冲击荷载作用下简支圆板的塑性动力响应统一解

Unified solutions of dynamic plastic response for circular plate under impulsive Load

采用统一强度理论求解了简支圆板在中等脉冲荷载作用下的动力响应问题,得出了统一的动力塑性极限荷载、内力场和速度场,并给出了上限解和下限解。讨论了静力许可条件和运动许可条件。利用本文的解还得出了简支圆板在静力荷载作用下的极限荷载、内力场和速度场。根据选择不同的拉压比参数α,本文所给出的解可以适用于各种拉压异性和拉压同性材料。Tresca解、Mohr Coulomb解和双剪统一屈服准则解是本文的特例,Mises解是本文当α=1和b=0.5时的线性逼近。研究结果表明,拉压比α和强度理论参数b对动力解的影响要大于对静力解的影响,所以,根据材料的不同选择合适的强度理论,对于更好的发挥材料的强度潜力,减轻结构的重量具有重要的意义。

The dynamic response of a simply supported circular plate under moderate impulsive loading is solved with the unified strength theory. The unified dynamic plastic limit load, internal stress field, and velocity field are obtained together with the upper and the lower bound solutions. Both the static and the dynamic admissible conditions are discussed. The limit load, the internal stress field, and the velocity field are also obtained for static loading case. The solutions given in this paper are applicable to various materials with and without the SD effect (strengthdifferent in tension and compression). The solutions based on the Tresca, Von Mises, Mohr-Coulomb theories and the unified yield criterion are special cases of the unified solutions herein. It is shown that the influence of the tension-compression ratio and the strength parameter on the dynamic solution is more significant than on the static solution.