Composing a stiffness matrix

• To: mathgroup at smc.vnet.net
• Subject: [mg20328] Composing a stiffness matrix
• From: "Toshiyuki (Toshi) Meshii" <meshii at mech.fukui-u.ac.jp>
• Date: Fri, 15 Oct 1999 20:20:51 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```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}}・瘢雹{u1,u2}
Eq (2)   {f2,f3}={{kb,-kb},{-kb,kb}}・瘢雹{u2,u3}
and want to construct Eq (3) from these two equations systematically.
Eq (3)   {f1,f 2,f3}=K・瘢雹{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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