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Transformation of Plane Stress01:18

Transformation of Plane Stress

211
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...
211
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

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Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
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Symmetric Member in Bending01:07

Symmetric Member in Bending

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In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
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General Case of Eccentric Axial Loading01:12

General Case of Eccentric Axial Loading

173
Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from symmetrical bending, which are essential for designing structures to withstand different loading conditions.
Consider a member subjected to equal and opposite forces that are applied along a line that does not coincide with the member's neutral axis. In unsymmetrical...
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

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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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Components of Stress01:23

Components of Stress

201
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...
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Related Experiment Video

Updated: Jun 6, 2025

Biaxial Mechanical Characterizations of Atrioventricular Heart Valves
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Penalty 4-Node Quadrilateral Element Formulation for Axisymmetric Couple Stress Problems.

Yongkang Jiang1, Yan Shang1

  • 1State Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.

Materials (Basel, Switzerland)
|November 27, 2024
PubMed
Summary

This study introduces a new finite element for analyzing small-scale solids, effectively capturing size effects in deformation. The proposed method enhances computational accuracy for axisymmetric problems.

Keywords:
FEMaxisymmetriccouple stress theorypenalty elementsize effect

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Area of Science:

  • Solid Mechanics
  • Computational Mechanics
  • Materials Science

Background:

  • Size effects are crucial in small-scale solids, influencing deformation behavior.
  • Existing models may not fully capture these size-dependent phenomena.
  • Axisymmetric deformation analysis requires specialized numerical approaches.

Purpose of the Study:

  • To develop a novel finite element for analyzing size effects in axisymmetric deformation.
  • To incorporate consistent couple stress theory (CCST) into a finite element framework.
  • To enhance computational accuracy and convergence for small-scale solid mechanics problems.

Main Methods:

  • A 4-node, 12-degree-of-freedom element based on consistent couple stress theory (CCST).
  • Utilized the unsymmetric finite element method framework.
  • Employed the penalty function method to introduce an assumed rotational field, satisfying C1 continuity.
  • Used enriched C0 isoparametric interpolation for displacement and rotation test functions.
  • Incorporated a force-stress field satisfying equilibrium equations.
  • Applied reduced integration to mitigate locking issues.

Main Results:

  • The new element accurately captures size-dependent phenomena in small-scale solids.
  • Demonstrated high computational accuracy and convergence rates.
  • Successfully applied to both static and modal analysis problems.
  • Validated the effectiveness of the CCST in capturing size effects.

Conclusions:

  • The proposed finite element provides an effective tool for analyzing size effects in axisymmetric deformation.
  • The method enhances the accuracy and reliability of computational solid mechanics for micro/nanoscale applications.
  • This work contributes to a better understanding of mechanical behavior in small-scale materials.