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Related Concept Videos

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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Elastic Strain Energy for Shearing Stresses01:20

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As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
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Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
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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.
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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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In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
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Elastic Snap-Through Instabilities Are Governed by Geometric Symmetries.

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Elastic structures undergo rapid shape transitions, like a hopper popper toy. This study reveals universal design rules for predicting these energy-releasing bifurcations using geometric symmetries.

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Area of Science:

  • Physics
  • Mechanical Engineering
  • Materials Science

Background:

  • Elastic structures exhibit rapid shape transitions, a phenomenon seen in natural and engineered systems like the Venus flytrap and mechanical metamaterials.
  • These shape transitions, or snap-through events, are crucial for storing and releasing elastic energy but lack a general mechanistic understanding of bifurcation selection.

Purpose of the Study:

  • To analyze and understand the mechanisms governing elastic shape transitions in buckled elastic strips.
  • To identify universal design principles for controlling these transitions based on underlying bifurcations.

Main Methods:

  • Numerical and analytical investigation of two distinct elastic strip systems driven by boundary rotation or translation.
  • Application of reduction order methods to establish the nature of bifurcations.
  • Analysis of geometric symmetries and symmetry-breaking mechanisms.

Main Results:

  • Demonstration of the mathematical equivalence between the two analyzed systems.
  • Identification of three distinct cases encompassing the full spectrum of observed elastic shape transitions.
  • Establishment that bifurcations can be predicted from geometric symmetries and symmetry-breaking principles.

Conclusions:

  • The study provides a unified framework for understanding elastic shape transitions.
  • Identified universal design rules enable prediction and control of these energy release mechanisms.
  • Findings are applicable to diverse fields ranging from biomechanics to advanced material design.