Re: Composing a stiffness matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg20362] Re: [mg20328] Composing a stiffness matrix
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Sun, 17 Oct 1999 03:01:50 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```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

In[1]:=
<< LinearAlgebra`MatrixManipulation`
In[2]:=
K1 = {{ka, -ka}, {-ka, ka}};
In[3]:=
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]] //
MatrixForm

Out[4]//MatrixForm=
ka        -ka       0

-ka       ka + kb   -kb

0         -kb       kb

--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: "Toshiyuki (Toshi) Meshii" <meshii at mech.fukui-u.ac.jp>
>To: mathgroup at smc.vnet.net
>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.
>
> 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 mech.fukui-u.ac.jp
>     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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