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Eccentric Axial Loading in a Plane of Symmetry01:16

Eccentric Axial Loading in a Plane of Symmetry

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Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

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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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Transformation of Plane Stress01:18

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Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
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Transformation of Plane Strain01:12

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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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Three-Dimensional Analysis of Strain01:29

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Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
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A novel method for 3D face symmetry reference plane based on weighted Procrustes analysis algorithm.

Yujia Zhu1,2,3,4,5, Shengwen Zheng6,7, Guosheng Yang6,7

  • 1Center of Digital Dentistry, Peking University School and Hospital of Stomatology, No.22 Zhongguancun Avenue South, Haidian District, Beijing, 100081, China.

BMC Oral Health
|November 12, 2020
PubMed
Summary
This summary is machine-generated.

A new weighted Procrustes analysis (WPA) algorithm creates a more accurate 3D facial symmetry reference plane (SRP) for patients with mandibular deviation, improving diagnostic simulation.

Keywords:
Anatomic landmarksMandibular deviationProcrustes analysisSymmetry reference planeThree-dimensional facial data

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Area of Science:

  • Medical imaging and analysis
  • Biomechanical engineering
  • Craniofacial surgery

Background:

  • Mandibular deviation presents challenges in achieving accurate 3D facial symmetry assessments.
  • Current methods for constructing facial symmetry reference planes (SRPs) may lack adaptability for severe cases.

Purpose of the Study:

  • To develop and validate a novel weighted Procrustes analysis (WPA) algorithm for constructing a 3D facial symmetry reference plane (SRP).
  • To compare the accuracy of the WPA-derived SRP against the standard Procrustes analysis (PA) algorithm in patients with mandibular deviation.

Main Methods:

  • Three-dimensional facial SRPs were generated using both WPA and standard PA algorithms on 15 patients with mandibular deviation.
  • Accuracy was evaluated by measuring position error of mirrored landmarks, facial asymmetry index (FAI) error, and angle error against a ground truth reference plane.

Main Results:

  • The WPA algorithm demonstrated a smaller average angle error (1.66° ± 0.81°) compared to the standard PA algorithm.
  • WPA resulted in lower position errors for mirrored landmarks in both global face and facial partitions.
  • The WPA algorithm showed a smaller facial asymmetry index (FAI) error (-7.77 ± 17.02 mm) than the PA algorithm.

Conclusions:

  • The novel WPA algorithm provides a more adaptable and accurate 3D facial symmetry reference plane (SRP) for severe mandibular deviation patients.
  • This WPA-based method more effectively simulates the diagnostic strategies employed by clinical experts.