What is a simply supported plate?
Edges 1 and 2 are Simply Supported. This means no displacement in the vertical direction and that the slope normal to the edge must be zero. Edges 3 and 4 are along lines of symmetry, and the plate must have a symmetric deformation shape across the lines of symmetry.
What are 3 shortcomings of plate theory?
Shortcomings: (1) presented more difficulties in analytical treatment. (2) ‘shear locking’ in the thin limit. (3) requiring a shear coefficient to satisfy the constitutive relationship between shear stress and shear strain.
Which theory is used for thin plate analysis?
Kirchhoff–Love theory for thin plates The Kirchhoff–Love theory is an extension of Euler–Bernoulli beam theory to thin plates. The theory was developed in 1888 by Love using assumptions proposed by Kirchhoff.
What assumptions have been made in thin plate bending theory?
One of the important assumptions made is that shear deformation is negligible. Some elements have also been developed by including the effect of transverse shear deformation. According to thin plate theory, the deformation is completely described by the transverse deflection of the middle surface of the plate (w) only.
What is simply supported?
Simply supported – a beam supported on the ends which are free to rotate and have no moment resistance. Fixed or encastré (encastrated) – a beam supported on both ends and restrained from rotation.
What is a simply supported edge?
For a simply supported edge, w = 0, and the moment perpendicular to the edge is zero. For a built-in edge, w = 0, and the tangent of the displacements perpendicular to the edge is zero. The mathematically correct condition for a free edge is not a trivial task, and it was determined by Kirchhoff in 1850.
What is thick plate?
Plate elements can be further categorized into thin and thick plates. Although the distinction between a thin versus a thick plate is not well defined, a thickness to width or length ratio of lower than 10% is generally considered a thin plate, while a ratio greater than 10% is regarded as a thick plate.
What is rate theory?
Rate theory is a concept in chemistry that describes the process of peak dispersion, and it provides an equation to calculate the variance per unit length of the column. This theory is very useful in column chromatography.
What is the shell theory?
Shell theories are based on the assumption that the strains in the shell are small enough to be discarded in comparison with unity. It is also assumed that the shell is thin enough that quantities, such as the thickness/radius ratio may be discarded in comparison with unity.
What is orthotropic plate theory?
A refined plate theory for orthotropic plate, based on stress formulation, was proposed by Medwadowski (1958). In this theory, a nonlinear system of equations was derived from the corresponding equations of the three-dimensional theory of elasticity.
What is a thin plate?
LAMINA. a thin plate or layer (especially of bone or mineral)
What is the thickness of thin plate?
Plates are categorized based on the thickness as thin plate and thick plate. In case of thin plate, the straight line normal to the middle plane remains normal even after deformation and the thickness of thin plate varies from 0.1 > t > 0.01.
What are the boundary conditions for a simply supported plate?
For a simply supported plate the deflection must satisfy the following boundary conditions on the plate boundary Γ. (6.82a)w=0. (6.82b)Mn=−D(∂2w∂n2+ν∂2w∂t2)=0. where Mn is the bending moment in the direction n normal to the boundary and t denotes the tangential to the boundary direction.
What are the bending and twisting moments of a simply supported plate?
The bending and twisting moments are given by the expressions For a simply supported plate the deflection must satisfy the following boundary conditions on the plate boundary Γ where Mn is the bending moment in the direction n normal to the boundary and t denotes the tangential to the boundary direction.
What is the aim of plate theory?
The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads. Of the numerous plate theories that have been developed since the late 19th century, two are widely accepted and used in engineering.
What are the different types of plate theories?
Plate theory 1 the Kirchhoff – Love theory of plates (classical plate theory) 2 The Uflyand-Mindlin theory of plates (first-order shear plate theory) More