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Global stiffness matrix from element stiffness matrices for a thin rectangular plate (Kirchhoff plate)

Computational Science Asked by Ahmed Hossam on June 9, 2021

I have the element stiffness matrix for a thin "kirchhoff" plate. The plate is 3 [m] x 5 [m] and is simply supported on all edges. It’s thickness is 0,2 [m]. On the plate there acts a constant load p = 5 [kN/m²]. For mu = 0,2 and E = 30000 [MPa] the displacement in the midpoint equals 0,168 [mm].

What’s the most efficient or quickest way and how to implement or code the assembly of finite elements of 0,5 [m] x 0,5 [m] for this plate and get the global stiffness matrix, the results as the nodal displacement vector and the nodal force vector?

Hints are appreciated. Thanks.

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EDIT: If somebody knows an open source free code or implementation for this very specific program written in Java, C++ or even in VBA, then this would be an answer for the question too!

EDIT: I found here a code that should work fine. How difficult is it to translate this code into another procedural programming language? How much pain is involved?

One Answer

What you are looking for is a Discrete Kirchhoff Quadrilateral plate or DKQ plate. Seems you are looking for a very straight forward formulation that simply give you the global stiffness matrix. But i'm afraid that most codes I've seen are dealing with integration and transformation. You can search for DKQ source code. There are documents for java which would be very helpful if you want to code it yourself. There are also C++ implementations of such element which you could find on the web, just google it. The codes i know are mostly using Gauss integration for calculating local stiffness matrix then convert it to global stiffness matrix. However this is the Java document I mentioned above:

  • "Development of Membrane, Plate and Flat Shell Elements in Java" thesis by Kaushalkumar Kansara (available here)

There is also a C#.NET code which worth a check (the code is not tested yet) available here

Answered by epsi1on on June 9, 2021

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