eid, long ri, long ci, vector &ifor)
void	load_matrix (long eid, matrix &lm)
void	mass_matrix (long eid, long ri, long ci, matrix &mm)
void	mass_matrix_expl (long eid, long ri, long ci, matrix &mm)
void	nodal_displ (long lcid, long eid)
void	nodal_forces (long lcid, long eid)
void	nodeforces (long eid, long le, double nv, vector &nf)
void	res_internal_forces (long lcid, long eid, vector &ifor)
void	res_mass_matrix (long eid, matrix &mm)
void	res_stiffness_matrix (long eid, matrix &sm)
void	stiffness_matrix (long eid, long ri, long ci, matrix &sm)
void	stiffness_matrix_local (long eid, long ri, long ci, matrix &sm)
void	stiffness_matrix_local2 (long eid, long ri, long ci, matrix &sm)
void	transf_matrix (ivector &nodes, matrix &tmat)
	~beamel3d (void)
Public Attributes
long *	cncomp
	array containing cumulative numbers of components of stress and strain tensors
long	intordism
	order of integration of initial stress matrix
long	intordmm
	order of integration of mass matrix
long **	intordsm
	order of integration of stiffness matrix
long	napfun
	number of approximated functions on the element
long	nb
	number of blocks
long *	ncomp
	array containing numbers of components of stress and strain tensors
long	ndofe
	number of DOFs on the element
long **	nip
	array of numbers of integration points in sets
long	nne
	number of nodes on one element
strastrestate	ssst
	stress/strain state
long	tncomp
	total number of components of stress and strain tensors
long	tnip
	total number of integration points

Detailed Description

class beamel3d

PF

Definition at line 16 of file beamel3d.h.

Constructor & Destructor Documentation

beamel3d ( void )

Definition at line 11 of file beamel3d.cpp.

References cncomp, intordism, intordmm, intordsm, napfun, nb, ncomp, ndofe, nip, nne, spacebeam, ssst, tncomp, and tnip.

~beamel3d ( void )

Definition at line 63 of file beamel3d.cpp.

References cncomp, intordsm, nb, ncomp, and nip.

Member Function Documentation

void beam_transf_matrix	(	matrix &	tmat,
		double &	dl,
		vector &	vec,
		vector &	x,
		vector &	y,
		vector &	z,
		long	eid
	)

The function assembles transformation matrix from local element coordinate system to global coordinate system x_g = T x_l.

Columns of the transformation matrix are created by coordinates of local base vectors expressed in global coordinate system.

Parameters:

	tmat	- transformation matrix
	dl	- lenght of the beam
	vec	- direction vector of local axis z (in global coordinates)
	x,y,z	- vectors of nodal coordinates in global system
	eid	- element id

JK, 3.2.2002, revised 1.9.2006

Definition at line 312 of file beamel3d.cpp.

References fillm(), and print_err().

Referenced by initstr_matrix(), internal_forces(), load_matrix(), mass_matrix(), nodal_displ(), nodal_forces(), stiffness_matrix(), stiffness_matrix_local(), and stiffness_matrix_local2().

void bf_matrix	(	matrix &	n,
		double	s,
		double	dl,
		double	gy,
		double	gz
	)

function assembles matrix of approximation functions

ordering of approximation functions u v w - displacement along x,y,z fix,fiy,fiz - rotation around x,y,z

Parameters:

	n	- matrix of approximation functions
	s	- natural coordinate from segment <0;1>
	dl	- length of the beam
	gy	- 6.0EI_y/k/G/A/l/l
	gz	- 6.0EI_z/k/G/A/l/l

PF, 20.12.2002, revised by JK 2.9.2006

Definition at line 160 of file beamel3d.cpp.

References ll.

Referenced by load_matrix().

void bf_matrix_transl	(	matrix &	n,
		double	xi,
		double	l,
		double	gy,
		double	gz
	)

function assembles matrix of approximation functions for translational DOFs

ordering of approximation functions u v w - displacement along x,y,z fix,fiy,fiz - rotation around x,y,z are neglected

ordering of nodal values u_1, v_1, w_1, phi_x1, phi_y1, phi_z1, u_2, v_2, w_2, phi_x2, phi_y2, phi_z2

Parameters:

	n	- matrix of approximation functions
	xi	- natural coordinate from segment <0;1>
	l	- length of the beam
	gy	- 6.0EI_y/k/G/A/l/l
	gz	- 6.0EI_z/k/G/A/l/l

JK, 16.11.2006

Definition at line 219 of file beamel3d.cpp.

References fillm().

Referenced by mass_matrix().

void define_meaning ( long eid )

The function defines meaning of DOFs at nodes.

Parameters:

eid

- element id

1.2.2005, JK

Definition at line 1267 of file beamel3d.cpp.

References mechtop::give_code_numbers(), mechtop::give_elemnodes(), node::meaning, Mt, ndofe, nne, nod, and mechtop::nodes.

Referenced by mechtop::define_meaning().

void geom_matrix	(	matrix &	n,
		double	s,
		double	dl,
		double	gy,
		double	gz
	)

function assembles geometric matrix (function assembles matrix of derivatives of approximation functions)

ordering of approximation functions

du/dx - strain e_xx phi+dv/dx - strain e_yz phi+dw/dx - strain e_xz dphix/dx - curvature dphiy/dx - curvature dphiz/dx - curvature

Parameters:

	n	- array containing geometric matrix
	s	- natural coordinate from segment <0;1>
	dl	- length of the beam
	gy	- 6.0EI_y/k/G/A/l/l
	gz	- 6.0EI_z/k/G/A/l/l

PF, 20.12.2002, revised by JK 2.9.2006

Definition at line 101 of file beamel3d.cpp.

References fillm(), and ll.

Referenced by internal_forces().

void initstr_matrix	(	long	eid,
		long	ri,
		long	ci,
		matrix &	ism
	)

Parameters:

	eid	- element id
	ri,ci	- row and column indices
	ism	- initial stress matrix

Definition at line 808 of file beamel3d.cpp.

References beam_transf_matrix(), mechtop::elements, fillm(), g, mechcrsec::give_area(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord3d(), mechcrsec::give_shearcoeff(), glmatrixtransf(), element::ipp, lgmatrixtransf(), ll, mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mp, Mt, nne, nodes, tncomp, transf_matrix(), and probdesc::zero.

void internal_forces	(	long	lcid,
		long	eid,
		long	ri,
		long	ci,
		vector &	ifor
	)

Definition at line 1151 of file beamel3d.cpp.

References vector::a, beam_transf_matrix(), copyv(), eldispl(), mechtop::elements, f, fillm(), g, gauss_points(), geom_matrix(), mechcrsec::give_area(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord3d(), mechcrsec::give_shearcoeff(), mechcrsec::give_vectorlcs(), element::ipp, lgvectortransf(), ll, mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mp, Mt, ndofe, nne, nodes, rl, tncomp, transf_matrix(), and probdesc::zero.

void load_matrix	(	long	eid,
		matrix &	lm
	)

function serves for computation of nodal forces and moments caused by body load

Parameters:

	eid	- element id
	lm	- load matrix

JK, 1.9.2006

Definition at line 906 of file beamel3d.cpp.

References matrix::a, beam_transf_matrix(), bf_matrix(), mechtop::elements, fillm(), g, gauss_points(), mechcrsec::give_area(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord3d(), mechcrsec::give_shearcoeff(), mechcrsec::give_vectorlcs(), glmatrixtransf(), intordmm, element::ipp, jac_1d(), lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mp, Mt, napfun, ndofe, nne, nnj(), nodes, tncomp, transf_matrix(), and probdesc::zero.

Referenced by loadmat().

void mass_matrix	(	long	eid,
		long	ri,
		long	ci,
		matrix &	mm
	)

function computes consistent mass matrix of 3D beam element rotational DOFs are neglected

Parameters:

	eid	- number of element
	ri,ci	- row and column indices
	mm	- mass matrix of one element

JK, 3.2.200

Definition at line 727 of file beamel3d.cpp.

References matrix::a, beam_transf_matrix(), bf_matrix_transl(), fillm(), gauss_points(), mechcrsec::give_area(), mechcrsec::give_densitye(), mechtop::give_elemnodes(), mechtop::give_node_coord3d(), mechcrsec::give_shearcoeff(), mechcrsec::give_vectorlcs(), glmatrixtransf(), intordmm, lgmatrixtransf(), mechtop::locsystems(), Mc, Mt, ndofe, nne, nnj(), nodes, and transf_matrix().

Referenced by res_mass_matrix().

void mass_matrix_expl	(	long	eid,
		long	ri,
		long	ci,
		matrix &	mm
	)

void nodal_displ	(	long	lcid,
		long	eid
	)

The function stores nodal displacements and rotations in the local element coordinate system. This is equivalent to functions computing strains. Nodal displacements and rotations are better quantities in case of beams.

Parameters:

	eid	- element id
	lcid	- load case id

JK, 20.2.2002

Definition at line 994 of file beamel3d.cpp.

References beam_transf_matrix(), copyv(), eldispl(), mechtop::elements, f, mechtop::give_elemnodes(), mechtop::give_node_coord3d(), mechcrsec::give_vectorlcs(), glvectortransf(), element::ipp, lgvectortransf(), mechtop::locsystems(), Mc, Mm, Mt, ndofe, nne, nodes, mechmat::storestrain(), and transf_matrix().

Referenced by compute_ipstrains(), and compute_nodestrains().

void nodal_forces	(	long	lcid,
		long	eid
	)

The function computes nodal forces and moments expressed in local coodinate system. This is equivalent to functions computing stresses on plane or space elements. Nodal forces and moments are better quantities in case of beams.

x-axis goes through the beam z-axis is defined in cross section y-axis is defined by right hand orientation

Parameters:

	eid	- element id
	lcid	- load case id

JK, 20.2.2002, revised 2.9.2006

Definition at line 1063 of file beamel3d.cpp.

References beam_transf_matrix(), copyv(), eldispl(), mechtop::elements, f, mechtop::give_elemnodes(), mechtop::give_node_coord3d(), mechcrsec::give_vectorlcs(), glvectortransf(), element::ipp, lgvectortransf(), mechtop::locsystems(), Mc, Mm, Mt, mxv(), ndofe, nne, nodes, stiffness_matrix(), mechmat::storestress(), and transf_matrix().

Referenced by compute_ipstresses(), compute_nodestresses(), and computestresses().

void nodeforces	(	long	eid,
		long *	le,
		double *	nv,
		vector &	nf
	)

The function calculates member forces due to continuous load of element.

Parameters:

	eid	- element id
	le	-
	nv	- nodal values of continuous load
	nf	- resulting vector of member forces

Returns:: The function returns resulting member forces in the parameter nf.

Created by Jan Zitny 10.2012

Definition at line 666 of file beamel3d.cpp.

References ivector::a, gelement::cne, condense_vector(), gtopology::gelements, gtopology::give_cn(), mechtop::give_node_coord3d(), Gtm, Mt, ndofe, nne, print_err(), and stiffness_matrix_local().

Referenced by loadel::edgeload().

void res_internal_forces	(	long	lcid,
		long	eid,
		vector &	ifor
	)

The function computes internal forces, i.e. member forces of the element expressed in the global coordinate system or local nodal coordinate systems.

Parameters:

	lcid	- load case id
	eid	- element id
	ri,ci	- row and column indices
	ifor	- vector of internal forces

20.12.2002

Definition at line 1136 of file beamel3d.cpp.

References vector::a, eldispl(), mxv(), ndofe, and stiffness_matrix().

Referenced by elem_internal_forces(), and elem_nonloc_internal_forces().

void res_mass_matrix	(	long	eid,
		matrix &	mm
	)

function computes consistent mass matrix of 3D beam element

Parameters:

	eid	- element id
	mm	- mass matrix

JK, 2.9.2006

Definition at line 795 of file beamel3d.cpp.

References mass_matrix().

Referenced by massmat().

void res_stiffness_matrix	(	long	eid,
		matrix &	sm
	)

function computes stiffness matrix of 3D beam element

Parameters:

	eid	- number of element
	sm	- stiffness matrix

JK, 3.2.2002

Definition at line 432 of file beamel3d.cpp.

References stiffness_matrix().

Referenced by stiffmat().

void stiffness_matrix	(	long	eid,
		long	ri,
		long	ci,
		matrix &	sm
	)

The function computes stiffness matrix of 3D beam element expressed in the global coordinate system or local nodal coordinate systems. Additionally, the condensation of the stiffness matrix is performed.

Parameters: