Optimal Design for Plate Buckling

This paper extends Keller's classic solution for the optimal design of columns to the case of plates. After the introduction of nondimensional variables, a calculus of variations technique is used to derive an optimality condition, which states that “the strain‐energy density is proportional to the thickness of an optimal plate design.” The case of a simply supported plate is then discussed, using a truncated Fourier series solution. For a square, isotropic plate, the buckling load of the optimal design is larger than that of the uniform plate by a factor of $1.71+1.37\nu$ (ν is Poisson's ratio). An appendix is included which discusses Keller's original solution and shows how it can be applied when a fourth‐order differential equation is used rather than the second‐order one used by Keller. This appendix also discusses the use of a truncated Fourier series and Rayleigh's method as an approximation of Keller's result, thus laying the groundwork for the use of Fourier series in the plate problem.