Unified Yield Criterion and Variational Calculus in Analysis of Uniformly Distributed Limit Load for Circular Plate

To obtain the unified analytical solution of plastic limit load of simply supported circular plate under uniformly distributed load,the principle of minimum energy and the first variation principle for rigid-plastic materials as well as the specific plastic work of unified yield criterion(called UYC for short)were simultaneously used.The solution from the research shows that the limit load is the function of the plate radius a,yield stress σ_s,plate thickness h and yield parameter b.Derived from the unified analytical solution,the analytical solutions based on Tresca,Mises,and TSS criteria can be obtained. B comparing the traditional Tresca analytical solution with Mises numerical solution,it shows that both the present analytical results of Tresca and Mises yield criteria are lower than that of the Tresca analytical solution and Mises numerical solution.The present TSS solution and Tresca solution are the upper bound and lower bound of the calculated results respectively.However,good agreement is found between the present Mises solution and traditional Mises solution since the relative error is only 4.2%.The discussion shows that as the plate thickness increases,the deflection increases.While the plate radius increases,the limit load increases.