2024b - Revision history

https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=2024b 2024b - Revision history 2026-04-06T16:06:12Z Revision history for this page on the wiki MediaWiki 1.27.0-wmf.10 https://www.scipedia.com/wd/index.php?title=2024b&diff=304965&oldid=prev JSanchez: JSanchez moved page Draft Sanchez Pinedo 156474465 to 2024b 2024-06-28T09:08:51Z

<p>JSanchez moved page <a href="/public/Draft_Sanchez_Pinedo_156474465" class="mw-redirect" title="Draft Sanchez Pinedo 156474465">Draft Sanchez Pinedo 156474465</a> to <a href="/public/2024b" title="2024b">2024b</a></p> <table class="diff diff-contentalign-left" data-mw="interface"> <tr style='vertical-align: top;' lang='en'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 09:08, 28 June 2024</td> </tr><tr><td colspan='2' style='text-align: center;' lang='en'><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

JSanchez https://www.scipedia.com/wd/index.php?title=2024b&diff=304964&oldid=prev JSanchez at 09:08, 28 June 2024 2024-06-28T09:08:48Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 09:08, 28 June 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3" >Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities in the large displacement/rotations field. The study employs a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach to develop higher-order onedimensional beam theories that account for geometric nonlinearities. The axis discretization is achieved through a finite element approximation. The equations of motion are solved around nonlinear static equilibrium states, which are determined using a Newton–Raphson algorithm combined with a path-following method of arc-length type. The CUF approach introduces two key innovations that are highly suitable for the evolution of the band gap: 1) Thin-walled structures can be effectively represented using a single one-dimensional beam model, overcoming the common limitations of standard finite elements. This is crucial as three-dimensional solid elements would result in significant computational costs, and twodimensional elements pose limitations for this type of investigation. Finally, employing onedimensional finite elements usually requires a combination of elements, leading to additional mathematical complexities in their connections and lacking geometric precision. 2) CUF enables the use of the full Green-Lagrange strain tensor without the need for assumptions, as is the case with von Karm´ an nonlinearities. ´ The paper specifically compares results obtained with linear and nonlinear stiffness matrices, highlighting the differences. Numerical investigations are conducted on thin-walled structures composed of repeatable cells, assessing mode changes under traction and compression loading. The findings emphasize that the band gap is an inherent property of the equilibrium state, underscoring the necessity of a proper nonlinear analysis for accurately evaluating frequency transitions</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities in the large displacement/rotations field. The study employs a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach to develop higher-order onedimensional beam theories that account for geometric nonlinearities. The axis discretization is achieved through a finite element approximation. The equations of motion are solved around nonlinear static equilibrium states, which are determined using a Newton–Raphson algorithm combined with a path-following method of arc-length type. The CUF approach introduces two key innovations that are highly suitable for the evolution of the band gap: 1) Thin-walled structures can be effectively represented using a single one-dimensional beam model, overcoming the common limitations of standard finite elements. This is crucial as three-dimensional solid elements would result in significant computational costs, and twodimensional elements pose limitations for this type of investigation. Finally, employing onedimensional finite elements usually requires a combination of elements, leading to additional mathematical complexities in their connections and lacking geometric precision. 2) CUF enables the use of the full Green-Lagrange strain tensor without the need for assumptions, as is the case with von Karm´ an nonlinearities. ´ The paper specifically compares results obtained with linear and nonlinear stiffness matrices, highlighting the differences. Numerical investigations are conducted on thin-walled structures composed of repeatable cells, assessing mode changes under traction and compression loading. The findings emphasize that the band gap is an inherent property of the equilibrium state, underscoring the necessity of a proper nonlinear analysis for accurately evaluating frequency transitions</div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Full Paper ==</ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"><pdf>Media:Draft_Sanchez Pinedo_1564744654.pdf</pdf></ins></div></td></tr>  </table>

JSanchez https://www.scipedia.com/wd/index.php?title=2024b&diff=304962&oldid=prev JSanchez at 09:08, 28 June 2024 2024-06-28T09:08:47Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 09:08, 28 June 2024</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">                                </ins></div></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">==Abstract==</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">This paper explores the dynamic behavior of metamaterial-like structures by investigating the evolution of their band gap under the influence of geometrical nonlinearities in the large displacement/rotations field. The study employs a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach to develop higher-order onedimensional beam theories that account for geometric nonlinearities. The axis discretization is achieved through a finite element approximation. The equations of motion are solved around nonlinear static equilibrium states, which are determined using a Newton–Raphson algorithm combined with a path-following method of arc-length type. The CUF approach introduces two key innovations that are highly suitable for the evolution of the band gap: 1) Thin-walled structures can be effectively represented using a single one-dimensional beam model, overcoming the common limitations of standard finite elements. This is crucial as three-dimensional solid elements would result in significant computational costs, and twodimensional elements pose limitations for this type of investigation. Finally, employing onedimensional finite elements usually requires a combination of elements, leading to additional mathematical complexities in their connections and lacking geometric precision. 2) CUF enables the use of the full Green-Lagrange strain tensor without the need for assumptions, as is the case with von Karm´ an nonlinearities. ´ The paper specifically compares results obtained with linear and nonlinear stiffness matrices, highlighting the differences. Numerical investigations are conducted on thin-walled structures composed of repeatable cells, assessing mode changes under traction and compression loading. The findings emphasize that the band gap is an inherent property of the equilibrium state, underscoring the necessity of a proper nonlinear analysis for accurately evaluating frequency transitions</ins></div></td></tr>  </table>

JSanchez https://www.scipedia.com/wd/index.php?title=2024b&diff=304961&oldid=prev JSanchez: Created blank page 2024-06-28T09:08:45Z

<p>Created blank page</p> <p><b>New page</b></p><div></div>

JSanchez