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Deformations in a Symmetric Member in Bending

Deformations in a Symmetric Member in Bending

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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When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
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The degree of curvature and the radius of curvature are fundamental concepts in determining the sharpness or smoothness of a curve. The degree of curvature is a measure of how steeply a curve bends and can be determined using the chord basis or the arc basis. In the chord basis method, the degree of curvature is defined as the central angle subtended by a chord of 30.48 meters, helping in the calculation of the radius of the curve. The arc basis method defines the degree of curvature as the...

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Related Experiment Video

Updated: Jun 13, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Large Deformation Diffeomorphic Metric Curve Mapping.

Joan Glaunès¹, Anqi Qiu, Michael I Miller

¹MAP5, CNRS UMR 8145, Université Paris Descartes, 75006 Paris, France.

International Journal of Computer Vision

|April 27, 2010

Summary

We developed a new method to match curves using large deformation diffeomorphic metric mapping (LDDMM). This approach quantifies curve similarity and enables optimal transformations for applications like shape classification.

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Published on: November 14, 2019

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Last Updated: Jun 13, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

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Published on: April 16, 2017

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Three-Dimensional Shape Modeling and Analysis of Brain Structures

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

Area of Science:

Computational geometry
Medical image analysis
Differential geometry

Background:

Curve matching is crucial for shape analysis and comparison.
Existing methods may struggle with large deformations and complex geometric structures.

Purpose of the Study:

To introduce a novel matching criterion for curves within the large deformation diffeomorphic metric mapping (LDDMM) framework.
To enable accurate computation of optimal transformations between curves in Euclidean space.

Main Methods:

Representing curves as vector-valued measures incorporating location and first-order geometric structure.
Imposing a Hilbert space structure on measures to define a curve closeness norm.
Developing a discretized version using vector-valued functionals for practical implementation.

Main Results:

Successfully derived and implemented a curve matching scheme within the LDDMM framework.
Demonstrated effective mapping of curves in 2D and 3D Euclidean spaces.
Showcased applications in shape classification and experiments with 3D brain cortical surface curves.

Conclusions:

The proposed matching criterion and LDDMM integration provide a robust method for curve transformation.
This approach offers practical utility for shape analysis, classification, and medical imaging applications.