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Related Concept Videos

Design Example: Traverse Angle Computations01:25

Design Example: Traverse Angle Computations

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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...
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Euler's Formula to Columns: Problem Solving01:23

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Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
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Euler's Formula for Pin-Ended Columns01:21

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In structural engineering, the stability of columns under compressive axial loads is a critical consideration, described as buckling. A typical example involves a column PQ, which is pin-connected at both ends and subjected to a centric axial load F applied at one end, with a reaction force of F' = -F at the other end. Here, it is crucial to understand that when an applied load exceeds the critical load, buckling occurs as the system becomes unstable.
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Factorial Design02:01

Factorial Design

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Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
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Euler's formula is very important in the field of structural engineering, providing a foundation for understanding the critical loading conditions of pin-ended columns. This formula links the modulus of elasticity, the moment of inertia of the cross-section, and the column's length, offering a precise calculation of the critical load at which a column is prone to buckling.
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Origami Inspired Self-assembly of Patterned and Reconfigurable Particles
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An additive algorithm for origami design.

Levi H Dudte1, Gary P T Choi1,2, L Mahadevan3,4,5

  • 1John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138.

Proceedings of the National Academy of Sciences of the United States of America
|May 18, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel additive algorithm for designing developable origami patterns. It enables the growth of folded surfaces from a seed, ensuring they remain isometric to a flat plane, transforming metastructure design.

Keywords:
additive fabricationcomputational designmetamaterialsorigami

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Area of Science:

  • Computational geometry
  • Materials science
  • Origami engineering

Background:

  • Additive fabrication inspires new approaches to geometric design.
  • Traditional origami design often involves global searches, posing challenges for complex patterns.
  • Ensuring folded surfaces are developable and isometric to the plane is a key geometric constraint.

Purpose of the Study:

  • To develop an inverse design algorithm for creating developable quad origami patterns.
  • To enable the growth of folded surfaces from a seed while maintaining planarity.
  • To explore the potential of local growth rules for origami-based metastructure design.

Main Methods:

  • Identifying geometric conditions for compatible fold completion into developable fourfold vertices.
  • Developing a marching algorithm to grow geometrically compatible fronts from a folded seed.
  • Applying the algorithm to generate diverse origami patterns, including ordered, disordered, straight, and curved folds.

Main Results:

  • A complete additive algorithm for the inverse design of developable quad origami.
  • Demonstration of growing various origami patterns, including those with curved folds.
  • Successful fitting of surfaces with given curvature using folded approximants.

Conclusions:

  • The developed algorithm provides a robust method for inverse origami design.
  • The local rule-based approach offers a powerful tool for creating complex origami structures.
  • This method has the potential to revolutionize the design of origami-based metastructures.