再生核质点法在非线性冲击动力学中的应用

Application of reproducing kernel particle method in non-linear impact dynamics

利用再生核方法来构造计算域函数的插值函数,通过区域内的质点参数来实现数值计算,满足一致性要求;在大变形、大转动、大应变的情况下,引入Jaumann应力和应变速率张量来表征实际应力和应变速率,进而可以表征出材料冲击条件下的本构关系;将本构关系引入冲击过程虚功原理,采取Lagrangian描述的方法,并通过再生核质点方法将能量积分方程离散,推导了非线性冲击过程的再生核质点法计算控制方程,给出了方程求解的Newmark递推公式和Newton-Raphson迭代方法.通过具体实例来说明了再生核质点法在非线性动力学中的应用过程,并验证了计算方法的正确性.

The interpolation function was constructed through the reproducing kernel method and the numerical calculations in the whole field could be realized on those particles. The consistency was easily satisfied in those methods. Under the conditions of large deformation, large rotation, and large strain, the Jaumann stress and the strain rates were introduced to express real stress and strain rates, and were further used to characterize the material constitutive laws under the impact conditions. By introducing discrete method though reproducing kernel particle method（RKPM） into the non-linear dynamic problems, and also taking into account of the non-linearity of the material constitutive model, the Lagrangian descriptive method, the RKPM control equation for non-linear impact process, the Newmark recursion formula, and the Newton-Raphson iterative method are derived. By using several examples the numerical analysis procedure for RKPM of non-linear impact is proved. dynamics is illustrated and the feasibility of the method is proved.