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Topic:
FEM: straindisplacement matrix for isoparametric elements
Replies:
2
Last Post:
Jul 10, 2012 1:50 AM



Jörg
Posts:
3
Registered:
7/8/12


FEM: straindisplacement matrix for isoparametric elements
Posted:
Jul 8, 2012 6:45 AM


Hi group,
I'm currently dealing with the basics of the Finite Element Method: I want to compute the strains of an element based on the nodal displacements. The nodal displacements are given from a FEProgram which is using isoparametric elements.
In [1] (section 4.2.5) it is given how to compute the strain vector '{eps}' using the straindisplacement matrix '[B]' and the nodal displacement vector '{q}': {eps} = [B] * {q}
To compute [B] numerically I have assemble it from several submatrices [B_i] (given at page 23 in [1]). The several [B_i] have to be computed by inverting the Jacobian matrix [J]. [J] itself is composed of the derivative of the shape function Ni.
What I do not understand:
 How many [B_i] I have to provide? Is i ranging from 1 to the count of nodes within the element?
 I can easily derive the shape functions Ni for the local coordinates 's' or 't'. But in general Ni * d/ds or Ni * d/dt remain dependet on 's' and/or 't'. Therefore I have to provide a value for 's' and 't' when I numerically calculate [J]. But what value of 's' and 't' I have to provide for the current [B_i] ?
In other words: for me it is not clear how to assemble numerically the matrix [B] for a general isoparametric element. Any help would be much appreciated.
Thanks in advance, Jörg
[1] http://homepages.cae.wisc.edu/~suresh/ME964Website/M964Notes/Notes/introfem.pdf


Date

Subject

Author

7/8/12


Jörg

7/8/12


AMX

7/10/12


Jörg


