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Element.beam2e - Revision history
2026-04-17T07:36:26Z
Revision history for this page on the wiki
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http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1927&oldid=prev
Fotis: /* Stiffness Matrix K */
2007-02-19T12:36:09Z
<p><span dir="auto"><span class="autocomment">Stiffness Matrix K</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Stiffness Matrix K==  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Stiffness Matrix K==  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The stiffness matrix K in global coordinates is given as:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The stiffness matrix K in global coordinates is given as:</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"><math>\alpha\,</math></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><pre></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><pre></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K(0,0)= K1;  K(0,1)= K2;  K(0,2)= K4;  K(0,3)=-K1;  K(0,4)=-K2;  K(0,5)= K4;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K(0,0)= K1;  K(0,1)= K2;  K(0,2)= K4;  K(0,3)=-K1;  K(0,4)=-K2;  K(0,5)= K4;</div></td></tr>
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Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1926&oldid=prev
Fotis: /* Stiffness Matrix K */
2007-02-19T12:27:58Z
<p><span dir="auto"><span class="autocomment">Stiffness Matrix K</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Stiffness Matrix K==  </div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==Stiffness Matrix K==  </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The stiffness matrix K in global coordinates is given as:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The stiffness matrix K in global coordinates is given as:</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><math>\alpha\,</math></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><pre></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><pre></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K(0,0)= K1;  K(0,1)= K2;  K(0,2)= K4;  K(0,3)=-K1;  K(0,4)=-K2;  K(0,5)= K4;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>K(0,0)= K1;  K(0,1)= K2;  K(0,2)= K4;  K(0,3)=-K1;  K(0,4)=-K2;  K(0,5)= K4;</div></td></tr>
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Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1925&oldid=prev
Fotis at 17:41, 14 February 2007
2007-02-14T17:41:30Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following article describes the use of the <tt>element.beam2e</tt> command.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following article describes the use of the <tt>element.beam2e</tt> command.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>This command defines a simple, two-node <del class="diffchange diffchange-inline">Euler-</del>Bernulli beam element.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>This command defines a simple, two-node <ins class="diffchange diffchange-inline">elastic </ins>Bernulli<ins class="diffchange diffchange-inline">-Euler </ins>beam element.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Syntax=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Syntax=</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The implementation of the <del class="diffchange diffchange-inline">Euler</del>-<del class="diffchange diffchange-inline">Bernoulli </del>beam follows closely the implementation of ''Cook et al''.<ref>R.D. Cook, d.S. Malkus and M.E. Plesha, ''"Concepts and Applications of Finite Element Analysis"'', 3<sub>rd</sub> Edition, John Wiley & Sons, 1989, p.216</ref> Special care is taken to avoid matrix multiplications in favor of efficiency.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The implementation of the <ins class="diffchange diffchange-inline">Bernulli</ins>-<ins class="diffchange diffchange-inline">Euler </ins>beam follows closely the implementation of ''Cook et al''.<ref>R.D. Cook, d.S. Malkus and M.E. Plesha, ''"Concepts and Applications of Finite Element Analysis"'', 3<sub>rd</sub> Edition, John Wiley & Sons, 1989, p.216</ref> Special care is taken to avoid matrix multiplications in favor of efficiency.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==General==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==General==</div></td></tr>
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Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1924&oldid=prev
Fotis: /* Comments */
2007-02-14T17:35:50Z
<p><span dir="auto"><span class="autocomment">Comments</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Comments=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Comments=</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Node]]s, [[material]] and [[section]] '''must''' be already defined.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[[Node]]s, [[material]] and [[section]] '''must''' be already defined.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">=Theory=</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td></tr>
</table>
Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1923&oldid=prev
Fotis: /* Residual vector R */
2007-02-14T17:33:56Z
<p><span dir="auto"><span class="autocomment">Residual vector R</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>R[4]=facS*(- K12*u[1] - K6*u[2] + K12*u[4] - K6*u[5]) - facG*( 0.5*b[1]*L);</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>R[4]=facS*(- K12*u[1] - K6*u[2] + K12*u[4] - K6*u[5]) - facG*( 0.5*b[1]*L);</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>R[5]=facS*(  K6*u[1]  + K2*u[2] - K6*u[4]  + K4*u[5]) - facG*(-b[1]*L*L/12.);</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>R[5]=facS*(  K6*u[1]  + K2*u[2] - K6*u[4]  + K4*u[5]) - facG*(-b[1]*L*L/12.);</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>R-=facP*Fext</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>R-=facP*Fext<ins class="diffchange diffchange-inline">;</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></pre></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></pre></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and transforming it from local to global,</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>and transforming it from local to global,</div></td></tr>
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Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1922&oldid=prev
Fotis at 17:24, 14 February 2007
2007-02-14T17:24:19Z
<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following article describes the use of the <tt>element.beam2e</tt> command.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following article describes the use of the <tt>element.beam2e</tt> command.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>This command defines a simple, two-node Euler beam <del class="diffchange diffchange-inline">member</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>This command defines a simple, two-node Euler<ins class="diffchange diffchange-inline">-Bernulli </ins>beam <ins class="diffchange diffchange-inline">element</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Syntax=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Syntax=</div></td></tr>
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Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1921&oldid=prev
Fotis: /* See also */
2007-02-14T17:22:58Z
<p><span dir="auto"><span class="autocomment">See also</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>R[4]=R4;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>R[4]=R4;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></pre></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></pre></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">=Notes=</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><references/></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=See also=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=See also=</div></td></tr>
</table>
Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1920&oldid=prev
Fotis: /* Implementation */
2007-02-14T17:22:19Z
<p><span dir="auto"><span class="autocomment">Implementation</span></span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The implementation of the Euler-Bernoulli beam follows closely the implementation of ''Cook et al''<ref>R.D. Cook, d.S. Malkus and M.E. Plesha, ''"Concepts and Applications of Finite Element Analysis"'', 3<sub>rd</sub> Edition, John Wiley & Sons, 1989, p.216</ref><del class="diffchange diffchange-inline">. </del>Special care is taken to avoid matrix multiplications in favor of efficiency.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The implementation of the Euler-Bernoulli beam follows closely the implementation of ''Cook et al''<ins class="diffchange diffchange-inline">.</ins><ref>R.D. Cook, d.S. Malkus and M.E. Plesha, ''"Concepts and Applications of Finite Element Analysis"'', 3<sub>rd</sub> Edition, John Wiley & Sons, 1989, p.216</ref> Special care is taken to avoid matrix multiplications in favor of efficiency.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==General==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==General==</div></td></tr>
</table>
Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1919&oldid=prev
Fotis: /* Implementation */
2007-02-14T17:21:49Z
<p><span dir="auto"><span class="autocomment">Implementation</span></span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 17:21, 14 February 2007</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=Implementation=</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The implementation of the Euler-Bernoulli beam follows closely the implementation of ''Cook et al''<ref>R.D. Cook, d.S. Malkus and M.E. Plesha, ''"Concepts and Applications of Finite Element Analysis"'', 3<sub>rd</sub> Edition, John Wiley & Sons, 1989, p.216</ref>. Special care is taken to avoid matrix multiplications in favor of efficiency.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==General==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==General==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The element length and directional cosines are given as:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The element length and directional cosines are given as:</div></td></tr>
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Fotis
http://www.nemesis-project.org/index.php?title=Element.beam2e&diff=1918&oldid=prev
Fotis: /* Syntax */
2007-02-14T17:09:10Z
<p><span dir="auto"><span class="autocomment">Syntax</span></span></p>
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<td colspan='2' style="background-color: white; color:black;">←Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 17:09, 14 February 2007</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>!width="150"|default</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>!width="150"|default</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|-</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|-</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>id                || The elemental id              ||align="center"| integer  ||align="center"|-</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">|</ins>id                || The elemental id              ||align="center"| integer  ||align="center"|-</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|-</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|-</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|dof<sub>1-2</sub> || The elemental [[node|nodes]]  ||align="center"| integer  ||align="center"|-</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>|dof<sub>1-2</sub> || The elemental [[node|nodes]]  ||align="center"| integer  ||align="center"|-</div></td></tr>
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Fotis