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Related Concept Videos

Unsymmetric Bending01:18

Unsymmetric Bending

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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 those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...
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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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Symmetry01:26

Symmetry

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The equation of an ellipse centered at the origin defines all points whose distances from the center maintain a constant ratio between the horizontal and vertical axes. This equation results in a smooth, closed curve that extends further along the x-axis than the y-axis, giving it a horizontal orientation. Such an ellipse demonstrates three kinds of symmetry: across the x-axis, across the y-axis, and about the origin. These symmetries are essential in understanding the graph's structure and...
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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
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States of Water01:23

States of Water

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Water exists in any one of the three classical states: solid (ice), liquid (water), and gas (steam or water vapor). The state of water depends on i) the intermolecular forces that draw molecules together and ii) the kinetic energy that leads to movements that pull them apart.
Water freezes when the intermolecular forces are greater than the kinetic energy. Unlike most other substances, water is less dense in its solid state than in its liquid state. This is because each water molecule can form...
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Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

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A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
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Related Experiment Video

Updated: Mar 17, 2026

Fabrication of Three-Dimensional Graphene-Based Polyhedrons via Origami-Like Self-Folding
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Symmetric waterbomb origami.

Yan Chen1, Huijuan Feng2, Jiayao Ma2

  • 1School of Mechanical Engineering, Tianjin University, 92 Weijin Road, Tianjin 300072, People's Republic of China; Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin 300072, People's Republic of China.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 21, 2016
PubMed
Summary

This study reveals the symmetric waterbomb origami pattern has one degree of freedom, enabling two folding paths. This rigid origami method efficiently folds thick panels for deployable structures.

Keywords:
rigid origamithick-panel origamiwaterbomb basewaterbomb tessellation

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Area of Science:

  • Origami mechanics
  • Robotics and deployable structures

Background:

  • The waterbomb origami pattern is a widely used origami design.
  • Symmetric folding of this pattern typically results in a single degree of freedom.

Purpose of the Study:

  • To conduct a thorough kinematic investigation of the symmetric waterbomb origami pattern.
  • To explore the folding behavior of thick panels using this origami pattern.

Main Methods:

  • Rigid origami kinematic analysis.
  • Mathematical modeling of folding paths and degrees of freedom.

Main Results:

  • Symmetric waterbomb origami exhibits a single degree of freedom.
  • Under specific conditions, two distinct folding paths are possible.
  • Folding thick panels with this pattern also results in single degree of freedom motion.
  • The folding process for thick panels is kinematically equivalent to zero-thickness sheets.

Conclusions:

  • The waterbomb origami pattern offers a versatile method for folding thick materials.
  • Its kinematic properties make it suitable for developing deployable structures like solar panels and roofs.