Plate-Bending.zip_plate_plate bending_plate matlab_zip

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Plate Bending

Siva Srinivas Kolukula

Structural Mechanics Laboratory

IGCAR, Kalpakkam

INDIA Email-allwayzitzme@gmail.com

1.1 Thin plate theory/ Kirchhoff plate theory

The basic assumption for the classical Kirchhoff plate bending theory is that a straight line normal to the

midplane of the plate before deformation remains normal even after deformation. In this theory

transverse shear deformation is neglected.

1.2 Mindlin theory/ Mindlin—Reissner theory

The plane normal to the midplane before deformation will not remain normal any longer after the

deformation. In this theory transverse shear deformation is accounted.

plate mid surface. Length of the plate is ‘a’ and its breadth ‘b’.

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2. Kirchhoff plate theory

In this theory the transverse deformation is neglected. The inplane displacement u, v are expresses as

(2.1)

Where x and y are the inplane axes located at the midplane of the plate, and z is along the thickness of

As the transverse deformation is not considered, we have

For a thin plate assuming the plane stress condition, we have

(2.4)

The above stresses give rise to the following moments

Thus the moment-curvature relations for a homogenous and isotropic Kirchhoff plate are

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It assumes that transverse deformation occurs in the plate. The deformations and strains are given by

The moment curvature relations will be for bending and shear deformations given as follows

(3.2)

Figure 2: Stresses and distributed lateral forces on plate