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Related Concept Videos

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

259
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...
259
Plastic Deformations01:14

Plastic Deformations

207
It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
207
Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

310
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...
310
Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

204
The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
204
Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

318
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...
318
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

180
When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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Three-Dimensional Shape Modeling and Analysis of Brain Structures
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Shape Estimation for Elongated Deformable Object using B-spline Chained Multiple Random Matrices Model.

Gang Yao1, Ryan Saltus1, Ashwin P Dani1

  • 1Department of Electrical and Computer Engineering, University of Connecticut, Storrs, Connecticut, USA.

International Journal of Intelligent Robotics and Applications
|August 23, 2021
PubMed
Summary
This summary is machine-generated.

This paper introduces a novel B-spline chained multiple random matrix models (RMMs) approach for accurately estimating the complex shapes of deformable objects. The method effectively models geometric characteristics, even with high degrees of freedom.

Keywords:
Elongated Deformable ObjectRandom MatricesState Estimation

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Area of Science:

  • Robotics and Computer Vision
  • Geometric Modeling
  • Machine Learning

Background:

  • Estimating the shape of elongated deformable objects is challenging due to their complex, high degrees of freedom structure.
  • Existing methods may struggle with intricate configurations, self-intersections, and dynamic manipulations.
  • Accurate geometric modeling is crucial for tasks like manipulation, simulation, and analysis of deformable objects.

Purpose of the Study:

  • To propose a novel B-spline chained multiple random matrix models (RMMs) representation for modeling the geometric characteristics of elongated deformable objects.
  • To develop an expectation-maximization (EM) algorithm for accurate shape estimation based on the proposed RMMs.
  • To evaluate the algorithm's performance in diverse scenarios, including static and dynamic object manipulation and assembly.

Main Methods:

  • A B-spline chained multiple random matrix models (RMMs) representation is introduced to capture the object's geometry.
  • An expectation-maximization (EM) algorithm is derived from the likelihood function of the RMMs for shape estimation.
  • A split and merge method utilizing the Euclidean minimum spanning tree (EMST) is employed for initializing the EM algorithm.

Main Results:

  • The proposed algorithm demonstrates effective shape estimation for static and continuously manipulated ropes and plastic tubes.
  • Performance is validated in scenarios involving object self-intersection and the assembly of multiple objects.
  • Accuracy is assessed by comparing estimated widths to ground truth and using the intersection over union (IoU) metric, with execution time also reported.

Conclusions:

  • The B-spline chained multiple RMMs with an EM algorithm provide a robust framework for estimating the shapes of elongated deformable objects.
  • The method shows promise for handling complex configurations, including intersections and dynamic changes.
  • The approach offers a valuable tool for applications requiring precise geometric understanding of deformable objects.