统一屈服准则与变分法求解圆板均布极限载荷

为获得均布载荷下简支圆板极限载荷统一解析解,以最小势能原理、刚塑性第一变分原理以及统一屈服准则(unified yield criterion,UYC)比塑性功进行联合解析.获得的解析解为圆板半径a、材料屈服极限σ_s、板厚h以及屈服参数b的函数.由该解可导出Tresca解、Mises解、双剪应力屈服(twin shear stress,TSS)解.与传统的Tresca解析解及Mises数值解比较表明:获得的TSS解和Tresca解分别为计算结果的上下限,该Mises解析解与传统的Mises数值解基本一致,二者误差仅为4.2%.分析表明:随着圆板厚度减小,挠度增加;圆板半径增加,极限载荷增加.

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 σs , 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.