Optimal design of elastic plates with a constraint on the slope of the thickness function

Abstract A constraint on the maximum absolute value of the slope of the thickness function is found to have a profound influence on the problem of optimal design of axisymmetric elastic plates by securing a unique, regular solution. It is also shown, that except for the case of axisymmetric deformation, the constraint is active everywhere and the optimal design is a plate, subdivided into annular regions of constant slope equal to the maximum value permitted.