An improved method for optimal shakedown design of circular plates

Abstract

The paper analyzes the problem of distributing an optimal limit bending moment of elastic-plastic circular and annular plates subjected to variable repeated loading at shakedown. The geometry of the plate is known and variable repeated loading is defined by time-independent upper and lower bounds (unloading phenomenon of a cross section is ignored). Equilibrium finite elements are applied for a discrete model. The safety of the plate is described with reference to nonlinear von Mises yield criterion while serviceability – by displacement limitations. The analysis problem of internal forces and deformations is formulated as a complete system of equations for an elastic-plastic plate in the shakedown state. The implementation of compatibility conditions for residual displacements and MATLAB nonlinear optimization tools allowed creating an improved mathematical model for optimizing the plate and its effective numerical realization. Research methods and numerical results are based on the assumption of small deformations.

DOI: http://dx.doi.org/10.5755/j01.mech.20.4.6542