Related Experiment Video
Updated: Aug 24, 2025

Addressing Practical Issues in Atomic Force Microscopy-Based Micro-Indentation on Human Articular Cartilage Explants
Published on: October 28, 2022
Calculation of the Meniscus Shape Formed under Gravitational Force by Solving the Young-Laplace Differential Equation
Kira Lewis1, Takeshi Matsuura2
1Horace Mann School, 231 West 246th Street, Bronx, New York10471, United States.
Abstract:
This work presents a method to calculate the meniscus shape by solving the differential equation based on the Young-Laplace equation. More specifically, the differential equation is solved by applying the cubic Bézier curve. A complicated nonlinear differential equation is solved using the Bézier control points and the least-squares method while maintaining computational simplicity. The results show all of the expected features of the meniscus under the gravitational force. A brief discussion is also made on the effect of the errors on the results. The method is further validated by its agreement with the numerical solutions reported in the existing literature.
Related Concept Videos
Deformations in a Symmetric Member in Bending
When the member is segmented into tiny cubic elements, it is observed that the primary stress...
Bending of Curved Members - Neutral Surface
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within...
Bending of Curved Members - Strain Analysis
The important part of bending analysis for such a member...
Equation of the Elastic Curve
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural...
Elastic Curve from the Load Distribution
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments.
Gravitational Potential Energy for Extended Objects

