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Deflection of a Beam01:19

Deflection of a Beam

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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
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Bending of Curved Members - Strain Analysis01:14

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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
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Singularity Functions for Shear01:26

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Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
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Active topological defect absorption by a curvature singularity.

Farzan Vafa1, David R Nelson2, Amin Doostmohammadi3

  • 1Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|July 5, 2023
PubMed
Summary
This summary is machine-generated.

We describe topological defect dynamics in active nematic materials on curved surfaces. Activity influences defect motility, with behavior changing based on cone geometry and deficit angle.

Keywords:
active nematiccurvature singularityp-atic

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Area of Science:

  • Soft Matter Physics
  • Materials Science
  • Geometry

Background:

  • Topological defects are crucial in materials science.
  • Understanding their dynamics on curved surfaces is complex.
  • Active materials exhibit unique behaviors driven by internal energy sources.

Purpose of the Study:

  • To provide a general description of topological defect dynamics in active nematic materials on curved surfaces.
  • To investigate the influence of activity on defect motility.
  • To analyze defect behavior on geometries with curvature singularities, like cones.

Main Methods:

  • Leveraging the Born-Oppenheimer approximation for theoretical analysis.
  • Developing an analytical framework for defect dynamics.
  • Employing numerical simulations for quantitative validation.

Main Results:

  • Activity introduces a geometric contribution to the motility of +1/2 defects.
  • Defect motility on a cone depends on the deficit angle, with a sign change occurring at π.
  • Identified the basin of attraction for defects to the cone apex and predicted trajectories.

Conclusions:

  • The study provides a comprehensive analytical framework for active nematic defect dynamics on curved surfaces.
  • Results highlight the interplay between material activity, geometry, and defect behavior.
  • Analytical predictions are validated by numerical simulations, confirming the model's accuracy.