两节点十六自由度新型夹层梁单元位移分析  

Displacement of a New Type of Sandwich Beam Element with Two Nodes and Sixteen Degrees of Freedom

作　　者：吴建强 谢素璞 董继蕾 卢小雨 Wu Jianqiang;Xie Supu;Dong Jilei;Lu Xiaoyu(School of Mechanics and Optoelectronic Physics,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学力学与光电物理学院,安徽淮南232001

出　　处：《黑河学院学报》2023年第4期179-183,共5页Journal of Heihe University

基　　金：安徽省质量工程项目“理论力学线上线下混合课程”(2020xsxxkc148);安徽省质量工程项目“理论力学教学示范课”(2020sjjxsfk0738);安徽理工大学研究生一流课程“弹塑性力学”;安徽理工大学重点教学研究项目“材料力学”(2019jyxm075)。

摘　　要：传统夹层梁理论认为梁在变形过程中,厚度方向尺寸保持不变;同时结构发生平面弯曲时平截面假设成立。当用该理论分析短、粗或软夹层梁时,误差较大。以一种两节点、十六自由度梁单元,用于解决上述问题。该单元摒弃传统的平截面假设,同时在计算过程中考虑梁在横向的可压缩性。将梁沿厚度方向视为三层,上下层使用传统梁单元理论建模,每层每节点三自由度;中间层视为平面问题,每节点两自由度。创建物理方程、几何方程及详细推导过程,利用最小势能原理得到单元体平衡方程。The traditional theory of sandwich beams holds that the thickness of a beam remains constant during deformation,and that the assumption of plane section is valid when the structure is curved in plane.However,big measurement errors exist,when using the theory to analyze short,thick or soft sandwich beams.Thus,the beam element characterized by two nodes and sixteen degrees of freedom gets applied to solve the problem,because it can disregard the plane cross-section assumption and take into account the compressibility of composite beams in lateral direction.The beam is divided into three layers along the thickness direction:the upper and lower layers are modeled using the traditional beam element theory with each layer having three degrees of freedom per node;the middle layer is regarded as a plane with two degrees of freedom per node.The equilibrium equation of element body is derived using the minimum potential energy principle and with the help of detailed derivation process,like creating physical equations and geometric equations.

关 键 词：夹层梁 软夹层 十六自由度 平截面假设 

分 类 号：O242[理学—计算数学] O39[理学—数学]