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Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

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When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
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When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
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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.
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One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...
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Virtual work is a powerful method used to solve problems involving several connected rigid bodies. When the system is in equilibrium, virtual work is zero. This allows the calculation of the resulting forces when a system undergoes a virtual displacement. When attempting to analyze such a system, first, use a free-body diagram, where an independent coordinate represents the configuration of the links, and mark its deflected position resulting from the positive virtual displacement.
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Design of Hierarchical Structures for Synchronized Deformations.

Hamed Seifi1, Anooshe Rezaee Javan1, Arash Ghaedizadeh1

  • 1Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, Victoria 3001, Australia.

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Researchers developed a new method for creating hierarchical structures with synchronized motions. This design offers controlled deformations and collision avoidance, verified through simulations and experiments.

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Area of Science:

  • Mechanical Engineering
  • Computational Geometry
  • Materials Science

Background:

  • Existing hierarchical structures often lack synchronized motion and have complex designs.
  • Controlling deformation and preventing unit collision in hierarchical systems remains a challenge.

Purpose of the Study:

  • To introduce a general method for creating novel hierarchical structures in 2D and 3D.
  • To achieve synchronized motions and uniform deformations in these structures.
  • To develop a method for collision avoidance during structural closure.

Main Methods:

  • A rotate-and-mirror procedure for generating multi-level hierarchies.
  • Mathematical analysis to derive an analytical collision avoidance formula.
  • Computational simulations and physical experiments for verification.

Main Results:

  • The proposed method creates hierarchical structures with significantly fewer degrees of freedom.
  • Structures exhibit synchronized opening/closure, enabling uniform and controllable deformations.
  • An analytical formula effectively prevents unit collision during closure.

Conclusions:

  • The novel design concept offers a simplified and controllable approach to hierarchical structures.
  • The method is validated across mathematical, computational, and experimental domains.
  • This work provides a foundation for advanced deployable and reconfigurable structures.