基于向量式有限元的三角形薄板单元

发布时间：2018-04-17 18:38

本文选题：平板结构 + 向量式有限元　；参考：《工程力学》2014年01期

【摘要】：向量式有限元是一种基于点值描述和向量力学理论的新型分析方法。该文基于向量式有限元基本原理,推导了三角形DKT薄板单元的基本公式,详细阐述了通过逆向运动处理薄板单元的平面内、外刚体位移从而获得单元节点纯变形位移的过程,以及进一步通过变形坐标系获得单元节点内力的求解方法;同时对质点的质量矩阵与惯性矩阵、应力计算的数值积分及插值方法、时间步长及阻尼参数的取值等问题提出了合理可行的处理方式。在此基础上编制了薄板单元的计算分析程序,并进行了算例验证。算例分析表明所编制的向量式有限元薄板单元程序可以很好地完成平板结构的静、动力分析,验证了理论推导的正确性和分析程序的可靠性。该文成果为进一步建立向量式有限元薄壳单元理论打下了必要的基础。
[Abstract]:The vector finite element method is a new analysis method based on point value description and vector mechanics theory.Based on the basic principle of vector finite element, this paper deduces the basic formula of triangular DKT thin plate element, and expounds in detail the process of dealing with the displacement of the plane and outer rigid body of the thin plate element by reverse motion so as to obtain the pure deformation displacement of the element node.At the same time, the mass matrix and inertia matrix of particle, the numerical integral and interpolation method of stress calculation,A reasonable and feasible way to deal with the problems of time step size and damping parameter is put forward.On this basis, the calculation and analysis program of thin plate element is worked out, and an example is given to verify it.The numerical examples show that the finite element finite element program can be used to perform the static and dynamic analysis of the plate structure, and the correctness of the theoretical derivation and the reliability of the analysis program are verified.The results of this paper lay the necessary foundation for further establishing the theory of thin shell element of vector finite element.
【作者单位】：浙江大学空间结构研究中心;浙江省建筑设计研究院;
【基金】：国家自然科学基金项目(51378459,50778159) 浙江省重点科技创新团队资助项目(2010R50034)
【分类号】：TU311

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