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 load in the package 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. > 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 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 > ******************************************************* > > > > >