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Related Concept Videos

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.
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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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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Unsymmetric Loading of Thin-Walled Members01:23

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
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Consider the elastic torsion formula, which applies to a circular shaft with a consistent cross-section. This formula assumes that the shaft's ends are loaded with rigid plates firmly attached. However, in many cases, torques are applied to the shaft through mechanisms like flange couplings or gears, which are connected by keys inserted into keyways. This application method modifies the stress distribution near the point of torque application, causing it to deviate from the distributions...
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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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Wrinkling and developable cones in centrally confined sheets.

Lucia Stein-Montalvo1, Arman Guerra1, Kanani Almeida1

  • 1Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA.

Physical Review. E
|October 18, 2023
PubMed
Summary
This summary is machine-generated.

Confining thin sheets causes them to wrinkle or form sharp stress-focusing cones. This study reveals how sheet geometry dictates the transition from wrinkles to cones and their subsequent patterning under confinement.

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Area of Science:

  • Physics
  • Materials Science
  • Mechanical Engineering

Background:

  • Thin sheets exhibit diverse responses to confinement, including wrinkling and stress focusing.
  • Understanding stress focusing and pattern formation in confined thin sheets is crucial across multiple disciplines.

Purpose of the Study:

  • To investigate the confinement response of circular thin sheets drawn through a ring.
  • To characterize the transition from wrinkling to stress focusing via cone formation.
  • To determine the geometric dependencies of force, wrinkle number, and cone formation.

Main Methods:

  • Experimental analysis of quasistatically drawn circular sheets.
  • Molecular dynamics simulations to probe sheet behavior under confinement.
  • Geometric analysis of cone formation and its relation to sheet properties.

Main Results:

  • Wrinkles in the free region are replaced by a truncated cone, indicating stress focusing.
  • Cone formation and patterning depend significantly on the sheet's in-plane geometry.
  • A coarse-grained description of geometric dependence is established, relating to the d-cone limit.

Conclusions:

  • The study elucidates the fundamental mechanisms of stress focusing in confined thin sheets.
  • It provides insights into the formation and scaling of d-cones in realistic scenarios.
  • This research contributes to the general understanding of thin sheet behavior under confinement.