不同积分路径对动态有限差分法计算精度的影响效应

发布时间：2018-02-04 12:06

本文关键词： 动态有限差分法不同积分路径沙漏效应能量误差计算精度　出处：《工程科学与技术》2017年S2期 　论文类型：期刊论文

【摘要】：动态有限差分法作为解决冲击动力学问题的有效方法而被广泛使用。作者针对该算法实现细节上,如网格中积分路径的形状和网格单元类型对计算结果的影响效应,进行深入讨论。基于拉格朗日动力学有限差分法求解框架,使用JAVA语言编写动力学程序。首先模拟长柱形物体中的应力波传播,利用已有的理论解,对比多种积分路径下的模拟结果。利用可变覆盖率的积分路径,得到覆盖率与节点加速度的影响关系,从理论上得出积分路径选取的一般原则。从能量误差的角度,讨论四边形单元相对三角形单元的缺陷,利用受分布冲击荷载的矩形模型,得出四边形单元沙漏控制系数与能量误差率的关系。模拟无限大介质中的点源冲击应力波的传播模型,利用理论解,验证四边形单元受集中荷载作用确实会造成过大的能量误差,从而造成计算错误。从对长柱模型中的应力传播模拟可以看出,只有完全覆盖计算模型的积分路径,才能得到正确的解;欠覆盖路径会导致波速偏快,峰值偏大,过覆盖则会导致相反的效果。对两种单元类型的讨论可以得出:四边形单元由于固有的沙漏效应缺陷,即若关闭沙漏阻尼修正,会产生单元沙漏变形,导致计算失败;若开启沙漏阻尼修正又会引入过大的能量误差,同样会造成计算错误,因此不适合集中荷载作用的环境,在这种情况下,三角形单元具有独特的优势。
[Abstract]:The dynamic finite difference method is widely used as an effective method to solve the impact dynamics problem. For example, the effect of the shape of the integral path and the type of the mesh element on the calculation results is discussed in detail. The frame is solved based on the Lagrange dynamics finite difference method. The dynamic program is written in JAVA language. Firstly, the stress wave propagation in a long cylindrical object is simulated, and the simulation results under various integral paths are compared by using the existing theoretical solutions, and the variable coverage integral paths are used. From the angle of energy error, the defect of quadrilateral element relative to triangular element is discussed. By using the rectangular model of distributed impact load, the relationship between the control coefficient of a quadrilateral element hourglass and the error rate of energy is obtained. The propagation model of point source shock stress wave in infinite medium is simulated, and the theoretical solution is used. It is verified that the quadrilateral element subjected to concentrated load will cause excessive energy error and thus result in a calculation error, which can be seen from the simulation of stress propagation in the long column model. Only when the integral path of the computational model is completely covered can the correct solution be obtained. Undercoverage path will lead to faster wave velocity, larger peak value, and overcoverage will lead to the opposite effect. The discussion of the two types of elements can be concluded: quadrilateral element is due to the inherent hourglass effect defects. If the hourglass damping correction is closed, the element hourglass deformation will be produced, which will lead to the failure of calculation. If the sandglass damping correction is opened, too much energy error will be introduced, which will also result in a calculation error, so it is not suitable for the environment of concentrated load. In this case, the triangular element has a unique advantage.
【作者单位】：能源工程安全与灾害力学教育部重点实验室;四川大学建筑与环境学院;
【基金】：油气藏地质及开发工程国家重点实验室资助项目(PLN1505) 四川省科技计划资助项目(2014JY0002) 国家自然科学基金资助项目(11672194)
【分类号】：O302
【正文快照】： 岩石动态数值模拟是岩石力学研究中一项关键的技术,特别是对于动态冲击问题,应用数值模拟技术对试验进行优化设计,或对试验结果进行佐证,甚至代替成本高昂的试验,已成为相当普遍的研究方法。在诸多动态数值算法中,有限差分法因其原理简单,易于编程实现的优点而被广泛使用,尤其

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