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Re: Composing a stiffness matrix

Your original message was sent with Japanese characters in place of . (Dot)
so I suppose people without Japanese fonts would have problems with it.

I am not sure what exactly you mean by "constructing a matrix from
equations". If you mean how to get the matrix K out of the two other
matrices in your equations, here is one possible way. It is convenient to
load in the package

<< LinearAlgebra`MatrixManipulation`
K1 = {{ka, -ka}, {-ka, ka}};
K2 = {{kb, -kb}, {-kb, kb}};

In[4]:= AppendColumns[AppendRows[K1, ZeroMatrix[2, 1]], ZeroMatrix[1, 3]] +
AppendColumns[ZeroMatrix[1, 3], AppendRows[ZeroMatrix[2, 1], K2]] //

ka        -ka       0

-ka       ka + kb   -kb

0         -kb       kb

Andrzej Kozlowski
Toyama International University

>From: "Toshiyuki (Toshi) Meshii" <meshii at>
>To: mathgroup at
>Subject: [mg20362] [mg20328] Composing a stiffness matrix
>Date: Sat, Oct 16, 1999, 9:20

> Hi,
> I am wondering whether we can use Mathematica to systematically compose a
> stiffness matrix in Finite Element Method.
> Please give me an advice on this problem.
> An example problem is as follows:
> I know
>    Eq (1)   {f1,f2}={{ka,-ka},{-ka,ka}}.{u1,u2}
>    Eq (2)   {f2,f3}={{kb,-kb},{-kb,kb}}.{u2,u3}
> and want to construct Eq (3) from these two equations systematically.
>    Eq (3)   {f1,f 2,f3}=K.{u1,u2,u3}
> Here, matrix K is called a stiffness matrix and it's elements are
>  K={{ka,-ka,0},{-ka,ka+kb,-kb},{0,-Kb,Kb}}
> How can we construct matrix K in Eq  (3) from Eq (1) and Eq (2) by using
> Mathematica's commands ?
> *******************************************************
>    Toshiyuki (Toshi) Meshii  meshii at
>     Associate Professor, Department of Mechanical Engineering
>     Fukui University, 3-9-1 Bunkyo, Fukui, 910-8507, JAPAN
>      Tel & Fax +81-776-27-8468
> *******************************************************

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