Module with subroutines for doing Component Mode Synthesis. More...

Functions/Subroutines
subroutine	eigval (sam, SSM, SMM, nEigVal, factorMass, iopSing, tolFactorize, tolEigval, eigShift, EVL, PHI, IPSW, LPU, IERR)
	Solves the eigenvalue problem of the FE model. More...

subroutine	gravfull (sam, smm, grav, ierr)
	Establishes the full gravitational force vectors. More...

subroutine	grav (sam, smm, BmatDisk, phi, gravg, ndim, ngen, lpu, ierr)
	Computes the gravitation force vector for the superelement DOFs. More...

subroutine	cmstrs (iopSing, sam, bmatDisk, SMII, SMIE, SMEE, SMMAT, SKII, SKEE, SKMAT, PHI, fullRHS, RHS, VGI, tolFactorize, iStiff, NGEN, NRHS, LPU, IERR)
	Performs CMS-transformation on the system matrices. More...

subroutine	jcms (M, UNDPOS, MEDOF, NDIM, NENOD, MASS, LPU, IERR)
	Computes and prints the inertia properties of the superelement. More...

subroutine	eigcms (sk, sm, Bmat, phi, lambda, Zequ, meqn1, meqn2, n, ndof1, ndof2, nVal, ipsw, lpu, ierr)
	Computes and prints the eigenvalues of the reduced system. More...

subroutine, private	reportsingeqns (mattype, sam, meqErr)
	Prints an error message on singular system system. More...

Detailed Description

Module with subroutines for doing Component Mode Synthesis.

Function/Subroutine Documentation

◆ cmstrs()

subroutine cmstrsmodule::cmstrs	(	integer, intent(in)	iopSing,
		type(samtype), intent(inout)	sam,
		type(diskmatrixtype), intent(inout)	bmatDisk,
		type(sysmatrixtype), intent(inout)	SMII,
		type(sparsematrixtype), intent(in)	SMIE,
		real(dp), dimension(:,:), intent(in)	SMEE,
		real(dp), dimension(:,:), intent(out)	SMMAT,
		type(sysmatrixtype), intent(inout)	SKII,
		real(dp), dimension(:,:), intent(in)	SKEE,
		real(dp), dimension(:,:), intent(out)	SKMAT,
		real(dp), dimension(:,:), intent(in)	PHI,
		real(dp), dimension(:,:), intent(in)	fullRHS,
		real(dp), dimension(:,:), intent(out)	RHS,
		real(dp), dimension(:,:), intent(out)	VGI,
		real(dp), intent(in)	tolFactorize,
		integer, intent(inout)	iStiff,
		integer, intent(in)	NGEN,
		integer, intent(in)	NRHS,
		integer, intent(in)	LPU,
		integer, intent(out)	IERR
	)

Performs CMS-transformation on the system matrices.

Parameters

[in]	iopSing	Option for handling matrix singularities
	sam	Data for managing system matrix assembly
	bmatDisk	Displacement recovery matrix
	SMII	System mass matrix associated with internal DOFs
[in]	SMIE	System mass matrix coupling the internal and external DOFs
[out]	SMMAT	Reduced mass matrix
[in]	SMEE	System mass matrix associated with external DOFs
	SKII	System stiffness matrix associated with internal DOFs
[in]	SKEE	System stiffness matrix associated with external DOFs
[out]	SKMAT	Reduced stiffness matrix
[in]	PHI	Computed eigenvectors (component mode shapes)
[in]	fullRHS	System right-hand-side vectors
[out]	RHS	Reduced right-hand-side vectors
[out]	VGI	Internal displacements due to gravitational forces
[in]	tolFactorize	Zero pivot tolerance (singular system matrix)
	iStiff	File handle for temporary storage of system stiffness matrix
[in]	NGEN	Number of component modes
[in]	NRHS	Number of right-hand-side vectors
[in]	LPU	File unit number for res-file output
[out]	IERR	Error flag

CMS : "Component Mode Synthesis".

Author: Ketil Aamnes

Date: Oct 1988

Author: Knut Morten Okstad

Date: Mar 2003

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◆ eigcms()

subroutine cmstrsmodule::eigcms	(	real(dp), dimension(:,:), intent(inout)	sk,
		real(dp), dimension(:,:), intent(inout)	sm,
		type(diskmatrixtype), intent(inout)	Bmat,
		real(dp), dimension(:,:), intent(in)	phi,
		real(dp), dimension(:), intent(out)	lambda,
		real(dp), dimension(:,:), intent(out)	Zequ,
		integer, dimension(:), intent(in)	meqn1,
		integer, dimension(:), intent(in)	meqn2,
		integer, intent(in)	n,
		integer, intent(in)	ndof1,
		integer, intent(in)	ndof2,
		integer, intent(in)	nVal,
		integer, intent(in)	ipsw,
		integer, intent(in)	lpu,
		integer, intent(out)	ierr
	)

Computes and prints the eigenvalues of the reduced system.

Parameters

	sk	Dense superelement stiffness matrix
	sm	Dense superelement mass matrix
	Bmat	Matrix relating the internal and external nodal DOFs
	phi	Component mode shapes
[out]	lambda	Computed eigenvalues
[out]	Zequ	Computed eigenvectors
[in]	meqn1	Matrix of status 1 (internal) equation numbers
[in]	meqn2	Matrix of status 2 (external) equation numbers
[in]	n	Dimension of the eigenvalue problem
[in]	ndof1	Number of internal nodal DOFs (status 1 equations)
[in]	ndof2	Number of external nodal DOFs (status 2 equations)
[in]	nVal	Number of eigenvalues to solve for
[in]	ipsw	Print switch for debug output
[in]	lpu	File unit number for res-file output
[out]	ierr	Error flag

The associated eigenvectors are optionally computed and expanded to all internal nodes of the superelement.

Author: Knut Morten Okstad

Date: Oct 2002

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◆ eigval()

subroutine cmstrsmodule::eigval	(	type(samtype), intent(in)	sam,
		type(sysmatrixtype), intent(inout)	SSM,
		type(sysmatrixtype), intent(inout)	SMM,
		integer, intent(in)	nEigVal,
		logical, intent(in)	factorMass,
		integer, intent(in)	iopSing,
		real(dp), intent(in)	tolFactorize,
		real(dp), intent(in)	tolEigval,
		real(dp), intent(in)	eigShift,
		real(dp), dimension(:), pointer	EVL,
		real(dp), dimension(:,:), pointer	PHI,
		integer, intent(in)	IPSW,
		integer, intent(in)	LPU,
		integer, intent(out)	IERR
	)

Solves the eigenvalue problem of the FE model.

Parameters

[in]	sam	Data for managing system matrix assembly
	SSM	System stiffness matrix
	SMM	System mass matrix
[in]	nEigVal	Number of eigenvalues to compute
[in]	factorMass	If .true., factorize the mass matrix
[in]	iopSing	Option for handling matrix singularities
[in]	tolFactorize	Zero pivot tolerance
[in]	tolEigval	Zero tolerance on eigenvalues
[in]	eigShift	Eigenvalue shift
[out]	EVL	Computed eigenvalues
[out]	PHI	Associated eigenvectors
[in]	IPSW	Print switch
[in]	LPU	File unit number for res-file output
[out]	IERR	Error flag

The nEigVal lowest eigenvalues and associated eigenvectors are computed using the Lanczos eigenvalue solver. The LAPack solver is used if the system matrices are dense/full, or if tolEigval is non-positive.

Author: Ketil Aamnes

Date: Oct 1988

Author: Knut Morten Okstad

Date: Mar 2003

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◆ grav()

subroutine cmstrsmodule::grav	(	type(samtype), intent(in)	sam,
		type(sysmatrixtype), intent(inout)	smm,
		type(diskmatrixtype), intent(inout)	BmatDisk,
		real(dp), dimension(:,:), intent(in)	phi,
		real(dp), dimension(:,:), intent(out)	gravg,
		integer, intent(in)	ndim,
		integer, intent(in)	ngen,
		integer, intent(in)	lpu,
		integer, intent(out)	ierr
	)

Computes the gravitation force vector for the superelement DOFs.

Parameters

[in]	sam	Data for managing system matrix assembly
	smm	System mass matrix
	BmatDisk	Displacement recovery matrix
[in]	phi	Computed eigenvectors (component mode shapes)
[out]	gravg	Gravitational force vectors
[in]	ndim	Superelement dimension
[in]	ngen	Number of component modes
[in]	lpu	File unit number for res-file output
[out]	ierr	Error flag

First, compute the full gravitation force vector (g) based on unit acceleration vectors (a) and the mass matrix (M):

       g = M*a   or    |g_i| = | M_ii M_ie ||a_i|
                       |g_e|   | M_ei M_ee ||a_e|

Note that the internal and external DOFs can be mixed, i.e., not necessarily having the nice 2*2 block structure indicated above.

Then transform this to the reduced DOF set for the superelement through the virtual work equation:

       dvs'*gs = dv'*g  where v = H*vs  or |v_i| = | B  phi ||vs_e|
                                           |v_e|   | I   0  ||vs_g|

This gives the transformation of the force vector as

       gs = H'*g   or   |gs_e| = |  B'  I ||g_i|
                        |gs_g| = | phi' 0 ||g_e|

where (gs) is the superelement force vector, _e indicates external DOFs, _i indicates internal DOFs, and _g indicates generalized DOFs.

Author: Ketil Aamnes

Date: Oct 1988

Author: Bjorn Haugen

Date: Nov 1998

Author: Knut Morten Okstad

Date: Mar 2003

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◆ gravfull()

subroutine cmstrsmodule::gravfull	(	type(samtype), intent(in)	sam,
		type(sysmatrixtype), intent(inout)	smm,
		real(dp), dimension(:,:), intent(out)	grav,
		integer, intent(out)	ierr
	)

Establishes the full gravitational force vectors.

Parameters

[in]	sam	Data for managing system matrix assembly
	smm	System mass matrix
[out]	grav	Gravitational force vectors
[out]	ierr	Error flag

The gravitatinal force vectors are calculated from the unit system mass matrix and unit accelerations:

    |g| = [M] |a|

Author: Knut Morten Okstad

Date: Feb 2018

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◆ jcms()

subroutine cmstrsmodule::jcms	(	real(dp), dimension(:,:), intent(in)	M,
		real(dp), dimension(:,:), intent(in)	UNDPOS,
		integer, dimension(:), intent(in)	MEDOF,
		integer, intent(in)	NDIM,
		integer, intent(in)	NENOD,
		real(dp), intent(out)	MASS,
		integer, intent(in)	LPU,
		integer, intent(out)	IERR
	)

Computes and prints the inertia properties of the superelement.

Parameters

[in]	M	Reduced dense superelement mass matrix
[in]	UNDPOS	Position matrices for the supernodes
[in]	MEDOF	Matrix of External DOF indices for the supernodes
[in]	NDIM	Dimension on the superelement matrices
[in]	NENOD	Number of supernodes
[out]	MASS	Total mass of the superelement
[in]	LPU	File unit number for res-file output
[out]	IERR	Error flag

Author: Knut Morten Okstad

Date: July 2002

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◆ reportsingeqns()

subroutine, private cmstrsmodule::reportsingeqns	(	character(len=*), intent(in)	mattype,
		type(samtype), intent(in)	sam,
		integer(ik), dimension(:), intent(in)	meqErr
	)

private

Prints an error message on singular system system.

Parameters

[in]	mattype	Type of system matrix (stiffness or mass)
[in]	sam	Data for managing system matrix assembly
[in]	meqErr	List of singular equation numbers

Author: Knut Morten Okstad

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ cmstrs()

◆ eigcms()

◆ eigval()

◆ grav()

◆ gravfull()

◆ jcms()

◆ reportsingeqns()