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Related Concept Videos

Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

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The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member...
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Equation of the Elastic Curve01:23

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The concept of curvature in plane curves, crucial in structural engineering, defines how sharply a beam bends under load. This curvature is determined using the curve's first and second derivatives.
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...
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Bending of Curved Members - Neutral Surface01:16

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In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
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Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

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Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
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Deformations in a Symmetric Member in Bending01:18

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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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Singularity Functions for Bending Moment01:18

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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 using a...
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Curvature Constrained Splines for DFTB Repulsive Potential Parametrization.

Akshay Krishna Ammothum Kandy1, Eddie Wadbro2, Bálint Aradi3

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Curvature Constrained Splines (CCS) efficiently parameterize repulsive potentials for SCC-DFTB calculations. New constraints and sparse data handling improve accuracy, but environment-dependent potentials are needed for transferability.

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Area of Science:

  • Computational materials science
  • Quantum chemistry
  • Solid-state physics

Background:

  • Self-consistent charge density functional theory (SCC-DFTB) requires accurate repulsive potentials for describing interatomic interactions.
  • Traditional methods for fitting these potentials can be labor-intensive and may lack robustness.

Purpose of the Study:

  • To enhance the Curvature Constrained Splines (CCS) methodology for fitting repulsive potentials.
  • To investigate the transferability of these potentials across different silicon polymorphs.
  • To explore the use of machine learning potentials for improved transferability.

Main Methods:

  • Developed advanced constraints and sparse data handling for the CCS methodology.
  • Applied CCS to generate repulsive potentials for bulk silicon polymorphs.
  • Trained a near-sighted Atomistic Neural Network potential incorporating many-body effects.

Main Results:

  • CCS provides a robust and efficient method for fitting unique, optimal two-body repulsive potentials.
  • A single CCS-fitted potential could not accurately describe various silicon polymorphs using a standard Slater-Koster table.
  • Adjusting potentials based on coordination number improved transferability.
  • Atomistic Neural Network potentials achieved full transferability for SCC-DFTB energetics across silicon polymorphs.

Conclusions:

  • The CCS method offers significant advantages in parametrization efficiency and robustness.
  • Accurate description of diverse materials requires accounting for environmental effects in repulsive potentials.
  • Near-sighted Atomistic Neural Networks present a promising avenue for achieving highly transferable SCC-DFTB potentials.