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Deformation 'Gradient', Right/Left Cauchy Green Compatibility

Submitted by Amit Acharya on

I post some (hand-written) notes on compatibility conditions for both small and finite strains that I have used for helping me in lecturing. These may be useful for our student friends on imechanica. I also post a paper on compatibility conditions for the Left Cauchy-Green field in three dimensions as well as the paper by Janet Blume on the same subject.

Strain compatibility equation in non-linear solid mechanics!!!

Submitted by ramdas chennamsetti on

We have six strain compatibility equations, which are obtained from strain-displacement relations by making an assumptions 'small strains'. Strain compatibility equations ensure a single valued and continuous displacemnet filed. These equations are used in stress based approach.

Now my queries are as following.

[1] Do we have strain compatibility equations for non-linear strain-displacement relations?

[2] Do we follow stress based approach in non-linear solid mechanics.

Analytical solution for deflection of plate

Submitted by J. K. Phadikar on

I am a third yr undergraduate student of Aerospace Engineering department, IIT Kharagpur. I have a very simple question in strucutral mechanics. Is there any analytical solution available for deflection of plate under distributed load? The governing equation is well known and has been attached as an image file. Only classical plate theory can be considered. The boundary conditions can be taken as classical boundary conditions. So that can be any combination of a) hinged b) clamped and c) free boundary conditions.