In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the...
36 KB (6,834 words) - 17:07, 26 May 2024
rotations are large enough to invalidate assumptions inherent in infinitesimal strain theory. In this case, the undeformed and deformed configurations of...
50 KB (10,030 words) - 08:18, 26 May 2024
biological soft tissue. Infinitesimal strain theory, also called small strain theory, small deformation theory, small displacement theory, or small displacement-gradient...
17 KB (2,760 words) - 22:53, 29 January 2024
Calculus (redirect from Infinitesimal calculus)
generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus...
73 KB (8,575 words) - 02:33, 6 May 2024
Leonhard Euler (section Number theory)
including geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory, and other areas of physics...
101 KB (10,210 words) - 08:09, 29 May 2024
mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word infinitesimal comes from a 17th-century...
37 KB (5,086 words) - 17:42, 25 May 2024
infinitesimal strain theory, these conditions are equivalent to stating that the displacements in a body can be obtained by integrating the strains....
24 KB (4,427 words) - 15:33, 18 April 2024
Deformation (engineering) (redirect from Engineering strain)
in external displacements on an object. Strain is the relative internal change in shape of an infinitesimal cube of material and can be expressed as...
17 KB (2,311 words) - 12:17, 21 May 2024
Linear elasticity (redirect from Linear elasticity theory)
theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or...
41 KB (8,206 words) - 21:28, 20 February 2024
chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands. The integral symbol is U+222B ∫ INTEGRAL in Unicode and \int...
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that develop within such systems is based on the theory of elasticity and infinitesimal strain theory. When the applied loads cause permanent deformation...
30 KB (4,293 words) - 23:36, 3 September 2023
Differential (mathematics) (redirect from Differential (infinitesimal))
ideas from topos theory are used to hide the mechanisms by which nilpotent infinitesimals are introduced. Differentials as infinitesimals in hyperreal number...
26 KB (3,892 words) - 07:16, 19 May 2024
Leibniz's notation (category Mathematics of infinitesimals)
Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite...
22 KB (2,889 words) - 12:58, 8 March 2024
Deformation (physics) (redirect from Homogenous strain)
beam theory Deformation (engineering) Finite strain theory Infinitesimal strain theory Moiré pattern Shear modulus Shear stress Shear strength Strain (mechanics)...
20 KB (3,071 words) - 14:42, 6 November 2023
online at the Internet Archive. Le Calcul infinitésimal (1823) Leçons sur les applications de calcul infinitésimal; La géométrie (1826–1828) His other works...
42 KB (5,414 words) - 15:13, 3 June 2024
Hyperreal number (category Mathematics of infinitesimals)
extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x {\displaystyle x} is said to be finite...
33 KB (4,894 words) - 09:16, 2 June 2024
preceding discussion. Bending Bending of plates Infinitesimal strain theory Linear elasticity Plate theory Stress (mechanics) Stress resultants Vibration...
26 KB (4,064 words) - 08:34, 28 May 2024
Law of continuity (category Mathematics of infinitesimals)
an infinite-sided polygon with infinitesimal sides, and adding the areas of infinitely many triangles with infinitesimal bases. Leibniz used the principle...
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be infinitely small, Gottfried Wilhelm Leibniz argued that the theory of infinitesimals implies the introduction of ideal numbers which might be infinitely...
32 KB (4,072 words) - 21:33, 30 May 2024
={\frac {\gamma E}{2(1+\nu )}}} Deformation (mechanics) Infinitesimal strain theory Finite strain theory Pure shear Ogden, R. W. (1984). Non-Linear Elastic...
5 KB (749 words) - 00:12, 3 February 2024
analysis for elastic structures is based on the theory of elasticity and infinitesimal strain theory. When the applied loads cause permanent deformation...
44 KB (5,558 words) - 18:42, 30 May 2024
477. ISBN 9780321016188. Alexander, Amir (2015). Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World. Great Britain: Oneworld....
14 KB (1,839 words) - 23:16, 15 May 2024
around the mid-surface. The original theory developed by Love was valid for infinitesimal strains and rotations. The theory was extended by von Kármán to situations...
36 KB (4,012 words) - 03:07, 25 September 2023
The Analyst (category Mathematics of infinitesimals)
specifically on Isaac Newton's notion of fluxions and on Leibniz's notion of infinitesimal change. From his earliest days as a writer, Berkeley had taken up his...
17 KB (2,032 words) - 13:11, 25 March 2024
Elementary Calculus: An Infinitesimal approach is a textbook by H. Jerome Keisler. The subtitle alludes to the infinitesimal numbers of the hyperreal number...
13 KB (1,371 words) - 18:08, 31 March 2024
mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is...
21 KB (2,280 words) - 13:54, 15 May 2024
projective line over dual numbers. Smooth infinitesimal analysis Perturbation theory Infinitesimal Screw theory Dual-complex number Laguerre transformations...
19 KB (2,754 words) - 03:01, 16 April 2024
Kirchhoff–Love theory φ α = w , α 0 . {\displaystyle \varphi _{\alpha }=w_{,\alpha }^{0}\,.} For the situation where the strains in the plate are infinitesimal and...
33 KB (6,056 words) - 15:35, 30 April 2024
Plasticity (physics) (redirect from Elastic and plastic strain)
is deformation theory (see e.g. Hooke's law) where the Cauchy stress tensor (of order d-1 in d dimensions) is a function of the strain tensor. Although...
29 KB (3,521 words) - 03:10, 16 April 2024
does not satisfy the Archimedean property. Such fields will contain infinitesimal and infinitely large elements, suitably defined. Suppose F is an ordered...
4 KB (474 words) - 05:05, 2 March 2024