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Related Concept Videos

Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

648
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...
648
Deformation in a Circular Shaft01:10

Deformation in a Circular Shaft

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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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Bending of Curved Members - Strain Analysis01:14

Bending of Curved Members - Strain Analysis

645
The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member...
645
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

618
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.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
618
Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

565
When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...
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Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

731
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.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
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Related Experiment Video

Updated: Apr 4, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Shape Deformation via Interior RBF.

Zohar Levi, David Levin

    IEEE Transactions on Visualization and Computer Graphics
    |September 11, 2015
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a new framework for real-time 3D shape deformation. It enables localized control and shape preservation using interior radial basis functions (IRBF), improving upon existing methods.

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    Area of Science:

    • Computer Graphics
    • Geometric Modeling
    • Computational Geometry

    Background:

    • 3D object manipulation often lacks localized control and shape preservation.
    • Existing cage-based deformation methods have limitations in flexibility and automation.
    • Controlling complex deformations while maintaining object integrity is a significant challenge.

    Purpose of the Study:

    • To develop a novel framework for real-time 3D shape deformation.
    • To achieve local shape preservation and volume control during manipulation.
    • To improve upon state-of-the-art deformation techniques.

    Main Methods:

    • Utilizing interior radial basis functions (IRBF) for deformation.
    • Minimizing local distortions by controlling the deformation of internal spheres.
    • Replacing traditional cages with flexible IRBF centers for enhanced control.

    Main Results:

    • The framework allows for convenient shape manipulation with localized influence.
    • It successfully preserves local shape and controls volume during deformation.
    • The IRBF-based approach offers greater flexibility and automated construction compared to cage-based methods.

    Conclusions:

    • The proposed IRBF framework provides an effective solution for real-time 3D shape deformation.
    • It enhances control, local shape preservation, and automation in 3D modeling.
    • The method offers a more flexible and simpler alternative to existing techniques.