Buckling of cantilever thin plate with free end subjected to uniform shear

This thesis is concerned with the buckling problem of a cantilever thin plate with its tree end subjected to uniform shear. The same problem waa originally solved by Prandtl in 1899, based on the equilibrium condition of a deep beam. The author baa used the energy method based on the thin plate theory to attack the problem.

After the displacement is assumed, the potential energy can be formulated. From the condition that the potential energy assume a minimum value in an equilibrium configuration, results a system of n linear homogeneous algebraic equations ot n parameters which are introduced in the assumed displacement. For a non-trivial solution, the determinant of the coefficients must vanish. This gives a characteristic equation from which the buckling load is determined. The author has obtained a curve for maximum stress at buckling state, which shows that the result 1a better than that obtained by Prandtl in certain cases.

The energy method has been generalized to a three dimensional problem to consider the displacement in all directions.