SIMEON DENIS POISSON BASICS AND TUTORIALS

SIMEON DENIS POISSON BASIC INFORMATION
Who Is Siméon Denis Poisson?

Siméon Denis Poisson is mathematician famous and responsible for an important mathematical expression known as Poisson's Ratio.


He was born on 21-Jun-1781 at Pithiviers, France.

Siméon Poisson was a protégé of Laplace. Poisson was an extremely prolific researcher and also an excellent teacher. In addition to important advances in several areas of physics, Poisson made important contributions to Fourier analysis, definite integrals, path integrals, statistics, partial differential equations, calculus of variations and other fields of mathematics.

The Poisson Distribution is a discrete distribution is also named after Poisson. He published its essentials in a paper in 1837. The Poisson distribution and the binomial distribution have some similarities, but also several differences.

Among the books he authored:

Traité de Mécanique (1811, science)
Théorie Nouvelle de l'Action Capillaire (1831, science)
Théorie Mathématique de la Chaleur (1835, science)
Recherches sur la Probabilité des Jugements en Matière Criminelle et en Matière Civile (1837)

POISSON’S RATIO BASIC INFORMATION AND TUTORIAL

POISSON'S RATIO TUTORIALS AND SAMPLE PROBLEM
What Is Poisson's Ratio? Sample Problem And Solution Using Poisson's Ratio


When a homogeneous slender bar is axially loaded, the resulting stress and strain satisfy Hooke’s law, as long as the elastic limit of the material is not exceeded.

In all engineering materials, the elongation produced by an axial tensile force P in the direction of the force is accompanied by a contraction in any transverse direction (Fig. 2.36).† In this section and the following sections (Secs. 2.12 through 2.15), all materials considered will be assumed to be both homogeneous and isotropic, i.e., their mechanical properties will be assumed independent of both position and direction.

It follows that the strain must have the same value for any transverse direction.\ Therefore, for the loading shown in Fig. 2.35 we must have Py 5 Pz. This common value is referred to as the lateral strain.

An important constant for a given material is its Poisson’s ratio, named after the French mathematician Siméon Denis Poisson (1781–1840) and denoted by the Greek letter n (nu). It is defined as

v = - lateral strain / lateral stress.

Sample Problem:


A 500-mm-long, 16-mm-diameter rod made of a homogenous, isotropic material is observed to increase in length by 300 mm, and to decrease in diameter by 2.4 mm when subjected to an axial 12-kN load. Determine the modulus of elasticity and Poisson’s ratio of the material.

Solution:

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