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critical buckling load of timoshenko beam


I am looking for a closed form analytical solution for the critical bucking load of a timoshenko beam with clamped-free BC.

please help me i'm in rush!!!

Thanks in advance



Edge crack boundary condition

Hi everyone

i'm working on modeling crack in plates and i'm a little confused about correct boundary condition of a single edge crack in a plate under tension! could you please tell me which corner should fixed and which one should defined as a roller???

i also attached a figure.

i tried 2 kind of BC for my problem:

1- node 1: roller (Ux=0) and node 3: fixed (Ux=Uy=0)

2- i only fixed node 2 (Ux=Uy=0)

and the stress intensity factor calculated by these BCs almost the same!!!

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