outer radius of plate power series functions of Y, B function of v, B, determined via the boundary conditions flexural rigidity depending on plate thickness, h, modulus of elasticity in tension and compression power series function of v, fi undetermined multiplier function of x, 8, h, maximum value of G corresponding to 8, at x, for first constraint plate thickness at outer radius, a plate thickness at center of plate plate thickness at x value of h, which makes plate weight a minimum for first constraint value of h,, for the ith value of Y plate thickness varying at center of plate, see Fig. 2 constant, see equation (18) functions of v, /?, see equations (16) and (17) bending moments/unit length subscript notation signifying a maximum or a minimum nth term, nth increment notation defined by equation (9) intensity of axisymmetric distributed load upper bound value of allowable load q notation defined in equation (32) shearing force parallel to z axis/unit length of a section of a plate perpendicular to T direction cylindrical coordinates; r, 13 in plane of plate displacement (deflection) in z direction of middle-plane (surface) of a thin plate deflection at center of plate weight of plate dimensionless ratio r/a value of x which maximizes G at x,, using p, in equation (31), for first constraint limits of interval in which G, > 1 dimensionless ratio h,/h, dimensionless variable defining shape of plate material density “pencil of curves” for a given h,i, see Fig. 3 value of B satisfying at least the first constraint, making the plate weight an extremum Poisson’s ratio uniaxial yield stress, equal values in tension and compression lower bound value of the yield stress, us, see equation (32) normal stresses in radial and tangential directions slope of middle surface as defined in equation (5)