LE2dFrm_w2ndOrdFF

Purpose

2d LE frame element with moderate deformations under linear or NL geometry

Synopsis

ElemResp = LE2dFrm_w2ndOrdFF (action,el_no,xyz,ElemData,ElemState)

Description

LE2dFRM_w2NDORDFF 2d LE frame element with moderate deformations under linear or NL geometry
  ELEMRESP = LE2dFRM_w2NDORDFF (ACTION,EL_NO,XYZ,ELEMDATA,ELEMSTATE)
  response of 2d linear elastic frame element under moderate deformations using
  force interpolation functions in the basic system (force formulation);
  Reference: Neuenhofer/Filippou, ASCE, JSE, June 1998, pp. 704-711;
  the element accounts for linear and nonlinear geometry for the nodal dof transformations; 
  depending on the value of the character variable ACTION the function returns information
  in data structure ELEMRESP for the element with number EL_NO, end node coordinates XYZ,
  and material and loading properties in the data structure ELEMDATA.
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When the character variable ACTION has one of the following values,
  the function performs the listed operations and returns the results in ELEMRESP:
  ACTION = 'size': report size of element arrays
           'chec': check element property data for omissions and assign default values
           'defo': report function handle for deformed shape

           'init': initialize element history variables
           'forc': report element resisting forces
           'stif': report element stiffness matrix and resisting forces
           'mass': report lumped mass vector and consistent mass matrix
           'post': report post-processing information
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  The data structure ELEMRESP stands for the following data object(s) for each ACTION:
  ELEMRESP = ARSZ        for action = 'size' 
  ELEMRESP = ELEMDATA    for action = 'chec'
  ELEMRESP = FunHandle   for action = 'defo'

  ELEMRESP = ELEMSTATE   for action = 'init'
  ELEMRESP = ELEMSTATE   for action = 'stif'
  ELEMRESP = ELEMSTATE   for action = 'forc'
  ELEMRESP = ELEMMASS    for action = 'mass'
  ELEMRESP = ELEMPOST    for action = 'post'
  ELEMRESP is empty      for unsupported keywords
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  ARSZ   is an Boolean array of size NDF x NEN,
         where NDF = number of DOFs/node, NEN = number of nodes,
         with unit values corresponding to the active element DOFs
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   ELEMDATA is a data structure with element property information in fields
         Geom    = character variable for geometric transformation of node variables
                   (linear, PDelta or corotational) (default=linear)
         A      = cross sectional area
         E      = modulus of elasticity
         I      = moment of inertia
         w      = uniform element load ( w(1) = longitudinal, w(2) = transverse )
         JntOff = rigid joint offsets in global X and Y at element ends;
                  column 1 for node i, column 2 for node j
         IntTyp = function name for element integration
         nIP    = number of integration points
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  ELEMSTATE is a data structure with the current element state; it has the fields
         u     = vector of total element displacements in global reference
         Du    = vector of element displacement increments from last convergence
         DDu   = vector of element displacement increments from last iteration
         ke    = element stiffness matrix in global reference; updated under ACTION = 'stif'
         p     = element resisting force vector in global reference; updated under ACTION = 'stif' or 'forc'
         Past  = element history variables at last converged state
         Pres  = current element history variables
         lamda = row vector of current load factor(s)
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
   ELEMPOST is a data structure with element response information for post-processing in fields
         v     = element deformations
         q     = element basic forces
      Sec{i}.e = section deformations at integration point i
      Sec{i}.s = section forces       at integration point i

Cross-Reference Information

This function calls:

• ElementLoading determines current distributed element load value
• ExtrReshu extracts displacements and increments from State and reshapes into array
• ElmLenOr element length and x-axis orientation (direction cosines)
• GeomTran_2dFrm kinematic matrices and deformations for a 2-node 2d frame element
• kg_2dFrm geometric stiffness matrix for 2-node 2d frame element for different options
• Lagrange Lagrange interpolation polynomials in interval -1<xi<1