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Related Concept Videos

Stress: General Loading Conditions01:15

Stress: General Loading Conditions

307
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
307
Components of Stress01:23

Components of Stress

211
Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and...
211
General State of Stress01:21

General State of Stress

183
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
183
Stresses under Combined Loadings01:23

Stresses under Combined Loadings

153
When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...
153
Transformation of Plane Stress01:18

Transformation of Plane Stress

222
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...
222
Stress Concentrations01:13

Stress Concentrations

229
The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress...
229

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Related Experiment Video

Updated: Jun 28, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180&#176; Curved Artery Test Section
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Multi-domain wavelet boundary element method for calculating two-dimensional stress intensity factors.

Jiaxing Chen1, Dongjie Yuan1, Ronggang Yang1

  • 1College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325035, PR China.

Heliyon
|April 22, 2024
PubMed
Summary

A new multi-domain wavelet boundary element method (WBEM) enhances stress intensity factor (SIF) calculations. This approach reduces numerical oscillations near crack tips for improved accuracy in fracture mechanics.

Keywords:
B-spline wavelet on the intervalStress intensity factorsTwo-dimensional crack problemsWavelet boundary element method

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Area of Science:

  • Fracture Mechanics
  • Computational Mechanics
  • Numerical Analysis

Background:

  • Traditional boundary element methods (BEM) face challenges in accurately calculating stress intensity factors (SIFs), particularly near crack tips.
  • Numerical oscillations near crack tips can compromise the accuracy of SIF calculations in conventional BEM.
  • Handling interface cracks and complex geometries requires advanced numerical techniques.

Purpose of the Study:

  • To propose an improved numerical method for accurate SIF calculation.
  • To address the limitations of traditional BEM in crack analysis.
  • To develop a robust method for evaluating SIFs in homogeneous and bi-material media.

Main Methods:

  • Development of crack-tip elements using B-spline wavelet on the interval (BSWI) for reduced numerical oscillations.
  • Integration of crack-tip elements into the multi-domain wavelet boundary element method (WBEM).
  • Application of multi-domain technology within WBEM to effectively handle interface cracks.

Main Results:

  • The proposed BSWI-based crack-tip elements effectively minimize numerical oscillations near crack tips.
  • The multi-domain WBEM successfully handles interface cracks.
  • The method directly and accurately evaluates SIFs for various crack problems.

Conclusions:

  • The multi-domain wavelet boundary element method (WBEM) offers a simple and highly accurate approach for SIF calculation.
  • The integration of BSWI crack-tip elements significantly enhances the precision of fracture analysis.
  • The proposed method is validated through numerical examples involving homogeneous and bi-material models.