Optimal design of piecewise-constant thickness circular plates for minimax axisymmetric deflection

摘要

A canonical exact deflection expression for piecewise constant circular plates under any rotationally symmetric transverse loading is presented. The circular plates may be simply supported or clamped at the edges. Based on the analytical deflection expression, we derive the optimality conditions for the optimum values of segmental thickness and boundaries that minimise the maximum (central) deflection of piecewise-constant thickness circular plates of a given volume. As certain portions of the optimal plate design may become rather thick, the effect of transverse shear deformation has been taken into consideration in accordance to the Mindlin plate theory for a more accurate calculation of the deflection.