Optimal design of rigid-plastic annular plates with piecewise constant thickness

Rigid-plastic stepped annular plates under uniform pressure load are considered. Both plate edges are supported. Four types of boundary conditions are studied. Tresca's yield condition is used. Such plate dimensions are sought for which the plate of constant volume has the maximal load carrying capacity.Notation a, d, R, h₁, h₂ plate dimensions (Fig. 1) - Q^* shear force - Q dimensionless shear force - M_r^* radial bending moment - M₁ dimensionless radial bending moment - M_t^* circumferential bending moment - M₂ dimensionless circumferential bending moment - M_k maximum value of bending moments in the rigid region - p^* uniform pressure load - p dimensionless uniform pressure load - r radial coordinate - x dimensionless radial coordinate - , , dimensionless parameters for plate (5) - V plate volume - dimensionless plate volume - M₀^* yield moment - ₀ yield stress - p₀ load carrying capacity - p₀^m maximum value of the load carrying capacity - p₀^u load carrying capacity for uniform plate - ^m, ^m optimal parameters, which correspond to the maximum value ofp₀ - s_i radius of circle between different plastic stages - () /x