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Related Concept Videos

Principal Stresses01:24

Principal Stresses

The graphical depiction of normal and shearing stress equations is represented by a circle, demonstrating the interplay between these stresses under different angular conditions. The center of this circle C, located on the vertical axis, represents the average normal stress, while its radius shows the range of stress variations. At points A and B, where the circle intersects the horizontal axis, the maximum and minimum normal stresses are observed, occurring without shearing stress. These...
General State of Stress01:21

General State of Stress

The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
Stress: General Loading Conditions01:15

Stress: General Loading Conditions

To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes.
Stress Concentrations01:24

Stress Concentrations

Stress concentration is when stress intensifies near discontinuities such as holes or abrupt cross-sectional changes in a structural member. This localized stress can often surpass the average stress within the member. The stress distribution in flat bars, either with a circular hole or varying widths connected by fillets, can be determined experimentally using a photoelastic method. The results are based on ratios of geometric parameters like the ratio of the hole's radius to the smaller width...
Stress Concentrations01:13

Stress Concentrations

The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress concentration...
Stress-Strain Diagram01:10

Stress-Strain Diagram

A stress-strain diagram is a crucial tool that graphically displays a material's mechanical characteristics. This diagram is derived from a tensile test performed on a carefully prepared cylindrical specimen. The specimen has two gauge marks inscribed on its central part, and the distance between these marks is known as the gauge length. The cylindrical specimen is placed in a testing machine, which applies an increasing centric load. As this load grows, so does the gauge length. This change in...

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Related Experiment Videos

A maxent-stress model for graph layout.

Emden R Gansner1, Yifan Hu, Stephen North

  • 1AT&T Labs Research, Florham Park, NJ 07932, USA.

IEEE Transactions on Visualization and Computer Graphics
|April 6, 2013
PubMed
Summary
This summary is machine-generated.

The maxent-stress model offers a scalable solution for graph visualization challenges with target edge lengths. This approach improves layout quality for large, high-dimensional graphs, addressing limitations of traditional stress models.

Related Experiment Videos

Area of Science:

  • Computer Science
  • Data Visualization
  • Graph Theory

Background:

  • Graph visualization often requires managing target edge lengths, posing scalability challenges for large graphs.
  • Traditional stress models, while effective, are computationally intensive due to all-pairs shortest path calculations, limiting their use on large datasets.
  • Existing approximation algorithms struggle with high-dimensional graphs, leading to suboptimal node placement and overlapping positions.

Purpose of the Study:

  • To introduce a novel, scalable approach for graph visualization that effectively handles target edge lengths.
  • To address the limitations of traditional stress models in terms of scalability and performance on high-dimensional graphs.
  • To develop an efficient algorithm for generating high-quality graph layouts for large and complex networks.

Main Methods:

  • Proposed the maxent-stress model, integrating the principle of maximum entropy to manage additional degrees of freedom in graph layouts.
  • Developed a force-augmented stress majorization algorithm to solve the maxent-stress model efficiently.
  • Evaluated the algorithm's performance on large, nonrigid graphs with intrinsic high dimensionality.

Main Results:

  • The maxent-stress model and its associated algorithm demonstrate excellent scalability for large graph visualization.
  • The proposed method produces acceptable and accurate layouts, even for graphs with complex structures and high dimensions.
  • The algorithm effectively prevents nodes from being placed too close together or overlapping, improving layout clarity.

Conclusions:

  • The maxent-stress model provides a scalable and effective solution for graph visualization problems with target edge lengths.
  • The developed force-augmented stress majorization algorithm offers a computationally efficient method for generating high-quality layouts.
  • This approach has potential applications in scalable statistical multidimensional scaling (MDS) with variable distances.