<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Well, it is a bit tricky.<div>The operators D1/D2 dealing with mechanics where added in relation to the basis functions.</div><div>You should use a function space where the derivatives are indicated:</div><div><br></div><div><div>FunctionSpace {</div><div> /* Meca_u : Mechanics - Displacement ux, uy formulations */</div><div><br></div><div> { Name H_u_Mec_2D ; Type Vector ;</div><div> BasisFunction {</div><div> /* ux = ux_n sx_n , for all nodes */</div><div> { Name sxn ; NameOfCoef uxn ; Function BF_NodeX ;<span class="Apple-tab-span" style="white-space:pre"> </span>dFunction {BF_NodeX_D12, BF_Zero} ;</div><div> Support DomainTot ; Entity NodesOf[ All ] ; }</div><div> { Name syn ; NameOfCoef uyn ; Function BF_NodeY ; dFunction {BF_NodeY_D12, BF_Zero} ;</div><div> Support DomainTot ; Entity NodesOf[ All ] ; }</div><div> }</div><div> Constraint {</div><div> { NameOfCoef uxn ; EntityType NodesOf ; NameOfConstraint DeplacementX ; }</div><div> { NameOfCoef uyn ; EntityType NodesOf ; NameOfConstraint DeplacementY ; }</div><div> }</div><div> }</div><div>}</div></div><div><br></div><div>And the formulation would look like:</div><div><br></div><div><br></div><div><div>Formulation {</div><div><br></div><div> { Name Mec_u_2D ; Type FemEquation ;</div><div> Quantity {</div><div> { Name u ; Type Local ; NameOfSpace H_u_Mec_2D ; }</div><div> }</div><div><br></div><div> Equation {</div><div> Galerkin { [C_m[] * Dof{D1 u}, {D1 u} ] ; </div><div> In Domain_Disp ; Jacobian JVol ; Integration GradGrad ; } </div><div> Galerkin { [ -F[] , {u} ] ; </div><div> In Domain_Force; Jacobian JSur ; Integration GradGrad; } </div><div> }</div><div> }</div><div><br></div><div>}</div></div><div><br></div><div><br></div><div><br></div><div>with e.g.</div><div><br></div><div><div>/* --------------------------------------------------------------------------*/</div><div><br></div><div>Function {</div><div> /* Elasticity */</div><div> //Mechanical constants E = 100 Gpa, v = 0.33</div><div><br></div><div> E[PlateINT] = 100e9 ; nu = 0.33 ;</div><div><br></div><div> f[] = E[]/(1-nu^2) ; </div><div> C_m[#{PlateINT}] = TensorSym[ f[], nu*f[], 0, f[], 0, (1-nu)/2*f[]] ; </div><div> </div><div> </div><div> F[#{Lin_Y1}] = Vector[0,-100, 0 ];</div><div> //F[#{Point_X1_u}] = Vector[0,-100, 0 ];</div><div>}</div></div><div><br></div><div><br></div><div>HTH,</div><div>Ruth</div><div><br></div><div><br></div><div><br><div apple-content-edited="true">
<div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>--</div><div>Dr. Ir. Ruth V. Sabariego</div><div>University of Liege, Electrical Engineering & Computer Science, </div><div>Applied & Computational Electromagnetics (ACE),</div><div>phone: +32-4-3663737 - fax: +32-4-3662910 - <a href="http://ace.montefiore.ulg.ac.be/">http://ace.montefiore.ulg.ac.be/</a></div><br class="Apple-interchange-newline"><br></div></div>
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<br><div><div>On 25 Nov 2011, at 10:17, Saurabh Srivastava wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">Dear Ruth, <br><br>Thank you for a prompt response, So essentially there is no way to access the components of exterior derivative, for e.g. {d u} [1,1] at any point in the computation? <br><br>Since basis functions are split in this case ..can we pass {d ux} or {d uy} as arguments to functions in weak formulation?<br>
<br>Although one can pass mu[{d u}] as an argument to a function mu?<br><br>best,<br>-saurabh<br><br><br><br><div class="gmail_quote">On Fri, Nov 25, 2011 at 7:37 AM, Ruth V. Sabariego <span dir="ltr"><<a href="mailto:r.sabariego@ulg.ac.be">r.sabariego@ulg.ac.be</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><div style="word-wrap:break-word">You can't use Dof{eps[{d u}]}, that is not allowed. Sorry!<div>That is the reason why we split the displacement in components with a basis function per compoment: BF_NodeX, BF_NodeY and BF_NodeZ.</div>
<div><br></div><div><br></div><div>HTH,</div><div>Ruth</div><div><br><div>
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<div>--</div><div>Dr. Ir. Ruth V. Sabariego</div><div>University of Liege, Electrical Engineering & Computer Science, </div><div>Applied & Computational Electromagnetics (ACE),</div><div>phone: <a href="tel:%2B32-4-3663737" value="+3243663737" target="_blank">+32-4-3663737</a> - fax: <a href="tel:%2B32-4-3662910" value="+3243662910" target="_blank">+32-4-3662910</a> - <a href="http://ace.montefiore.ulg.ac.be/" target="_blank">http://ace.montefiore.ulg.ac.be/</a></div>
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<br><div><div><div class="h5"><div>On 25 Nov 2011, at 00:51, Saurabh Srivastava wrote:</div><br></div></div><blockquote type="cite"><div><div class="h5">Hello,<br><br>I am interested in the elasticity example, as I realized a new operator was D1/D2 was hard-coded to obtain symmetric gradient (which are unlike curl, grad, or div) of displacements. I'm attempting to get around this using the following approach ...essentially, I compute the exterior derivative of displacement vector then pass it to a function which converts this 2nd rank tensor into a vectorial (Voigt's) notation, <br>
<br>Thus I replace these lines ...<br><br>Formulation {<br> { Name Mec2D_u ; Type FemEquation ;<br> Quantity {<br> { Name u ; Type Local ; NameOfSpace H_u_Mec2D ; }<br> }<br> Equation {<br> //gu = Tensor[{d u}];<br>
Galerkin { [ C_m[] * Dof{D1 u}, {D1 u} ] ;<br> In Domain_Disp ; Jacobian Vol ; Integration GradGrad ; } <br> Galerkin { [ -F[] , {u} ] ; <br> In Domain_Force; Jacobian SurLinVol; Integration GradGrad; } <br>
}<br> }<br>}<br><br>-----------------with these lines------------------------<br>Function {<br> eps[] = Vector[CompXX[$1], CompYY[$1], CompXY[$1] ];<br>}<br><br>Formulation {<br> { Name Mec2D_uxuy ; Type FemEquation ;<br>
Quantity {<br> //{ Name ux; Type Local ; NameOfSpace H_uxuy_Mec2D ; }<br> //{ Name uy; Type Local ; NameOfSpace H_uxuy_Mec2D ; }<br> { Name u ; Type Local ; NameOfSpace H_u_Mec2D ; }<br> }<br> Equation {<br>
Galerkin { [ C_m[] * Dof{eps[{d u}]}, {eps[{d u}]} ]; //line 175<br> In Domain_Disp ; Jacobian Vol ; Integration GradGrad ; } <br> Galerkin { [ -F[] , {u} ] ; <br> In Domain_Force; Jacobian SurLinVol; Integration GradGrad; } <br>
}<br> }<br><br>But I get the following error during pre-processing...<br><br>GetDP : 'C:/Documents and Settings/xx/Desktop/getdp-2.1.1-Win32c/<a href="http://elasticity2d2.pro/" target="_blank">elasticity2d2.pro</a>', line 175 : syntax error ([)<br>
<br>Doesn't looks like its any bracketing issue as i fiddled around with that, What am I doing wrong?<br><br>Any help is appreciated.<br><br>Thank You,<br>-ss<br><br><br><br><br></div></div>
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