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相关概念视频

Mohr's Circle for Moments of Inertia: Problem Solving01:14

Mohr's Circle for Moments of Inertia: Problem Solving

1.9K
Mohr's circle is a graphical method for determining an area's principal moments by plotting the moments and product of inertia on a rectangular coordinate system. This circle can also be used to calculate the orientation of the principal axes.
Consider a rectangular beam. The moments of inertia of the beam about the x and y axis are 2.5(107) mm4 and 7.5(107) mm4, respectively. The product of inertia is 1.5(107) mm4. Determine the principal moments of inertia and the orientation of the major and...
1.9K
Mohr's Circle for Moments of Inertia01:10

Mohr's Circle for Moments of Inertia

525
Mohr's circle is a graphical method to determine an area's principal moments of inertia by plotting the moments and product of inertia on a rectangular coordinate system.
525
Mohr's Circle for Plane Stress01:23

Mohr's Circle for Plane Stress

216
Mohr's circle is a graphical method for identifying the state of stress at a point in a material, making it easier to analyze stress transformations under plane stress conditions. This two-dimensional technique visualizes both normal and shearing stresses on an element.
Consider a set of Cartesian coordinates. The horizontal and vertical axes correspond to normal stress (σ) and shearing stress (τ), respectively. Two points, points A and B, are defined by the normal and shear...
216
Mohr's Circle for Plane Strain01:18

Mohr's Circle for Plane Strain

458
Mohr's circle is a crucial graphical method used to analyze plane strain by plotting strain on a set of cartesian coordinates, where the abscissa is normal strain ∈ and the ordinate is shear strain γ. Similarly to Mohr’s circle for plane stress, two points X and Y are plotted. Their coordinates are (∈x, -γXY) and (∈Y, γXY), respectively.
Mohr's circle visually represents the strain states under various conditions, which is essential for...
458
Radius of Gyration of an Area01:12

Radius of Gyration of an Area

1.4K
The second moment of area, also known as the moment of inertia of area, is a crucial factor in understanding an object's resistance against bending deformation, or stiffness. To accurately estimate the second moment of area along any axis, one needs to concentrate all areas associated with that object into a thin strip, which should be placed parallel to that particular axis.
1.4K
Centroid of a Body: Problem Solving01:03

Centroid of a Body: Problem Solving

1.1K
The centroid of a body is a crucial concept in engineering and physics. Finding the centroid of a body can help determine its stability, its balance point, and even its design. In this context, consider a thin wire bent in the form of a quarter circular arc. Polar coordinates are used to calculate the centroid. The wire is first divided into small differential elements of a length equal to the radius multiplied by the differential angle.
The x-coordinates and y-coordinates of each element's...
1.1K

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Traditional Trail Making Test Modified into Brand-new Assessment Tools: Digital and Walking Trail Making Test
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评估最小区域圆圈的两点方法.

Xiuming Li1,2, Xuedi Hao1, Guangjie Wang1

  • 1School of Mechanical and Electronic Engineering, China University of Mining & Technology (Beijing), Beijing 100083, China.

The Review of scientific instruments
|December 3, 2024
PubMed
概括
此摘要是机器生成的。

这项研究提出了一种新的两点方法,用于确定有限和刻字圆上的控制点. 该算法通过使用二分法来处理冗余数据点来提高计算效率.

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科学领域:

  • 计算几何学的计算几何学
  • 几何算法的几何算法

背景情况:

  • 确定圆的控制点在各种几何应用中至关重要.
  • 现有的方法可能缺乏效率或适用于注册和有限的圈子.

研究的目的:

  • 提出一种新的两点方法,用于识别有限和刻字圆上的控制点.
  • 为了提高计算几何算法的效率.

主要方法:

  • 开发四点条件,基于最小区域圆圈控制点的交叉分布.
  • 实施两点方法,适用于有界和刻字的圆圈.
  • 利用二分法,在代过程中高效处理冗余数据点.

主要成果:

  • 一个经过验证的两点算法,用于确定圆的控制点.
  • 与现有方法相比,计算效率有明显的改善.
  • 对各种示例的成功应用,证实了算法的有效性.

结论:

  • 拟议的两点方法为确定圆圈控制点提供了一种高效和多功能解决方案.
  • 算法的有效性通过实践示例得到证实.
  • 这一进步有助于更高效的几何计算.