Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

210
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
210
Types of Limits I01:23

Types of Limits I

119
Limits are a key mathematical concept for understanding how functions behave as their input approaches specific values, particularly when the function is undefined. They help reveal trends and discontinuities by examining the values a function approaches rather than its actual value.One-sided limits focus on the direction from which a value is approached. When a function behaves differently depending on whether the input approaches from the left or the right, the two one-sided limits may not...
119
Introduction to Limits01:30

Introduction to Limits

147
A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...
147
Types of Limits II01:24

Types of Limits II

106
When observing how a curve behaves near a specific point along the horizontal axis, there are cases where the curve’s height increases or decreases without limit as the position draws closer to that point. The curve does not settle at any particular value; instead, the values grow more extreme—upward or downward—the nearer they get. No defined value exists exactly at that location, yet the surrounding behavior becomes more dramatic, indicating a sharp change in direction.The...
106
Limits at Infinity01:24

Limits at Infinity

128
The function that decreases as the input becomes very large provides a clear example of how mathematical functions can behave at extreme values. When the input increases continuously, the output becomes smaller and smaller, getting closer to a particular fixed value. Although the output never actually reaches this value, it moves nearer to it without limit. This behavior is a fundamental concept in understanding how functions behave as the input grows indefinitely. The graphical representation...
128
The Squeeze Theorem01:30

The Squeeze Theorem

136
Certain mathematical functions exhibit unpredictable or highly variable behavior near specific input values, making direct evaluation of their limits challenging. This complexity may arise from rapid oscillations or irregular patterns that obscure the function’s trend. In such cases, the Squeeze Theorem offers a reliable method for determining limits.According to the Squeeze Theorem, if a function is confined between two other functions near a particular point, and both outer functions...
136

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Sequential buckling mechanics of the ermine moth's aeroelastic tymbal: an origami-like creased shell analogue.

Journal of the Royal Society, Interface·2026
Same author

A rapid-response soft end effector inspired by the hummingbird beak.

Journal of the Royal Society, Interface·2024
Same author

Buckling-induced sound production in the aeroelastic tymbals of <i>Yponomeuta</i>.

Proceedings of the National Academy of Sciences of the United States of America·2024
Same author

Probing the stability landscape of cylindrical shells for buckling knockdown factors.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2023
Same author

Increasing reliability of axially compressed cylinders through stiffness tailoring and optimization.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2023
Same author

Probing in situ capacities of prestressed stayed columns: towards a novel structural health monitoring technique.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2023

Related Experiment Video

Updated: Dec 28, 2025

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.9K

Beyond the fold: experimentally traversing limit points in nonlinear structures.

Robin M Neville1, Rainer M J Groh1, Alberto Pirrera1

  • 1Bristol Composites Institute (ACCIS), University of Bristol, Bristol BS8 1TR, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 22, 2020
PubMed
Summary
This summary is machine-generated.

Researchers developed a new experimental method to follow nonlinear structures beyond unstable points. This technique enables the study of novel engineering designs that utilize elastic instabilities for functions like shape adaptation and energy harvesting.

Keywords:
experimental mechanicsexperimental path-followingnonlinear structuresstructural stability

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

427
DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
08:00

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

7.2K

Related Experiment Videos

Last Updated: Dec 28, 2025

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

8.9K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

427
DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
08:00

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

7.2K

Area of Science:

  • Engineering Science
  • Applied Physics
  • Materials Science

Background:

  • Nonlinearities and elastic instabilities are increasingly recognized for enabling novel functionalities.
  • Traditional experimental methods struggle with analyzing structures exhibiting instabilities.
  • Numerical continuation techniques have advanced the analysis of such structures, but experimental analogues were lacking.

Purpose of the Study:

  • To develop an experimental path-following method analogous to numerical continuation.
  • To enable the study of structures that exploit nonlinearities and instabilities.
  • To overcome limitations of traditional quasi-static experimental methods at limit points.

Main Methods:

  • A novel quasi-static experimental path-following technique was proposed.
  • The method combines control of displacement at a main load point with overall shape control using additional actuators and sensors.
  • This approach allows continuation along both stable and unstable equilibrium paths.

Main Results:

  • The proposed method successfully enables experimental path-following beyond limit points.
  • It allows for the traversal of statically unstable regions in the structure's response.
  • The technique facilitates extended testing of structures utilizing nonlinearities and instabilities.

Conclusions:

  • A new experimental method for path-following in nonlinear structures has been established.
  • This technique overcomes limitations of traditional methods, enabling the study of unstable equilibria.
  • The method opens new avenues for designing and testing advanced structures with novel functionalities.