关键词: 曲梁, 精确几何, 数值流形方法, 独立覆盖, 梁板壳分析

Abstract: On the basis of straight beam analysis using Numerical Manifold Method (NMM) based on independentcovers proposed in previous study, a novel method for curved beam analysis is presented. In the mode of solid analysis, 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.

Key words: curved beam, exact geometry, Numerical Manifold Method (NMM), independent covers, beam, plate and shell analysis