在前期研究的直梁和曲梁分析新方法的基础上,提出了基于独立覆盖流形法的曲壳分析方法。采用实体分析模式,只需使多项式覆盖函数中的某些项不参与计算,就能准确模拟三维平板和曲壳的Reissner-Mindlin假设,从而避免了推导曲壳控制方程及相应数值计算公式的复杂性。借助随中面参数方程变化的局部坐标系,并计算该坐标系的局部坐标和方向余弦关于整体坐标的导数,就能实现精确几何描述下的曲壳分析。给出了具体计算过程,包括刚度矩阵积分方式,以及相关的曲壳几何计算公式。通过球面壳和平板算例,验证了方法的收敛性。最后,结合前期的二维直梁和曲梁研究,以及本文的三维曲壳和平板研究,总结了基于独立覆盖流形法的梁板壳分析新方法的特点和优势,特别是彻底解决了自锁问题。
Abstract
On the basis of the new methods for straight and curved beam analysis proposed in previous study, a Numerical Manifold Method for curved shell analysis based on independent covers is presented. In the mode of solid analysis, the Reissner-Mindlin assumption for 3D plate and curved shells is strictly simulated just by eliminating some terms of polynomial cover functions. And therefore the complexity of the derivation for the governing equation of curved shells and the corresponding numerical calculation formula is avoided. By means of the local coordinate system varying with the middle layer of the shell described by parametric equations, and also by calculating the derivatives of the local coordinates and the direction cosines with respect to the global coordinates, curved shell analysis based on exact geometric description can be realized. The detailed procedures including the integrating method and geometric formula are given. Examples of a spherical shell and a plate are used to verify the convergence of the method. In the end, the characteristics and advantages of the new method for beam, plate and shell analysis are summarized, including the complete solution for locking problem, via previous studies of 2D straight and curved beams as well as the study of 3D plates and curved shells in this paper.
关键词
曲壳 /
精确几何 /
数值流形方法 /
独立覆盖 /
梁板壳分析
Key words
curved shell /
exact geometry /
Numerical Manifold Method (NMM) /
independent covers /
beam, plate and shell analysis
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基金
国家自然科学基金项目(51509020);中央级公益性科研院所基本科研业务费项目(CKSF2016022/CL, CKSF2016266/CL)
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