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Related Concept Videos

Prismatic Beams: Problem Solving01:15

Prismatic Beams: Problem Solving

In the design of a supported timber beam subjected to a distributed load, both the beam's physical dimensions and the timber's characteristics, such as its grade and species, are critical. These factors determine the allowable stress values, which are crucial for calculating the necessary beam depth to ensure structural integrity and safety.
The design begins with analyzing the beam as a free body to identify moments and force balances, thereby determining support reactions. Next, the designer...
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's first...

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Related Experiment Video

Updated: May 18, 2026

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
05:57

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

Characterizing the combinatorial beam angle selection problem.

Mark Bangert1, Peter Ziegenhein, Uwe Oelfke

  • 1Department of Medical Physics in Radiation Oncology, German Cancer Research Center, Im Neuenheimer Feld 280, D-69120 Heidelberg, Germany. markbangert@gmail.com

Physics in Medicine and Biology
|October 2, 2012
PubMed
Summary
This summary is machine-generated.

This study optimizes beam angle selection for radiation therapy using metaheuristics. Non-coplanar beams and specific termination criteria significantly improve treatment plan quality, offering a reference for future research.

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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
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The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Related Experiment Videos

Last Updated: May 18, 2026

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station
05:57

Characterization of SiN Integrated Optical Phased Arrays on a Wafer-Scale Test Station

Published on: April 1, 2020

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
12:14

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

Published on: August 12, 2013

Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Computational Biology

Background:

  • The beam angle selection (BAS) problem in intensity-modulated radiation therapy (IMRT) is a complex combinatorial optimization challenge.
  • Existing metaheuristics like simulated annealing and genetic algorithms can solve the BAS problem efficiently.
  • Key parameters, including non-coplanar beam inclusion, angular resolution, and convergence criteria, require systematic investigation.

Purpose of the Study:

  • To systematically investigate open questions in combinatorial BAS for IMRT treatment planning.
  • To provide a reference for future research by comparing different metaheuristic strategies.
  • To introduce a high-performance inverse planning engine for efficient BAS.

Main Methods:

  • A meta-analysis of four combinatorial optimization strategies: genetic, cross-entropy, simulated annealing, and a naive iterative algorithm.
  • Utilized a high-performance inverse planning engine capable of ≈3600 full fluence optimizations per hour.
  • Simulated ≈3,000,000 treatment plans for three head and neck patients, varying beam ensemble sizes, coplanarity, and angular resolutions (5°-20°).

Main Results:

  • All four strategies significantly improved objective function values and dose distributions compared to standard equi-spaced coplanar beams.
  • Genetic and cross-entropy algorithms showed faster initial convergence; simulated annealing achieved similar final objective function values.
  • Non-coplanar beams significantly improved plans for challenging head and neck cases, while increased angular resolution yielded minor improvements.

Conclusions:

  • Metaheuristic strategies (genetic, cross-entropy, simulated annealing) yield clinically equivalent treatment plans, outperforming the iterative algorithm.
  • Terminating optimization after 1000 beam combinations without objective function decrease is recommended, showing minimal deviation from 10,000 ensembles.
  • Considering non-coplanar beams is crucial for optimizing challenging head and neck IMRT plans.