基于变分渐近法的双周期梯形波纹板等效模型
时间：2021-01-30 08:04:09 来源：达达文档网 本文已影响 人 
邓兵 钟轶峰 席森彪 禹辽
摘要：雙周期梯形波纹板是沿两个平面方向均呈周期性梯形波纹变化的新型轻质结构，现阶段对其力学性能与结构参数之间关系的研究较少，限制了该结构的推广应用。针对该问题，以凸起为中心的典型代表单元单胞为研究对象，利用变分渐近法建立单胞等效刚度的数值计算模型。再通过均匀化技术将双周期梯形波纹板转换为具有相同刚度特性的正交异性板进行分析。基于该方法分别计算出不同结构参数下的等效刚度、宏观变形和屈曲模态，通过与三维有限元模拟结果对比验证等效模型的精确性。计算结果表明：由于形貌变化，双周期梯形波纹板的等效刚度较平板的拉伸刚度降低，弯曲刚度增加;随着凸起间距的增大和板高度的减小，波纹板的拉伸刚度逐渐增大，弯曲刚度逐渐降低;而随着板厚度和腰部长度的增加，弯曲刚度呈上升的趋势。构建模型适用于波纹周期远小于结构尺寸的情况，由于等效板模型的近似能量与原三维波纹板能量尽可能接近（通过对能量泛函变分主导项的渐近扩展分析加以保证），可用于计算不同材料波纹板等效弯矩和等效最大拉压应力等，能有效减少计算量和节省计算资源。
关键词：变分渐近法;梯形波纹板;等效刚度;等效模型;降维分析
中图分类号：TU501;TB333 文献标志码：A 文章编号：20966717（2020）04017510
收稿日期：20191124
基金项目：国家自然科学基金（51778088）;重庆市自然科学基金 （cstc2017jcyjBX00036）
作者简介：邓兵（1993 ），男，主要从事轻质高强结构与材料研究，Email：
20171602025t@cqu.edu.cn。
钟轶峰（通信作者），男，教授，博士生导师，Email：
zhongjy58@sina.com。
Received：20191124
Foundation items：National Natural Science Foundation of China （No. 51778088）; Chongqing Natural Science Foundation （No. cstc2017jcyjBX00036）
Author brief：Deng Bing（1993 ）， main research interests：
lightweight and high strength structure and materials， Email：
20171602025t @cqu.edu.cn.
Zhong Yifeng（corresponding author）， professor， doctorial supervisor， Email：
zhongjy58@sina.com.
Equivalent model of biperiodic trapezoidal corrugated plate based on variational asymptotic method
Deng Bing， Zhong Yifeng， Xi Senbiao， Yu Liao
（School of Civil Engineering; Key Laboratory of New Technology for Construction of Cities in Mountain Area， Ministry of Education， Chongqing University， Chongqing 400045， P.R. China）
Abstract：
The biperiodic trapezoidal corrugated plate is a new type of lightweight structure with periodic trapezoidal corrugated changes along two plane directions. At present， there is little research on the relationship between its mechanical properties and structural parameters， limiting the popularization and application of this structure. In this article， a numerical model of the represent element （or called unit cell） is established by using the variational asymptotic method to calculate the equivalent stiffness. Then， the biperiodic trapezoidal corrugated plate is converted to orthotropic plate with the same stiffness characteristics by homogenization technology. Based on this method， the equivalent stiffness with different structural parameters， global deformation and buckling modes are calculated， and the accuracy of the equivalent model is verified by comparing with the threedimensional finite element simulation results. The results show that the equivalent stiffness of the biperiodic trapezoidal corrugated plate is lower than that of the plate due to the change of the shape， and the bending stiffness is increased. The tensile stiffness increase and the bending stiffness decrease with increasing interval length and decreasing plate height. While with the increase of plate thickness and web length， the bending stiffness shows an upward trend. The constructed model is suitable for the case that the period of corrugation is far less than the structure size. The approximate energy of the equivalent plate model is as close as that of the original threedimensional corrugation plate， which is guaranteed by the asymptotic expansion analysis of the leading terms of energy functional. The equivalent plate model can be used to calculate the equivalent bending moment and the equivalent maximum tensile/compressive stress of corrugated plates with different material properties， which can effectively reduce the calculation amount and save the calculation resources.
Keywords：variational asymptotic method; trapezoidal corrugated panel; equivalent stiffness; equivalent model; dimensional reduction analysis
