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相关概念视频

Singularity Functions for Shear01:26

Singularity Functions for Shear

129
In structural analysis, singularity functions are crucial in simplifying the representation of shear forces in beams under discontinuous loading. These functions describe discontinuous  variations in shear force across a beam with varying loads by using a single mathematical expression, regardless of the complexity of the loading conditions. The singularity functions are derived from creating a free-body diagram of the beam and then making conceptual cuts at specific points to examine the...
129
Deflection of a Beam01:19

Deflection of a Beam

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Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
256
Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

215
Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented...
215
Divergence and Curl of Electric Field01:25

Divergence and Curl of Electric Field

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The divergence of a vector is a measure of how much the vector spreads out (diverges) from a point. For example, an electric field vector diverges from the positive charge and converges at the negative charge. The divergence of an electric field is derived using Gauss's law and is equal to the charge density divided by the permittivity of space. Mathematically, it is expressed as
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Divergence and Stokes' Theorems01:06

Divergence and Stokes' Theorems

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The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write...
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Divergence and Curl of Magnetic Field01:26

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The magnetic field due to a volume current distribution given by the Biot–Savart Law can be expressed as follows:
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相关实验视频

Updated: Jun 23, 2025

Operation of the Collaborative Composite Manufacturing CCM System
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通过代奇点调整计算平滑和可整合的交叉场.

Long Ma, Ying He, Jianmin Zheng

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    概括
    此摘要是机器生成的。

    我们介绍了一种用于在表面上产生光滑,可整合的交叉场的新方法. 我们的方法自动确定奇点配置,确保无表面参数化和网格化的整合性.

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    相关实验视频

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    科学领域:

    • 计算几何学的计算几何学
    • 计算机图形 计算机图形
    • 应用数学 应用数学 应用数学

    背景情况:

    • 在计算机图形和几何处理中的各种应用中,光滑和可整合的交叉场是至关重要的.
    • 计算交叉场的现有方法通常依赖于复杂的优化或整数编程技术.
    • 确保整合性仍然存在挑战,特别是在多个连接领域.

    研究的目的:

    • 开发一种新的自动方法,用于计算2D和3D表面上的光滑和可整合的交叉场.
    • 通过提供更强大,更易于使用的解决方案来解决现有方法的局限性.
    • 为了实现诸如无合规参数化和无T连接的四角化等应用.

    主要方法:

    • 将迪里克莱特能量最小化以计算初始平滑交叉场.
    • 代调整奇点 (位置,合并,分裂) 来确定它们的配置.
    • 构建一个向量场来指导奇点优化以保证可整合性,特别是在多个连接域.

    主要成果:

    • 一种完全自动的方法,用于计算可控制的奇点配置的平滑交叉场.
    • 在简单连接的领域保证了整合性,并在多个连接的领域实现它的一种方法.
    • 该方法避免了专门的数值解析器,并且非常适合需要精确边界对齐的光滑模型.

    结论:

    • 拟议的方法在计算可整合的交叉场方面取得了重大进展.
    • 它为现有的基于优化和整数编程方法提供了更直接和自动的替代方案.
    • 该技术促进了高质量的表面参数化和网格化,并且将发布源代码.