层合压电材料冲击问题的时域间断Galerkin有限元方法求解  

A time discontinuous Galerkin finite element method for the solution of impact problem of laminated piezoelectric material

作　　者：郭攀 卫洪涛 武文华[2] 徐广涛[3] 赵军 GUO Pan;WEI Hongtao;WU Wenhua;XU Guangtao;ZHAO Jun(School of Mechanics and Engineering Science,Zhengzhou University,Zhengzhou450001,China;The State Key Laboratory for Structural Analysis of Industrial Equipment,School of Aeronautics and Astronautics,Faculty of Vehicle Engineering and Mechanics,Dalian University of Technology,Dalian116024,China;School of Mechanical Engineering,Zhengzhou University,Zhengzhou450001,China)

机构地区：[1]郑州大学力学与工程科学学院,郑州450001 [2]大连理工大学运载与力学学部工程力学系工业装备结构分析国家重点实验室,大连116024 [3]郑州大学机械工程学院,郑州450001

出　　处：《振动与冲击》2018年第24期195-200,共6页Journal of Vibration and Shock

摘　　要：构建了压电耦合动力学问题的时域间断Galerkin有限元方法,在此基础上针对冲击作用下压电材料耦合问题进行了数值模拟。强间断、高梯度的冲击荷载作用下,传统的时域连续Galerkin有限元方法在压电耦合动力学问题模拟时,间断的波阵面及层合界面处会出现强烈的虚假数值振荡,这类振荡使得问题求解的精度大大降低。为了消除这类高频数值振荡,依据所发展的时域Galerkin有限元方法原理,在最终的有限元方法求解公式中引入了比例刚度阻尼。冲击作用下一维、二维压电动力学问题算例结果表明,所发展的时域间断Galerkin有限元方法,较好地消除了这类虚假的数值振荡,并捕捉了应力波及电势波的波前波后间断特性。A time discontinuous Galerkin finite element method(DGFEM)is used to simulate the problem of laminated piezoelectric material subjected to the high-frequency impulsive load.At present,the traditional numerical method for solving the dynamic problem of piezoelectric solid subjected to high frequency impulsive load generally fails to properly capture discontinuities of waves in space and interface between two layers,and produces spurious numerical oscillations in the simulation of high modes and sharp gradients.In order to filter out the spurious oscillations,an artificial damping scheme,which based on the DGFEM,was implemented in the final finite element formula.Numerical results of one dimension and two dimension show that the developed DGFEM presents good abilities and provides much more accurate solutions for piezoelectric problem.It can capture the discontinuities effectively at the wave front and wave after and filter out the effects of spurious numerical oscillation induced by high-frequency impulsive load.

关 键 词：时域间断Galerkin有限元方法 冲击荷载 层合压电材料 数值振荡 

分 类 号：O322[理学—一般力学与力学基础]