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Related Concept Videos

Virtual Work for a System of Connected Rigid Bodies01:06

Virtual Work for a System of Connected Rigid Bodies

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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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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Temperature Dependent Deformation01:12

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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...

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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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A Moving Grid Framework for Geometric Deformable Models.

Xiao Han1, Chenyang Xu, Jerry L Prince

  • 1CMS Software, Elekta Inc., St. Louis, MO 63043.

International Journal of Computer Vision
|December 1, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a simpler moving grid method for geometric deformable models, improving accuracy and efficiency. The new approach avoids complex data structures and reduces contour points in results.

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Area of Science:

  • Computer Vision
  • Image Analysis
  • Computational Geometry

Background:

  • Geometric deformable models using level sets are popular for image analysis.
  • Adaptive grid techniques like local grid refinement improve accuracy and efficiency.
  • Existing methods face challenges with complex data structures and topology preservation.

Purpose of the Study:

  • To investigate the moving grid method as an alternative adaptive technique for geometric deformable models.
  • To develop a consistent framework for moving grid geometric deformable models.
  • To introduce novel components for enhanced performance and implementation.

Main Methods:

  • Developed a consistent moving grid geometric deformable model framework.
  • Introduced a new grid nondegeneracy constraint.
  • Designed a new grid adaptation criterion and novel numerical methods.
  • Implemented an efficient scheme for the moving grid method.

Main Results:

  • The moving grid method is simpler to implement than grid refinement.
  • It avoids large, complex, hierarchical data structures.
  • The method automatically reduces the number of contour vertices in final results.
  • Demonstrated performance on simulated and real images.

Conclusions:

  • The moving grid method offers a simpler and more efficient alternative for geometric deformable models.
  • This approach enhances computational efficiency and simplifies implementation.
  • The method effectively handles contour point reduction and demonstrates robust performance.