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Related Concept Videos

Shearing Stress01:19

Shearing Stress

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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
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Shearing Strain01:20

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The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
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In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
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Singularity Functions for Shear01:26

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In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
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When a beam is subjected to different loads, such as weight, pressure, or other external forces, internal forces are generated within the beam. These forces can have a significant impact on the overall stability and strength of the structure. Engineers use various methods to analyze and determine the magnitude and direction of these internal forces. One common technique used to determine internal forces in beams is the method of sections. This method involves considering an imaginary point or...
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Related Experiment Video

Updated: Jan 26, 2026

A Rapid Method for Modeling a Variable Cycle Engine
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Möllenstedt biprism based shearing ptychographic iterative engine method.

Zhilong Jiang1, Yuanjie Li1, Yan Kong1

  • 1Computational Optics Laboratory, Department of Optoelectric Information Science and Technology, School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China.

Ultramicroscopy
|April 13, 2019
PubMed
Summary
This summary is machine-generated.

A novel Möllenstedt biprism based shearing ptychographic iterative engine (PIE) simplifies imaging systems by using voltage-controlled wave deflection for sample scanning. This method accurately retrieves sample amplitude and phase distributions without mechanical scanning, proving effective for quantitative short-wavelength imaging.

Keywords:
Electron beam imagingMöllenstedt biprismShearing ptychographic iterative engine

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Area of Science:

  • * Optics and Photonics
  • * Materials Science
  • * Quantitative Phase Imaging

Background:

  • * Classical lensless ptychographic iterative engine (PIE) offers high-resolution imaging but requires complex mechanical scanning.
  • * Traditional PIE systems are cumbersome, especially for short-wavelength applications like X-ray and electron microscopy.
  • * Simplifying imaging systems is crucial for broader adoption and application in advanced microscopy.

Purpose of the Study:

  • * To develop a simplified PIE method that eliminates the need for mechanical sample scanning.
  • * To introduce a Möllenstedt biprism based shearing PIE technique for efficient amplitude and phase retrieval.
  • * To validate the method's accuracy and speed using numerical simulations and visible light experiments.

Main Methods:

  • * Utilized a Möllenstedt biprism to generate two deflected waves with relative motion.
  • * Employed voltage control on the biprism to achieve sample scanning without mechanical movement.
  • * Applied PIE algorithms to reconstruct sample amplitude and phase from shearing diffraction patterns.

Main Results:

  • * Successfully retrieved accurate sample amplitude and phase distributions.
  • * Demonstrated high accuracy and fast convergence speed comparable to traditional PIE.
  • * Showcased the method's robustness, performing well even without precise biprism calibration.

Conclusions:

  • * Möllenstedt biprism based shearing PIE offers a simplified and effective alternative to traditional PIE.
  • * The technique is suitable for quantitative imaging in short-wavelength microscopy.
  • * This advancement facilitates more accessible and efficient high-resolution imaging applications.