Euler's critical load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: where * , Euler's critical load (longitudinal compression load on column), * , Young's modulus of the column material, * , minimum area moment of inertia of the cross section of the column (second moment of area), * , unsupported length of column, * , column effective length factor This formula was derived in 1757 by the Swiss mathematician Leonhard Euler. The column will remain straight for loads less than the critical load. The critical load is the greatest load that will not cause lateral deflection (buckling). For loads greater than the critical load, the column will deflect laterally. The critical load puts the column in a state of unstable equilibrium. A load beyond the critical load causes the column to fail by buckling. As the load is increased beyond the critical load the lateral deflections increase, until it may fail in other modes such as yielding of the material. Loading of columns beyond the critical load are not addressed in this article. Around 1900, J. B. Johnson showed that at low slenderness ratios an alternative formula should be used. (Wikipedia).
Andrew Thomas (7/1/2020): Functional limit theorems for Euler characteristic processes
Title: Functional limit theorems for Euler characteristic processes Abstract: In this talk we will present functional limit theorems for an Euler Characteristic process–the Euler Characteristics of a filtration of Vietoris-Rips complexes. Under this setup, the points underlying the simpli
From playlist AATRN 2020
Mahir HADZIC - Nonlinear stability of expanding stars in the mass-critical Euler-Poisson system
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From playlist Trimestre "Ondes Non Linéaires" - May Conference
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From playlist Differential Equations
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From playlist Differential Equations
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From playlist Mathematics General Interest
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From playlist Mathematics named after Leonhard Euler
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From playlist MIT 3.054 Cellular Solids: Structure, Properties and Applications, Spring 2015
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From playlist A Second Course in Differential Equations
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From playlist Differential Equations
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From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
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From playlist Variational Methods in Geometry
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From playlist Differential Equations