Search results
Results from the WOW.Com Content Network
The Kirchhoff–Love theory of plates is a two-dimensional mathematical model that is used to determine the stresses and deformations in thin plates subjected to forces and moments. This theory is an extension of Euler-Bernoulli beam theory and was developed in 1888 by Love [ 1 ] using assumptions proposed by Kirchhoff .
The Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory was developed in 1888 by Love [2] using assumptions proposed by Kirchhoff. It is assumed that a mid-surface plane can be used to represent the three-dimensional plate in two-dimensional form.
In the Kirchhoff–Love plate theory for plates the governing equations are [1], = and , = In expanded form, + = ; + = and + + = where () is an applied transverse load per unit area, the thickness of the plate is =, the stresses are , and
The Reissner–Mindlin theory of plates is an extension of Kirchhoff–Love plate theory that takes into account shear deformations through-the-thickness of a plate. The theory was proposed in 1951 by Raymond Mindlin. [1] A similar, but not identical, theory in static setting, had been proposed earlier by Eric Reissner in 1945. [2]
The governing equations for the dynamics of a Kirchhoff-Love plate are , = ¨, + (,) = ¨ ¨, where are the in-plane displacements of the mid-surface of the plate, is the transverse (out-of-plane) displacement of the mid-surface of the plate, is an applied transverse load pointing to (upwards), and the resultant forces and moments are defined as
Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
Element of a bent beam: the fibers form concentric arcs, the top fibers are compressed and bottom fibers stretched. Bending moments in a beam. In the Euler–Bernoulli theory of slender beams, a major assumption is that 'plane sections remain plane'. In other words, any deformation due to shear across the section is not accounted for (no shear ...
This model has the general form and the isotropic form respectively =: = +. where : is tensor contraction, is the second Piola–Kirchhoff stress, : is a fourth order stiffness tensor and is the Lagrangian Green strain given by = [() + + ()] and are the Lamé constants, and is the second order unit tensor.