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Related Concept Videos

Design Example: Traverse Angle Computations01:25

Design Example: Traverse Angle Computations

250
Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
250
Angle of Twist: Problem Solving01:13

Angle of Twist: Problem Solving

656
An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque...
656
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

226
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
226
Unsymmetric Bending - Angle of Neutral Axis01:15

Unsymmetric Bending - Angle of Neutral Axis

753
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...
753
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

433
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
433
Adjusting a Traverse01:12

Adjusting a Traverse

298
In the site survey of a four-sided traverse, internal angles are essential to ensure geometric accuracy. The survey revealed that the sum of the measured internal angles was 359 degrees and 48 minutes, which is 12 minutes less than the expected 360 degrees. This discrepancy signals an error likely arising from measurement inaccuracies during the fieldwork.To rectify this error, the adjustment process involved distributing the 12-minute shortfall equally across the four internal angles. By...
298

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Related Experiment Video

Updated: Dec 21, 2025

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

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Mesh smoothing algorithm based on exterior angles split.

Yongqing Hai1, Siyuan Cheng2, Yufei Guo1

  • 1Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing, China.

Plos One
|May 13, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a new mesh smoothing method using an exterior-angle-split process to enhance mesh quality. The technique improves accuracy in finite element analysis and various applications for triangular and polygonal meshes.

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Area of Science:

  • Computational geometry
  • Numerical analysis
  • Computer-aided design

Background:

  • Poor mesh quality significantly impacts the accuracy of finite element analysis (FEA) and other computational applications.
  • Existing mesh smoothing techniques often face limitations in effectiveness and applicability.

Purpose of the Study:

  • To propose a novel mesh smoothing method that enhances mesh quality.
  • To provide a robust and versatile solution applicable to various mesh types.

Main Methods:

  • A three-stage process involving independent element geometric transformation via exterior-angle-split operations.
  • Offsetting scaling and displacement resulting from element transformations.
  • A weighted strategy to determine the final positions of nodes.

Main Results:

  • Theoretical analysis confirms the method's regularity and convergence.
  • Numerical experiments demonstrate effective quality improvements on triangular and quadrilateral meshes.
  • The method is naturally extendable to arbitrary polygonal surface meshes.

Conclusions:

  • The proposed exterior-angle-split mesh smoothing method effectively improves mesh quality.
  • This technique offers enhanced accuracy for finite element analysis and broader applications.
  • Its adaptability to different mesh types makes it a valuable tool in computational fields.