Hello,
I have condensed a Finite element model from 8 nodes with 6 dof at each node into 2 nodes with 6 dof at each node using a static condensation method (or Guyan reduction). Now i would like to translate this nodal data (represented in stiffness matrix) into a 3D beam element. So for that i need the beam element properties (like Moment of inertia (Iyy and Izz), Polar moment of inertia (J), Shear modulus (G), Young's Modulus (E), Cross sectional Area and length (L)) from the 12 by 12 stiffness matrix.
What makes it difficult is that the model which i have reduced is made of different material at each sides hence the model does not have a constant Young's Modulus (E) or shear modulus (G).
Can anyone help me in finding out the beam element properties using the beam element stiffness matrix? Well we all know how to do the opposite.
The 3D beam element stiffness matrix definition and Finite element model descriptions are given in the attached .doc. The finite element model shown in figure 1 is before condensation, then the model is condensed into 2 nodes and the condensed stiffness matrix is given by Table 1.
Any help will be appreciated.
Thank You,
Paul Thomas
Dear Paul,
apparently you have both the value and the definition of 26 terms (the non vanisching terms in stiffness matrix) that depends on 6 parameters. The problem seems overdetermined but you can try to manage this problem eliminating suitable equations...
Anyway you question seems to be related to the homogeneoization techniques. I suggest you the following reference:
Cartraud, Patrice, and Tanguy Messager. "Computational homogenization of periodic beam-like structures."
It will be highly non-linear paramterization/root finding problem. And as you know there can be multiple solutions or no real solution at all. But still worth giving a try.
Hello all,
Thank You for the valuable answers.
It is not a homogenization problem. I have a 3D beam stiffness matrix and I am trying to retrieve the data like E, A, I, G and J from the stiffness matrix shown in Table 1(attached document). For example, the first cell value in stiffness matrix is 1040000 and the corresponding in data in Figure 1 is EA/L. So, EA/L=1040000. Here I know only the length of the beam (L), which is L=10 inch. How can I separate the value E and A from 104000? Similarly I need to find out the other beam parameters like Iy, Iz, J and G.
Thank You,
Paul Thomas
Dear Paul,
I known that this might sound as a very trivial hint that you already applied, but I would follow a "from simple to complex" approach. To start with, I would consider a very simple element (e.g. 1D truss element or 2D beam) to understand the problem clearly and to try a method (for example, Claudio's) to see if a solution really exists. Only then, I would make things more complex moving to your real 3D case
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