the stiffness matrix of a beam element do not match with the computed result

- July 31, 2023 at 2:39 pm
  
  567
  Subscriber
  
  this are apdl commands：
  finish
  /clear
  /PREP7
  /NUMBER,-1
  /VIEW,1,1,1,1
  /ANG,1
  ET,1,BEAM188 ! BEAM
  SECTYPE,1,BEAM,CSOLID
  SECDATA,0.005
  MP,EX ,1,6.9E10
  MP,PRXY,1,0.3
  MP,DENS,1,2700
  zl=1
  N,1,-1*zl,0,0
  N,2,0,0,0
  TYPE,1
  secnum,1
  MAT,1
  E,1,2
  /SOLU
  ANTYPE,2
  MODOPT,LANB,10
  MXPAND,10,,,0
  SOLVE
  /AUX2
  FILE,file,full
  HBMAT,stiff,txt,,ascii,stiff,yes,yes
  HBMAT,mass,txt,,ascii,mass,yes,yes
  The exported stiffness matrix is shown in the following diagram：
  ansysstiffness：
  The stiffness matrix is calculated as
  The calculation result of ansysstiffness(2,2) does not match the formula
  i do not know why!
  thank you very much;
- August 1, 2023 at 2:36 pm
  
  mrife
  Ansys Employee
  
  Hi 567
  Here is a hint: what beam theory does MAPDL use and is it the same as what you are comparing to....?
  MAPDL beams are based on Timoshenko beam theory. Whereas the stiffness matrix shown is based on Euler-Bernoulli beam theory. Timoshenko accounts for shear deformation and rotary inertia effect (that E-B does not), but the resulting beam stiffness is slightly lower than E-B theory.
  Mike