基于精确几何的曲梁分析新方法

摘要

On the basis of straight beam analysis using Numerical Manifold Method (NMM) based on independent covers proposed in previous study,a novel method for curved beam analysis is presented.In the mode of solid anal ysis,the fundamental assumptions of beams are simulated by only eliminating some terms of polynomial cover functions.And therefore the relative complexity of the derivation procedures for the governing equation and the corresponding numerical calculation formula of curved beam is avoided.By means of the local coordinate system varying with the middle plane of the beam described by parametric equations,and in subsequence by calculating the derivatives of the local coordinates and the direction cosines with respect to the global coordinates,curved beam analysis based on exact geometric description can be realized.Two examples are given to verify the feasibility of the method:one is a circular curved beam with constant curvature,and the other is an ellipse curved beam with variable curvature.The proposed method provides a new way for the analysis of curved beams and further study of curved shells.It is also a new approach for geometric shape preserving in addition to Isogeometric Analysis (IGA) method.%在前期研究的直梁的独立覆盖分析方法基础上,提出曲梁的独立覆盖分析方法.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,就能模拟梁的基本假设,从而避免了推导曲梁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梁分析.采用常曲率的一段圆形曲梁和变曲率的一段椭圆形曲梁的算例,验证了方法的可行性.研究方法为曲梁和下一步的曲壳分析提供了全新的途径,也是除了等几何分析方法之外的实现几何保形性的新方式.