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Related Concept Videos

Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Bending and Torsional Moments01:20

Bending and Torsional Moments

Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions.
The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...
Residual Stresses in Bending01:18

Residual Stresses in Bending

In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
Flexural Stress01:16

Flexural Stress

When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to its distance...
Bending Moment Diagram01:30

Bending Moment Diagram

A bending moment diagram is a graphical representation of the bending moments experienced by a beam under load along the beam length. It is an essential tool for engineers and designers to analyze structures and ensure they can withstand applied forces. The steps to create the bending moment diagram for a beam are listed below.
Determine reactive forces and couple moments: Calculate all the reactive forces and couple moments acting on the beam. In certain cases, when the beam is inclined at an...
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

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 centroidal axes. The...

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Related Experiment Video

Updated: Jun 10, 2026

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
12:33

Origami Inspired Self-assembly of Patterned and Reconfigurable Particles

Published on: February 4, 2013

Note: Supplements and corrections to the generalized conic flexure hinge model.

Guimin Chen1, Yunlei Du, Xiaoyuan Liu

  • 1School of Mechatronics, Xidian University, Xi'an, Shaanxi 710071, China.

The Review of Scientific Instruments
|August 7, 2010
PubMed
Summary
This summary is machine-generated.

Supplementary equations for the generalized model of conic flexure hinges resolve programming division-by-zero errors. These revised equations offer a more concise and effective solution for computational applications.

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Area of Science:

  • Mechanical Engineering
  • Computational Physics
  • Applied Mathematics

Background:

  • The generalized model for conic flexure hinges, as presented by G. Chen et al., is crucial for precision engineering.
  • Existing formulations can lead to division-by-zero errors in computational implementations, hindering practical application.
  • Accurate modeling of flexure hinges is essential for designing compliant mechanisms and micro-devices.

Purpose of the Study:

  • To provide supplementary equations for the generalized model of conic flexure hinges.
  • To address and eliminate division-by-zero issues encountered in programming languages like MATLAB, C, and FORTRAN.
  • To enhance the conciseness and effectiveness of the existing hinge model for practical use.

Main Methods:

  • Derivation of supplementary mathematical formulations for conic flexure hinges.
  • Analysis of potential division-by-zero scenarios in the original model.
  • Correction of identified typographical errors within the model's equations.
  • Comparative assessment of the new equations against the original model.

Main Results:

  • A set of supplementary equations has been successfully developed.
  • The new equations effectively circumvent division-by-zero problems, ensuring robust computation.
  • Identified typos in the original publication have been corrected.
  • The revised equations demonstrate improved conciseness and computational effectiveness.

Conclusions:

  • The supplementary equations provide a more numerically stable and practical implementation of the generalized conic flexure hinge model.
  • These enhancements facilitate reliable use of the model in various programming environments for engineering design.
  • The corrected and refined model contributes to more accurate simulations and analyses in mechanical systems.