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rafaelpsilva07 committed Oct 9, 2024
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Expand Up @@ -363,7 +363,7 @@ <h1>Critical Buckling Examples<a class="headerlink" href="#Critical-Buckling-Exa
<div class="section" id="Simply-Supported-study-case-(SSSS)">
<h2>Simply Supported study case (SSSS)<a class="headerlink" href="#Simply-Supported-study-case-(SSSS)" title="Permalink to this heading">#</a></h2>
<p>This study case aims to verify the Rayleigh-Ritz implementation made with Composipy (Silva, R.P. 2023). Mathematical verification of the Rayleigh-Ritz implementation is made against analytical buckling equation and FEM model. The benchmarking example is a simply supported plate with biaxial load, which considers a quasi-isotropic layup [(45/-45)2/02/902]s and properties according Table below. This example came from Kassapoglou (2010).</p>
<p><img alt="c9ac5d83f4064e31bb39a8831febdac2" class="no-scaled-link" src="../_images/mechanical_prop_verification_problem.png" style="width: 400px; height: 200px;" /></p>
<p><img alt="7cbe8d06dd5d45ed8ca0016fe91f732b" class="no-scaled-link" src="../_images/mechanical_prop_verification_problem.png" style="width: 400px; height: 200px;" /></p>
<p>Dimension of the square plate is 100 mm and the load ratio (𝑁𝑦/𝑁𝑥) is 0.5. Analytical solution for this problem using Equation below is 234.7 N/mm.</p>
<div class="math notranslate nohighlight">
\[\lambda = \pi^2\frac{[D_{11}m^4 +2(D_{12}+2D_{66})m^2n^2(a/b)^2 + D_{22}n^4(a/b)^4 ]}{a^2 (m^2 + (N_{x}/N_{y}) n^2 (a/b)^2)}\]</div>
Expand Down Expand Up @@ -427,7 +427,7 @@ <h2>Simply Supported study case (SSSS)<a class="headerlink" href="#Simply-Suppor
<div class="section" id="Different-boundary-conditions">
<h2>Different boundary conditions<a class="headerlink" href="#Different-boundary-conditions" title="Permalink to this heading">#</a></h2>
<p>Table below extends the study for different boundary conditions in order to verify polynomial functions presented in section 2.1.3. The results are verified against a NASTRAN FEM model and the maximum difference is 0.7%. Table 6 presents the first buckling mode deformation shape.</p>
<p><img alt="60980b06684640a59b6711015a6a5941" class="no-scaled-link" src="../_images/first_eigenvalue_BC.png" style="height: 150px;" /></p>
<p><img alt="23104f479acc4f51855822024f692237" class="no-scaled-link" src="../_images/first_eigenvalue_BC.png" style="height: 150px;" /></p>
<div class="section" id="Clamped-study-case-(CCCC)">
<h3>Clamped study case (CCCC)<a class="headerlink" href="#Clamped-study-case-(CCCC)" title="Permalink to this heading">#</a></h3>
<div class="nbinput docutils container">
Expand Down Expand Up @@ -499,7 +499,7 @@ <h3>Simply supported with one free edge study case (SSSC)<a class="headerlink" h
</div>
<div class="section" id="Comparison-with-NASTRAN-deformed-shape">
<h3>Comparison with NASTRAN deformed shape<a class="headerlink" href="#Comparison-with-NASTRAN-deformed-shape" title="Permalink to this heading">#</a></h3>
<p><img alt="b7b257ae36f14349b7cc80b72558a43a" class="no-scaled-link" src="../_images/Nastran_deformed.png" style="width: 600px;" /></p>
<p><img alt="7bff613abe5446f5b48d180719b0f2f5" class="no-scaled-link" src="../_images/Nastran_deformed.png" style="width: 600px;" /></p>
</div>
</div>
<div class="section" id="References">
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