LE9nodeQuad

Purpose

isoparametric 9 node quadrilateral element with linear elastic material

Synopsis

ElemResp = LE9nodeQuad (action,el_no,xyz,ElemData,ElemState)

Description

LE9NODEQUAD isoparametric 9 node quadrilateral element with linear elastic material
 ELEMRESP = LE9NODEQUAD (ACTION,EL_NO,XYZ,ELEMDATA,ELEMSTATE)
  response of isoparametric 9-node quadrilateral element with linear elastic material under plane stress/strain; 
  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
           '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
           'stre': integration point stress projection to nodes
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  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 = 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 = STRSREC     for action = 'stre'
  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 or corotational) (default=linear)
         t     = element thickness (default t=1)
         b     = element body forces (default b=[0;0] )
         nIP   = number of integration points (default nIP =3)
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  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
         Tr0        = transformation matrix from local to global coordinates
         Mat{i}.xyz = coordinates   of integration point i
         Mat{i}.eps = strain tensor at integration point i
         Mat{i}.sig = stress tensor at integration point i
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  STRSREC is a data structure with nodal stress information in field(s)
         sigNd = nodal stresses

Cross-Reference Information

This function calls:

• ExtrReshu extracts displacements and increments from State and reshapes into array
• TransformStr2GL transformation of strain and stress tensors from local to global reference system
• shape2d shape functions for 4-9 node quadrilateral element
• DefGeom_Quad determines local coordinates and corotational triad of quadrilateral element
• GeomTran_QuadMemb kinematic matrices and local displacements for a quadrilateral membrane element
• kg_QuadMemb geometric stiffness matrix for quadrilateral membrane element for different options
• Gauss2d Gauss integration rule in two dimensions