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Thin-Walled Hollow Shafts01:15

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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...
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Design of Transmission Shafts - Stress Analysis01:15

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Designing a transmission shaft requires a thorough understanding of the stresses induced by bending moments and torques, especially in systems where power is transferred through gears. These forces create force-couple systems at the centers of the shaft's cross-sections, leading to both transverse and torsional loading. Although shearing stresses from transverse loads are typically smaller than those from torques and are often overlooked, the significant normal stresses from these loads...
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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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Temperature Dependent Deformation01:12

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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Transformation of Plane Stress01:18

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Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
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Updated: Aug 30, 2025

Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
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Steady-State Thermal Analysis of Functionally Graded Rotating Disks Using Finite Element and Analytical Methods.

M M Shahzamanian1,2, A Shahrjerdi3, B B Sahari4

  • 1Department of Mechanical Engineering, McMaster University, Hamilton, ON L8S 4L7, Canada.

Materials (Basel, Switzerland)
|August 26, 2022
PubMed
Summary
This summary is machine-generated.

This study analyzed a rotating functionally graded (FG) disk, comparing an in-house finite element (FE) program with analytical solutions. Results show material gradation significantly impacts thermal stress and strain in FG disks.

Keywords:
finite element method (FEM)functionally graded materials (FGMs)steady-state thermal analysis

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Computational Engineering

Background:

  • Functionally graded materials (FGMs) offer tailored properties by varying composition.
  • Rotating disks are critical components in many engineering applications, experiencing thermal and mechanical stresses.
  • Understanding thermal behavior in FGMs is crucial for designing reliable components.

Purpose of the Study:

  • To perform a steady-state thermal analysis of a hollow, axisymmetric functionally graded rotating disk.
  • To compare temperature distribution results from an in-house finite element (FE) program, ANSYS Parametric Design Language (APDL), and an analytical solution.
  • To investigate the influence of material gradation on thermal stress and strain.

Main Methods:

  • Developed an in-house finite element (FE) program utilizing the weighted residual method for temperature distribution analysis.
  • Simulated a functionally graded (FG) disk with metal and ceramic materials using a power law distribution for material properties.
  • Validated the in-house FE program against APDL and analytical solutions for temperature distribution.

Main Results:

  • The in-house FE program accurately predicted temperature distribution, matching APDL and analytical solutions.
  • Material gradation significantly affects the temperature, thermal strain, and stress within the FG disk.
  • The in-house FE program offers more efficient post-processing and optimization capabilities compared to commercial software.

Conclusions:

  • The developed in-house FE program is a validated and efficient tool for analyzing FG materials.
  • Material gradation is a key parameter influencing the thermomechanical behavior of rotating FG disks.
  • The in-house code facilitates optimization for minimizing thermal stress and strain while maintaining stiffness.