分析层合材料槽孔应力的新型特殊层合杂交应力元  

A new special multilayer hybrid stress finite element for stress analyses around notches in laminated composites

作　　者：杨庆平[1] 王安平[2] 田宗漱 

机构地区：[1]南京理工大学能源与动力工程学院,南京210094 [2]中国科学院空间应用工程与技术中心,北京100094 [3]中国科学院大学,北京100080

出　　处：《船舶力学》2018年第1期61-72,共12页Journal of Ship Mechanics

摘　　要：基于一种新的非匀质材料的扩展Hellinger-Reissner原理,及当一个单元域划分为不同材料特性子域,其元内位移及应力沿子域表面不连续时有限元刚度列式的简便方法,建立了新的具有一个无外力圆柱表面层合杂交应力元。单元各层内以整体坐标表示并以自然坐标插值的应力场,通过以非协调位移为权函数使齐次平衡方程变分满足的理性方法得到,此应力场同时严格满足给定圆柱面上无外力条件。单元间及各层间位移连续条件分别通过Largrange乘子进行了松弛。数值算例表明:在相当粗的网格下,新型元可提供较一般假定位移元及一般假定应力元更为准确的槽孔层板孔边应力。A new assumed stress hybrid multilayer element with a traction-free cylindrical surface was developed based on an extended Hellinger-Reissner variational principle which provides a convenient procedure for deriving the element stiffness matrix of a non-homogeneous element that can be subdivided into regions of different material properties.In such case,some of stress components along the interface and the displacement across the interface may become discontinuous.The stresses of each layer are interpolated by the natural coordinates and are obtained by the use of internal displacement as weight function to impose the equilibrium conditions in a variational sense.The stresses also satisfy the traction-free conditions over the cylindrical surface exactly.The continuous conditions of the displacement between the layers and the elements are relaxed by using Lagrange multipliers respectively.Numerical results show that the present elements are more efficiency than the ordinary assumed stress hybrid elements and the conventional assumed displacement elements for analyzing laminated composites with holes when very coarse meshes are used.

关 键 词：扩展的Hellinger-Reissner原理 圆柱形槽孔 特殊层合杂交应力元 三维应力分析 

分 类 号：O242.21[理学—计算数学] TB330.1[理学—数学]