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Related Concept Videos

Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...
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Volumes of Solids of Revolution01:29

Volumes of Solids of Revolution

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Volumes of irregularly shaped objects can be systematically determined using the concept of solids of revolution. This approach begins with a region defined by a curve in a two-dimensional plane. When this region is rotated about a fixed line, known as the axis of revolution, it generates a three-dimensional object with rotational symmetry. Such objects frequently arise in mathematical modeling, physics, and engineering applications.When the region being rotated lies directly against the axis...
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Stress Concentrations in Circular Shafts01:18

Stress Concentrations in Circular Shafts

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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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Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

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One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
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Circular Shafts - Elastoplastic Materials01:24

Circular Shafts - Elastoplastic Materials

637
The study of solid circular shafts under stress shows that within the elastic limit, stress increases directly to the distance from the shaft's center. This relationship holds until the shaft reaches a critical point of stress, beyond which it begins to yield, marking the transition from elastic to plastic deformation. At this crucial juncture, the maximum torque the shaft can endure without permanent deformation is determined, signifying the limit of its elastic behavior.
As torque on the...
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Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

789
Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
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Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
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A semi-analytical solution for elastic analysis of rotating thick cylindrical shells with variable thickness using

Mohammad Zamani Nejad1, Mehdi Jabbari1, Mehdi Ghannad2

  • 1Mechanical Engineering Department, Yasouj University, P.O. Box 75914-353, Yasouj, Iran.

Thescientificworldjournal
|April 11, 2014
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Summary

A new semi-analytical solution determines displacements and stresses in rotating, variable-thickness cylindrical shells. This method, using disk multilayers and first-order shear deformation theory, offers accurate results for engineering applications.

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Area of Science:

  • Solid Mechanics
  • Mechanical Engineering
  • Materials Science

Background:

  • Thick cylindrical shells with variable thickness are crucial in various engineering applications.
  • Analyzing stresses and displacements in these structures is complex due to varying geometry and shear effects.
  • Existing analytical methods may not fully capture the behavior of variable-thickness shells.

Purpose of the Study:

  • To develop a semi-analytical solution for displacements and stresses in rotating, variable-thickness cylindrical shells under uniform pressure.
  • To apply first-order shear deformation theory (FSDT) to account for shear stress effects.
  • To validate the proposed solution against numerical methods like the finite element method (FEM).

Main Methods:

  • Discretization of the thick cylinder into disk-form multilayers.
  • Derivation of governing differential equations for each layer based on FSDT.
  • Solving the set of differential equations using boundary and continuity conditions.
  • Comparison with a finite element method (FEM) numerical solution.

Main Results:

  • A semi-analytical solution was successfully derived for displacements and stresses.
  • The method effectively handles variable thickness and rotational effects.
  • The results showed good agreement with the finite element method (FEM) validation.

Conclusions:

  • The proposed semi-analytical approach provides an accurate and efficient method for analyzing rotating cylindrical shells with variable thickness.
  • FSDT is essential for capturing the behavior of thick shells where shear deformation is significant.
  • This solution can be valuable for the design and analysis of mechanical components involving such structures.