BInel2dFrm_wEPLHNMYS

Purpose

2d elasto-plastic, linear hardening basic frame element

Synopsis

BElemResp = BInel2dFrm_wEPLHNMYS (action,L,BElemData,BElemState)

Description

BINELP2dFRM_WEPLHNMYS 2d elasto-plastic, linear hardening basic frame element
  BELEMRESP = BINELP2dFRM_WEPLHNMYS (ACTION,L,BELEMDATA,BELEMSTATE)
  the function determines the 2d response of an elasto-plastic basic frame element of length L 
  with elasto-plastic behavior with linear isotropic and kinematic hardening
  under axial force (N) - bending moment (M) interaction at two plastic hinges at ends i and j
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  When the character variable ACTION has one of the following values,
  the function performs the listed operations and returns the results in BELEMRESP:
  ACTION = 'chec': check element property data for omissions and assign default values
           'init': initialize element history variables
           'forc': report basic element forces
           'stif': report basic element stiffness matrix and basic element forces
           'post': report post-processing information
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  The data structure BELEMRESP stands for the following data object(s) for each ACTION:
  BELEMRESP = BELEMDATA    for action = 'chec'
  BELEMRESP = BELEMSTATE   for action = 'init'
  BELEMRESP = BELEMSTATE   for action = 'stif'
  BELEMRESP = BELEMSTATE   for action = 'forc'
  BELEMRESP = BELEMPOST    for action = 'post'
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  BELEMDATA is a data structure with basic element property information; it has the fields
         E   = Young's Modulus
         A   = cross-sectional area
         I   = moment of inertia
         Np  = plastic axial capacity at hinges near ends i, j ( Np = [Npi ; Npj] )
         Nb  = axial force at balance point at hinges near ends i, j; default = zeros(2,1)
         Mp  = plastic moment capacity at hinges near ends i, j ( Mp = [Mpi ; Mpj] )
         Hir = isotropic plastic modulus ratio (default = [ 0 ; 0 ] )
         Hkr = kinematic modulus ratio (default = [ 0 ; 0  ; 0 ] )
         w   = uniformly distributed element load [wx ;wy] (default = [ 0 ; 0 ] )
         GPYSC = coefficients for polynomial yield surface
                 (default = [ 1.2 2 0 ; 1 0 2 ; 3.5 2 2 ; -1 0 0 ] )
         YFtol = yield criterion tolerance (default = 1e-12)
         Wtol  = work tolerance for return map algorithm (default = 1e-16)
         MaxIter = max no of iterations for return map algorithm (default = 15)         
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
  BELEMSTATE is a data structure with the current basic element state; it has the fields
         v    = vector of total element deformations
         ke   = basic element stiffness matrix; updated under ACTION = 'stif'
         q    = basic element forces; updated under ACTION = 'stif' or 'forc'
         Past = element history variables at last converged state
         Pres = current element history variables
         the element history variables of this element are
             ehp   = plastic hinge   deformations   (4x1 array)
             sbk   = plastic hinge back forces      (4x1 array)
             alpha = isotropic hardening variable   (2x1 array)

Cross-Reference Information

This function calls:

• ElementLoading determines current distributed element load value
• GPYS function value, gradient and Hessian of polynomial yield surface