基于非均匀光滑有限元法的功能梯度压电梁的动力学分析

发布时间：2018-01-12 20:39

本文关键词：基于非均匀光滑有限元法的功能梯度压电梁的动力学分析　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着科学技术的发展,生产水平的提高,成功制备了功能梯度压电材料,并因其优良的力电耦合性能,国内外学者展开了广泛研究,发展成为现阶段研究的热点。由于功能梯度压电材料结构的非均匀性及其力电耦合特性,增大了对功能梯度压电材料进行动力学分析的难度。二维固体力学问题中,Cell-based光滑有限元将求解域内的面积分转换成线积分,降低了网格的质量要求,提高了求解精度,成功应用于功能梯度压电板静力学问题的求解。在实际运用中,为了对结构进行有效控制,掌握功能梯度压电材料动力学特性是十分有必要的。本文基于非均匀有限单元法和光滑梯度技术,构造了非均匀Cell-based光滑有限元法,并对功能梯度压电梁的动力学问题进行了求解。本文总结了功能梯度压电材料和光滑有限元法的研究进展,并对其发展现状进行了分析,发现了相关研究现阶段所存在的问题,基于均匀有限元法、压电基本原理和光滑梯度技术构造了非均匀Cell-based光滑有限元法,该方法采用高斯散度定理,将光滑域上的面积分转化为边界的线积分,不需要对形函数求导,网格质量要求低,直接采用在高斯积分点处的功能梯度压电材料相应位置的材料参数进行计算,这样的话,模型能够更好地体现功能梯度压电材料其材料属性的梯度变化,克服了非均匀有限元法刚度矩阵过硬的问题,提高了求解精度,推导了非均匀Cell-based光滑有限元法,对功能梯度压电梁的模态和瞬态动力学问题进行了研究,在模态分析时将与电势相关的自由度进行凝聚;在瞬态动力学分析时采用Newmark法求解了动力学平衡方程,并与ANSYS的求解结果进行了对比。数值算例表明,该方法具有较高的精度。
[Abstract]:With the development of science and technology and the improvement of production level, functionally graded piezoelectric materials have been successfully prepared, and due to their excellent mechanical and electrical coupling performance, scholars at home and abroad have carried out extensive research. Due to the nonuniformity of functionally graded piezoelectric materials and the characteristics of electromechanical coupling, it has become a hot research topic at the present stage. The dynamic analysis of functionally graded piezoelectric materials is more difficult. In two-dimensional solid mechanics problems, Cell-based smooth finite element transforms the area in the solution domain into a line integral. The mesh quality requirement is reduced and the precision is improved. It is successfully applied to solve the static problem of functionally gradient piezoelectric plate. In practice, in order to control the structure effectively. It is necessary to master the dynamic characteristics of functionally graded piezoelectric materials. Based on the non-uniform finite element method and smooth gradient technique, a non-uniform Cell-based smooth finite element method is constructed. The dynamic problems of functionally graded piezoelectric beams are solved. The research progress of functionally graded piezoelectric materials and smooth finite element method is summarized in this paper. Based on the uniform finite element method, piezoelectric basic principle and smooth gradient technique, the non-uniform Cell-based smooth finite element method is constructed. In this method, Gao Si's divergence theorem is used to transform the area on the smooth domain into the line integral of the boundary, which does not require the derivation of the shape function, and the quality of the mesh is low. The material parameters of the functionally graded piezoelectric material at the Gauss integral point are calculated directly, so the model can better reflect the gradient change of the material properties of the functionally graded piezoelectric material. The problem of stiffness matrix of non-uniform finite element method is overcome, and the accuracy of the solution is improved. The non-uniform Cell-based smooth finite element method is deduced. The modal and transient dynamics of functionally graded piezoelectric beams are studied. The degree of freedom associated with EMF is condensed in modal analysis. The Newmark method is used to solve the dynamic equilibrium equation in transient dynamic analysis, and the results are compared with those obtained by ANSYS. The numerical results show that the method has a high accuracy.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O342;TB34

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