Reissner板断裂问题的半解析等几何分析方法  

A semi-analytical isogeometric analysis for fracture of Reissner plates

作　　者：官高菲 张滢睿 余雄 徐新生[1] GUAN Gao-fei;ZHANG Ying-rui;YU Xiong;XU Xin-sheng(School of Mechanics and Aerospace Engineering,State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学力学与航空航天学院工业装备结构分析优化与CAE软件全国重点实验室,大连116024

出　　处：《计算力学学报》2025年第1期53-60,共8页Chinese Journal of Computational Mechanics

基　　金：航空科学基金(2018ZC63003)资助项目。

摘　　要：板结构是工程中一类重要的基本构件,但是由于材料或者工艺的影响,其在制造过程中难免会产生不同程度的缺陷,从而在服役环境下逐渐演变成宏观裂纹,导致断裂事故。现阶段板结构断裂分析的方法主要分为解析和数值方法两类。解析方法大多仅适用于无限大或半无限大结构以及简单边界条件情况,数值方法需在裂尖附近区域划分高密度的网格,并且无法准确给出结构的断裂参数,需要复杂的后处理程序。为解决上述问题,本文针对含裂纹Reissner板的弯曲断裂问题,提出一种高精度的半解析等几何分析方法。首先,求解含裂纹Reissner板裂纹尖端附近的广义位移(挠度和转角)和广义应力(弯矩和剪力)的级数展开解。其次,将整板的等几何模型划分为两类区域,即裂尖附近的奇异区和不包含裂尖的非奇异区。在奇异区内,利用获得的级数解进行节点未知量变换,将该区域内大量的节点未知量转换为少量的级数解待定系数,而在非奇异区内保持节点未知量不变,从而获得含裂纹Reissner板弯曲断裂分析的半解析等几何分析方法计算列式,直接获得裂纹尖端附近奇异应力场和对应的应力强度因子的显式表达式。数值算例验证了该方法的精确性,并分析了相关影响参数对应力强度因子的作用规律。A plate is an important fundamental component in engineering.Due to the influence of materials or manufacturing techniques,some defects are inevitable during the manufacturing process,which gradually develop into macroscopic cracks in service,leading to fracture.At present,the methods for fracture analysis of plates are mainly divided into two categories:analytical and numerical methods.Most analytical methods are only applicable to infinite or semi-infinite structures and simple boundary conditions.Numerical methods require high-density grids in the vicinity of the crack tip,and cannot accurately predict fracture parameters of the structure,requiring complex post-processing procedures.To solve the above issues,this paper proposes a high-precision semi-analytical isogeometric analysis(IGA)for bending fracture problems of cracked Reissner plates.Firstly,the series expansions solutions of generalized displacements(deflections and rotation angles)and generalized stresses(bending moments and shear forces)near the crack tip of a cracked Reissner plate are obtained.Secondly,the isogeometric model of the overall plate is divided into two regions:singular regions near the crack tip and non-singular region without the crack tip.In the singular region,the obtained series solutions are employed to change the large number of nodal unknowns into a small number of undetermined coefficients.However,in the non-singular region,the nodal unknowns remain unchanged.Thus,the formulation of the semi-analytical IGA for bending fracture problems of cracked Reissner plates is obtained,and explicit expressions of singular stress fields and corresponding stress intensity factors(SIFs)are derived simultaneously.Numerical examples verify the accuracy of the present approach and effects of influencing parameters on SIFs are discussed too.

关 键 词：含裂纹Reissner板 弯曲断裂 半解析等几何方法 应力强度因子 解析解 

分 类 号：O346.1[理学—固体力学]