The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.num-analysis

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 3
Registered: 7/8/12
FEM: strain-displacement matrix for isoparametric elements
Posted: Jul 8, 2012 6:45 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 FE-Program which is using isoparametric

In [1] (section 4.2.5) it is given how to compute the strain vector '{eps}'
using the strain-displacement matrix '[B]' and the nodal displacement vector
{eps} = [B] * {q}

To compute [B] numerically I have assemble it from several sub-matrices
[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

Thanks in advance,


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.