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第36卷第2期结构工程师¥。1.36，心.2 2020年4 月Structural Engineers Apr.2020考虑剪切变形的变截面欧拉梁单元刚度矩阵
张军锋p李杰1尹会娜1陈淮1叶雨山2
lembiof(1.郑州大学土木工程学院，郑州450001; 2.中国建筑第七工程局有限公司，郑州450001)试模
摘要ANSYS中的Beam44单元是考虑剪切变形的变截面欧拉梁单元，为明确其单元刚度矩阵推导 方法，以形函数为基础，根据虚功原理，系统给出了考虑剪切变形的变截面欧拉梁单元刚度矩阵推导过 程。以矩形、圆形、圆环和箱形截面梁为例，经与ANSYS中Beam44单元刚度矩阵对比，明确了其单元刚 度矩阵的推导方法、相关假定和使用要求。研究发现：变截面欧拉梁因形函数本身的近似性和截面参数 随截面位置变化的复杂性，难以给出普适性的单元刚度矩阵理论表达式。ANSYS对Beam44单刚矩阵 推导时，采用了以下3种处理方式以简化计算：采用与等截面梁相同的厄米特形函数，在纯弯模式单刚 去巨阵的积分计算中对几何矩阵和截面参数分别积分，不考虑截面剪切系数随截面位置的变化，由此所 得单刚矩阵形式与等截面梁Bearn4 —致_ANSYS对Beam44单元所给等效截面参数，如面积、抗扭惯矩 和抗弯惯矩的表达式，源于梁单元两端截面形状为相似形且截面尺寸随杆件线性梯度变化的情况，应用 于其他情况时会与理论值有一定偏差.由此可知，在使用Beam44单元时为提高计算精度，应尽量减小 单元长度来控制两端截面参数比值，同时对剪切系数宜取单元中截面的/c值或左右截面的均值
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关键词变截面梁，欧拉梁，单元刚度矩阵，剪切变形，等效截面参数mushroom
Element Stiffness Matrix of Tapered Euler Beam Element
Including Shear Deformation
唐顿庄园第三季圣诞特辑ZHANG Junfeng1'LI Jie1YIN Huina1CHEN Huai1YE Yushan2
(1.School of Civil Engineering, Zhengzhou University, Zhengzhou 450001, China；
2.China Construction Seventh Engineering Division CORP.LTD, Zhengzhou 450001, China)
Abstract Element Beam44 in ANSYS is a tapered Euler beam element including shear deformation and the study was initiated for its element stiffness matrix.The derivation process was prented bad on the shape functions and the principle of minimum potential energy.Then the theoretical element stiffness matrixes were compared with tho obtained from Beam44, taking four tapered-ction beams with rectangular,circular, tubular and box ctions as examples.Following the comparison，the derivation method,hypothes and application suggestions of element Beam44 were deduced.lt was found that the universal expression of element stiffness matrix of tapered Euler beam element couldn’t be obtained theoretically for two reasons.First，variations of ction paramet
ers along element are complicated,even couldn’t be expresd by formula; cond,the exact shape functions are also not available.The element stiffness matrix of Beam44 shares the same form of that of Beam4 by virtue of three simplifications：employing the shape functions of constant-ction Euler beam element directly;splitting the single integration of element stiffness matrix for pure bending m ode into tw o integrations;and regarding the shear factor k as a constant.The equivalent ction parameters of Beam44such as area,torsion and bending moments of inertia are just obtained from a tapered beam element who tw o end-ctions are proportional,and would show some differences for other tapered beam elements.*gre高分作文
收稿日期：2018-12-24
mature woman基金项目：国家自然科学基金项目（51508523)；河南省科技厅科技攻关项目（192102310484)
李阳口语宝典*联系作者：张军锋（丨983->，男，河南平顶山人，副教授，博士，从事结构和桥梁抗风研究E-mail:**********************简体翻译繁体
