beamel2d Class Reference

#include <beamel2d.h>

Public Member Functions
void	beam_transf_matrix (long eid, vector &x, vector &z, matrix &tmat)
	beamel2d (void)
void	bf_matrix (matrix &n, double xi, double l, double kappa)
void	dbf_matrix (matrix &n, double xi, double l, double kappa)
void	define_meaning (long eid)
void	geom_matrix (matrix &gm, double xi, double l, double kappa)
void	initstr_matrix (long eid, long ri, long ci, matrix &ism)
void	initstr_matrix_expl (long eid, long ri, long ci, matrix &ism)
void	internal_forces (long lcid, long eid, vector &ifor)
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_expl (long eid, long ri, long ci, matrix &sm)
void	stiffness_matrix_expl_local (long eid, long ri, long ci, matrix &sm)
void	transf_matrix (ivector &nodes, matrix &tmat)
	~beamel2d (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

Detailed Description

class beamel2d defines beam element for 2D analysis

JK

Definition at line 16 of file beamel2d.h.

Constructor & Destructor Documentation

beamel2d ( void )

Definition at line 13 of file beamel2d.cpp.

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

~beamel2d ( void )

Definition at line 57 of file beamel2d.cpp.

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

Member Function Documentation

void beam_transf_matrix	(	long	eid,
		vector &	x,
		vector &	z,
		matrix &	tmat
	)

function assembles transformation matrix from local element coordinate system to the global problem coordinate system x_g = T x_l

this beam element is formulated in x-z plane, x axis is identical with beam axis and it is oriented horizontally, z axis is oriented vertically (downwards)

Parameters:

	x,z	- node coordinates
	tmat	- transformation matrix

JK, 3.2.2002

Definition at line 225 of file beamel2d.cpp.

References fillm(), and print_err().

Referenced by initstr_matrix(), initstr_matrix_expl(), mass_matrix(), mass_matrix_expl(), nodal_displ(), nodal_forces(), nodeforces(), stiffness_matrix(), and stiffness_matrix_expl().

void bf_matrix	(	matrix &	n,
		double	xi,
		double	l,
		double	kappa
	)

function assembles matrix of approximation functions

ordering of approximation functions u - displacement along x w - deflection - displacement along z phi - rotation around y

Parameters:

	n	- array containing matrix of approximation functions
	xi	- natural coordinate from segment <0;1>
	l	- length of the beam
	kappa	- 6.0EI/k/G/A/l/l

JK, 20.2.2002

Definition at line 88 of file beamel2d.cpp.

References vector::a, defl2D_fun(), dilat(), fillm(), and roty_fun().

Referenced by mass_matrix().

void dbf_matrix	(	matrix &	n,
		double	xi,
		double	l,
		double	kappa
	)

function assembles matrix of derivatives of approximation function of deflection

Parameters:

	n	- matrix of derivatives
	xi	- natural coordinate from segment <0;1>
	l	- length of the beam
	kappa	- shear coefficient 6.0EI/k/G/A/l/l

JK

Definition at line 122 of file beamel2d.cpp.

References vector::a, der_defl2D_fun(), and fillm().

Referenced by initstr_matrix().

void define_meaning ( long eid )

function defines meaning of DOFs at nodes

Parameters:

eid

- element id

1.2.2005, JK

Definition at line 1076 of file beamel2d.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 &	gm,
		double	xi,
		double	l,
		double	kappa
	)

function assembles strain-displacement (geometric) matrix

ordering of strain components du/dx - strain e_xx phi+dw/dx - strain e_xz dphi/dx - curvature

Parameters:

	gm	- geometric matrix
	xi	- natural coordinate from segment <0;1>
	l	- length of the beam
	kappa	- 6.0EI/k/G/A/l/l

JK, 20.2.2002

Definition at line 152 of file beamel2d.cpp.

References vector::a, der_defl2D_fun(), der_dilat(), der_roty_fun(), fillm(), and roty_fun().

Referenced by stiffness_matrix().

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

function computes consistent geometric-stiffness matrix notation based on R. Clough, J. Penzien: Dynamic of Structures, McGraw-Hill, 2nd edition, 1993, pages 195-196

notation initial stress matrix is also used

Parameters:

	eid	- number of element
	ri,ci	- row and column indices
	ism	- inital stress matrix

JK

Definition at line 697 of file beamel2d.cpp.

References matrix::a, vector::a, beam_transf_matrix(), dbf_matrix(), mechtop::elements, fillm(), g, gauss_points(), mechcrsec::give_area(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), mechcrsec::give_shearcoeff(), glmatrixtransf(), intordism, element::ipp, lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mt, ndofe, nne, nnj(), nodes, print_err(), tncomp, and transf_matrix().

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

function computes consistent geometric-stiffness matrix notation based on R. Clough, J. Penzien: Dynamic of Structures, McGraw-Hill, 2nd edition, 1993, pages 195-196

notation initial stress matrix is also used

initial stress matrix is formulated explicitly

Parameters:

	eid	- number of element
	ri,ci	- row and column indices
	ism	- inital stress matrix

JK

Definition at line 774 of file beamel2d.cpp.

References vector::a, beam_transf_matrix(), mechtop::elements, fillm(), g, gauss_points(), mechcrsec::give_area(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), mechcrsec::give_shearcoeff(), glmatrixtransf(), intordism, element::ipp, lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mt, ndofe, nne, nodes, print_err(), tncomp, and transf_matrix().

Referenced by initstiffmat().

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

Function computes internal forces (nodal forces and moments) that are expressed in global problem or local nodal coordinate system.

Parameters:

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

JK, 12.8.2001

Definition at line 1013 of file beamel2d.cpp.

References addv(), eldispl(), fillv(), mxv(), ndofe, nne, nodes, and stiffness_matrix_expl().

Referenced by res_internal_forces().

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

function computes consistent mass matrix of 2D beam element influence of inertial forces from rotations is accounted

Parameters:

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

JK, 3.2.2006

Definition at line 498 of file beamel2d.cpp.

References matrix::a, vector::a, bdbj(), beam_transf_matrix(), bf_matrix(), mechtop::elements, fillm(), g, gauss_points(), mechcrsec::give_area(), mechcrsec::give_densitye(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), mechcrsec::give_shearcoeff(), glmatrixtransf(), intordmm, element::ipp, lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mt, napfun, ndofe, nne, nodes, print_err(), tncomp, and transf_matrix().

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

function computes consistent mass matrix of 2D beam element influence of inertial forces from rotations is accounted

Parameters:

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

JK, 3.2.2006

Definition at line 590 of file beamel2d.cpp.

References beam_transf_matrix(), mechtop::elements, fillm(), g, mechcrsec::give_area(), mechcrsec::give_densitye(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), mechcrsec::give_shearcoeff(), glmatrixtransf(), element::ipp, lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mt, ndofe, nne, nodes, print_err(), tncomp, and transf_matrix().

Referenced by nodal_forces(), and res_mass_matrix().

void nodal_displ	(	long	lcid,
		long	eid
	)

function stores end displacements and rotations to integration points

Parameters:

	lcid	- load case id
	eid	- element id

JK, 24.5.2006

Definition at line 861 of file beamel2d.cpp.

References beam_transf_matrix(), copyv(), eldispl(), mechtop::elements, f, mechtop::give_elemnodes(), mechtop::give_node_coord2dxz(), glvectortransf(), element::ipp, lgvectortransf(), mechtop::locsystems(), Mm, Mt, ndofe, nne, nodes, mechmat::storestrain(), and transf_matrix().

Referenced by compute_ipstrains(), and compute_nodestrains().

void nodal_forces	(	long	lcid,
		long	eid
	)

function computes nodal forces and moments expressed in local coordinate system this is equivalent to functions computing stresses nodal forces and moments are better quantities in case of beams

Parameters:

	lcid	- load case id
	eid	- element id

JK, 20.2.2002, revised 2.9.2006

Definition at line 918 of file beamel2d.cpp.

References beam_transf_matrix(), cmulv(), copyv(), loadel::eid, eigen_dynamics, eldispl(), mechtop::elements, f, forced_dynamics, mechtop::give_elemnodes(), mechtop::give_node_coord2dxz(), glvectortransf(), element::ipp, mechbclc::lc, lgvectortransf(), mechtop::locsystems(), loadcase::loe, Lsrs, mass_matrix_expl(), Mb, Mm, Mp, Mt, mxv(), ndofe, loadel::nf, loadcase::nle, nne, nodes, stiffness_matrix_expl(), mechmat::storestress(), probdesc::tprob, transf_matrix(), and lhsrhs::w.

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

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

function assembles end forces and moments cuased by a load acting on element

Parameters:

	eid	- element id
	le	- type of coordinate system
	nv	- values defining load
	nf	- vector of end forces and moments

30. 9. 2012

Definition at line 1104 of file beamel2d.cpp.

References ivector::a, beam_transf_matrix(), gelement::cne, condense_vector(), mechtop::elements, gtopology::gelements, mechcrsec::give_area(), gtopology::give_cn(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), Gtm, h(), element::ipp, lgvectortransfblock(), mechmat::matstiff(), Mc, Mm, Mt, ndofe, nne, stiffness_matrix_expl(), and tncomp.

Referenced by loadel::edgeload().

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

function computes internal forces

Parameters:

	lcid	- load case id
	eid	- element id
	ifor	- vector of internal forces

JK, 12.8.2001

Definition at line 1064 of file beamel2d.cpp.

References internal_forces().

Referenced by elem_internal_forces(), and elem_nonloc_internal_forces().

void res_mass_matrix	(	long	eid,
		matrix &	mm
	)

function computes consistent mass matrix of 2D beam element influence of inertial forces from rotations is accounted

Parameters:

	eid	- number of element
	mm	- mass matrix

JK, 3.2.2006

Definition at line 574 of file beamel2d.cpp.

References mass_matrix_expl().

Referenced by massmat().

void res_stiffness_matrix	(	long	eid,
		matrix &	sm
	)

function computes stiffness matrix of two-dimensional beam finite element element is based on Mindlin theory (shear stresses are taken into account)

Parameters:

	eid	- number of element
	sm	- stiffness matrix

JK, 3.2.2002

Definition at line 337 of file beamel2d.cpp.

References stiffness_matrix_expl().

Referenced by stiffmat().

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

function computes stiffness matrix of two-dimensional beam finite element element is based on Mindlin theory (shear stresses are taken into account)

Parameters:

	eid	- number of element
	ri,ci	- row and column indices
	sm	- stiffness matrix

JK, 3.2.2002

Definition at line 263 of file beamel2d.cpp.

References matrix::a, vector::a, bdbj(), beam_transf_matrix(), mechtop::elements, fillm(), g, gauss_points(), geom_matrix(), mechcrsec::give_area(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), mechcrsec::give_shearcoeff(), glmatrixtransf(), intordsm, element::ipp, lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mt, ndofe, nne, nodes, print_err(), tncomp, and transf_matrix().

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

Definition at line 422 of file beamel2d.cpp.

References ivector::a, beam_transf_matrix(), gelement::cne, condense_matrix(), mechtop::elements, fillm(), g, gtopology::gelements, mechcrsec::give_area(), gtopology::give_cn(), mechtop::give_elemnodes(), mechcrsec::give_mominer(), mechtop::give_node_coord2dxz(), mechcrsec::give_shearcoeff(), glmatrixtransf(), Gtm, element::ipp, lgmatrixtransf(), mechtop::locsystems(), mechmat::matstiff(), Mc, Mm, Mt, ndofe, nne, nodes, stiffness_matrix_expl_local(), tncomp, and transf_matrix().

Referenced by internal_forces(), nodal_forces(), nodeforces(), and res_stiffness_matrix().

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

function computes stiffness matrix of two-dimensional beam finite element element is based on Mindlin theory (shear stresses are taken into account) stiffness matrix is formulated explicitly

Parameters: