CALCS BAS012
MATRIX STIFFNESS ANALYSIS

APPLICATION

The program obtains solutions to structural analysis tasks within the following boundaries:
  • Structures which may be idealised as being composed of rod, beam, rope & four node quadrilateral membrane elements
  • Small scale problems
  • Linear Elastic Material Properties
  • Static Loading
  • Bandwidth solution allows equivalent to fully populated array of 35 nodes (approx).
    For problems ouside of these boundaries recourse to full Finite Element Analysis is suggested.

    OUTPUT

    Nodal Displacements, Reactions and Element Internal loads
    Problem definition plot showing nodes & elements

    SEE ALSO

    BAS020

    THEORY

    Finite Element Method
  • KEYWORDS

    JTITLEjob title
    CCOMBcase, combination
    CDISPcase, displacement set
    CLOADcase, load set
    CTITLEcase, title
    CUNITcase, unit
    DMPCdisplacement, multi-point constraint
    DSPCdisplacement, single point constraint
    EBARelement, bar
    EELRelement, elastic load reaction
    ENDDATinput file terminator marker
    EPB element, shear & biaxial stress panel
    EPSelement, shear panel
    ERODelement, rod
    EROPEelement, rope
    LACCELacceleration
    LBARload, bar
    LNODEload, nodal
    NOnode, orientation
    NSnode, structural
    PBARproperty, bar
    PMATproperty, isotropic material
    PPANELproperty, shear panel & shear&biaxialstress panel
    PRODproperty, rod
    PROPEproperty, rope
    REMremarks at any points in the input file
    SOLsolution control

    DATA ELEMENTS

    Aarea, cross section
    CAScase, comb or unit
    CSETcase set
    DSETdisplacement, prescribed set
    Eyoung's modulus
    Enentity id number
    FDfreedom, dependent
    FIfreedom, independent
    Gshear modulus
    Iy Iz 2nd MoA about y & z local axes
    Jshear constant, of cross section
    Kfactor
    Kt Krstiffness- translation or rotation
    L1 to L6loads, corresponding to freedoms 1 to 6
    LSETload set
    Mmoment
    MNmass, nodal
    NDnode, dependent
    NInode, independent id
    NPARTSnumber of rope parts connecting two nodes
    NSETnode set
    ODdisplacement output, 0 or 1
    OEelement output, 0 or 1
    Pforce
    ROPEidentity, rope
    Tthickness , area
    UDLx yudl's applied to bar local xy & xz planes
    UTMupper triangular matrix
    vpoisson's ratio
    X Y Zglobal coordinates
    x y zlocal coordinates

    GUIDANCE

    REM

    text
    Remark cards may be placed anywhere in the input file and form no part of the analysis data

    JTITLE

    job title
    The job title appears in the headers of the output file

    CDISP

    CSETDSET
    CSET must be a CUNIT type case
    More than one displacement set DSET may be referenced

    CLOAD

    CSETLSET
    CSET must be a CUNIT type case.
    More than one load set LSET may be referenced.

    CTITLE

    CSETcase title
    CSET may be CUNIT or CCOMB type cases

    CUNIT

    CSETUTM
    The stiffness matrix is modified by a prescribed displacement set having the corresponding case number and the resulting decomposed matrix remains resident for writing the solution displacement vector file providing the upper triangular matrix ID is unchanged from that immediately preceding it (no DSET change). Thereby, when solving for unit cases the stiffness matrix is not repeatedly decomposed unnecessarily but the solution displacement vector is calculated from scratch.

    CCOMB

    CSETCASEK
    No stiffness matrix decomposition is invoked.
    Cards having the same CSET may be used in a single block enabling superposition of any number of factored cases.
    CASE may be any preceding CUNIT or CCOMB cards.
    The solution displacement vector is calculated as the sum of factored preceding cases, CASE may be either CUNIT or CCOMB types.

    NO

    NSETEnXYZ
    Node IDs may be in the range 1 to 50.
    Orientation nodes do not form part of the problem.
    IDs must not duplicate NS IDs.
    They are typically used to orientate elastic reaction axes and bar element planes.

    NS

    NSETEnXYZMN
    Node IDs may be in the range 1 to 400.
    Structural nodes provide the freedoms on which any solution is based.
    Major axis freedoms are:
    1-3 translations parallel to X Y & Z axes
    4-6 rotations about axes parallel to X Y & Z axes.
    The present formulation provides for IDs in the range 1 to 400.
    Nodal Coordinates- Mutually perpendicular position coordinate vectors of the node relative to a datum point parallel to the major axes and in the order X Y & Z form a right handed set.
    If bars form part of the structure the number of freedoms per node is six, otherwise three. The object of this adjustment is to minimise the number of freedoms, solution time and data storage requirements.
    Stiffness matrix bandwidth is a function of element connectivity and the order in which the nodes are listed in the input data file. This order may therefore be manipulated to minimise bandwidth.

    PMAT

    EnEGv
    Material IDs may be in the range 1 to 50.
    Materials are intended to be isotropic and homogenous through elements.
    The present formulation does not use the relationship G=E/(2*(1+v))
    This may be useful where panel stiffnesses must reflect the effect of modifying influences such as stiffeners, lightening or access holes.

    PROD

    EnA
    Rod property data.
    Property IDs may be in the range 1 to 50.

    PBAR

    EnAI1I2J
    Bar property data
    Property IDs may be in the range 1 to 50.
    Properties may be zero.

    PPANEL

    EnT
    Panel property data, use for EPS and EPB
    Property IDs may be in the range 1 to 50.

    PROPE

    ROPEKAE
    Property card associated with EROPE element.
    K.A.E is the rope stiffness per unit length and is the product of an effectivity factor, which accounts for rope fibre cross section fill density and rope twist flexibility, the nominal cross section and Young's Modulus.
    K is typically taken to be 0.3
    A maximum of 10 cards may be used.

    EELR

    EnN1N2KtKr
    Constraint of a structure at a node- force or torque.
    N1 must be a structural node.
    N2 may be a structural or orientation node.
    Contribution to the stiffness matrix is made only at N1.
    Kt or Kr may be zero.

    EROD

    EnN1N2PMATPROD
    Structural element capable of transmitting axial force.
    N1 and N2 must be structural nodes.
    PMAT referred to must have a non-zero value for Young's Modulus.

    EBAR

    EnN1N2N3PMATPBAR
    Structural element capable of transmitting moment and shear in two mutually perpendicular planes, axial force and torque.
    N1 and N2 must be structural nodes.
    N3 may be a structural or orientation node.
    Contribution to the stiffness matrix is made at N1 and N2.
    PMAT referred to must have a non-zero value for Young's Modulus.

    EPS

    EnN1N2N3N4PMATPPANEL
    Structural element of quadrilateral form capable of transmitting in-plane membrane shear force.
    N1 to N4 must be structural nodes.
    PMAT referred to must have a non-zero value for the shear modulus.
    N1 to N4 must lie in a flat plane as this is assumed in the formulation.

    EPB

    EnN1N2N3N4PMATPPANEL
    Structural element of quadrilateral form capable of transmitting in-plane membrane shear and biaxial loads.
    N1 to N4 must be structural nodes.
    PMAT referred to must have a non-zero value for Young's Modulus, the shear modulus and Poisson's ratio.
    N1 to N4 must lie in a flat plane as this is assumed in the formulation.

    EROPE

    ROPEN1N2NPARTS
    Structural element in which the the axial force acting in all rope parts (connecting two nodes) is equal. This is an idealisation of a multiple part rope/sheaves combination.
    Multiple EROPE cards may be used to define the parts composing any single rope and up to ten ropes may be used, with ROPE ids in the range 1 to 10.
    ROPE ids must correspond with those used on PROPE cards.
    This element will often prove to oppose formulating compact banded solutions as a rope may cover large areas of structure modelled with elements more 'bandwidth' friendly. The memory usage associated with the use of this element must be accounted for when building a model.
    In the present formulation sheave radii are not used because of difficulty in determining the points of impingement of rope parts on sheaves. Is is considered that this limitation will only infrequently be significant, when a rope part connects two closely spaced large diameter sheaves. Sheave 'friction', typically taken to be in the range 2 to 4% is not implimented but this will typically not be significant.
    The NPARTS term allows multiple parts connecting the same two nodes to be defined without using more than one card. When this factor is greater than unity it increases rope length and hence flexibility & the force acting between two nodes but does not increase rope stiffness.

    DMPC

    DSETNDFDNIFIK
    In which the freedoms of a node are constrained by a relationship of the form:
    Aii = Ci.Ai1 ... + Cij.Aij ... + Ci
    To effect a multi-point constraint use one card for each independent freedom of the equation.
    Use with CUNIT type cases only.
    CUNITs may reference more than one DSET.

    DSPC

    DSETNSF1F2F3F4F5F6
    Prescribed displacements are labled 'F' or 0 or non-zero.
    Use with CUNIT type cases only.
    CUNITs may reference more than one DSET.

    LACCEL

    LSETNSETKxKyKz
    Acceleration factors are applied to members of NSET only. It is envisaged that this facility will be most useful when rotational accelerations are incorporated.

    LNODE

    LSETNSL1L2L3L4L5L6
    Forces and moments parallel to global axes freedoms 1 to 6 applied at a structural node.
    CUNIT type cases may reference multiple LSETs.
    Loads 1 to 6 may be zero.

    LBAR

    LSETEBARUDLyUDLz
    Line loads w applied to EBAR parallel to the local y and z axes respectively.
    CUNIT type cases may reference multiple LSETs.
    Bars EBAR must be in the same order as EBAR data cards.
    UDLs y or z may be zero.
    The formulation assumes that bars referenced contribute to the stiffness matrix.

    SOL

    0ODOE
    Solution control flags, 0 output off, 1 output on.

    ENDDAT

    End of input file marker.

    INPUT FORMAT

    Data entries start with a keyword
    Data components are seperated by TAB characters
    The required form, content and order of the file is as follows:
    DAT012
    SOL0ODOE
    REMtext
    JTITLEjob title
    CCOMBCSETCASEK
    CDISPCSETDSET
    CLOADCSETLSET
    CTITLECSETcasetitle
    CUNITCSETUTM
    DMPCDSETNDFDNIFIK
    DSPCDSETNSF1F2F3F4F5F6
    EBAREnN1N2N3MATPBAR
    EELREnN1N2KtKr
    EPBEnN1N2N3N4MATPPANEL
    EPSEnN1N2N3N4MATPPANEL
    ERODEnN1N2MATPROD
    EROPEROPEN1N2NPARTS
    LACCELLSETNSETKxKyKz
    LBARLSETEBARUDLyUDLz
    LNODELSETNSL1L2L3L4L5L6
    NONSETEnXYZ
    NSNSETEnXYZMN
    PBAREnAIyIzJ
    PMATEnEGv
    PPANELEnT
    PRODEnA
    PROPEROPEKAE
    ENDDAT

    EXAMPLE

    Input

    DAT012
    SOL011
    JTITLEtest case
    CDISP11
    CLOAD11
    CTITLE1unit load
    CUNIT11
    DSPC11000FFF
    DSPC14000FFF
    EROD11211
    EROD22311
    EROD33411
    EROD41311
    EROD52411
    LNODE120-10000
    NS110000
    NS124000
    NS134300
    NS140300
    PMAT1111
    PROD11
    ENDDAT

    Output

    BAS012 OUTPUT
    BAS012RUNTIME Mon,13 Jan 2003.21:37:22
    CTITLE1unit load
    NODAL DISPLACEMENTS
    CASENODETXTYTZRXRYRZ
    11000000
    12-2.84-11.20000
    132.49-9.80000
    14000000
    BAS012RUNTIME Mon,13 Jan 2003.21:37:22
    CTITLE1unit load
    CASEERODN1N2P
    1112-0.711
    12230.467
    13340.622
    1413-0.778
    15240.889
    END012