FRP层合板自由边效应的变分渐近降维模型  

A VARIATIONAL ASYMPTOTIC DIMENSIONAL-REDUCED MODEL FOR FREE-EDGE EFFECT OF FRP LAMINATES

作　　者：王鹏[1,2] 钟轶峰[1,2] 罗丹[1,2] 彭啸 WANG Peng;ZHONG Yi-feng;LUO Dan;PENG Xiao(School of Civil Engineering,Chongqing University,Chongqing 400045,China;Key Laboratory of New Technology for Construction of Cities in Mountain Area(Chongqing University),Ministry of Education,Chongqing 400045,China)

机构地区：[1]重庆大学土木工程学院,重庆400045 [2]山地城镇建设与新技术教育部重点实验室(重庆大学),重庆400045

出　　处：《工程力学》2020年第S01期157-163,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(51778088);重庆市自然科学基金项目(cstc2017jcyjBX00036)。

摘　　要：为准确预测因相邻层弹性性能不同产生的自由边应力,避免分层或横向开裂等过早破坏,基于变分渐近法构建FRP层合板的多尺度模型。利用板厚宽比很小的特点,严格将原三维各向异性弹性问题分解为代表单胞分析和二维板宏观分析。前者可提供板宏观分析所需的本构关系和三维重构关系。基于最小势能原理,通过对二维板能量泛函中主导变分项的渐近分析,得到表征板几何非线性的系列波动函数解;通过本构关系和求解得到的翘曲函数解重构自由边附近的局部三维应力场分布。通过拉伸、弯曲和扭矩共同作用下的对称铺设层合板算例表明:构建降维模型可准确预测沿自由边厚度方向和层间界面的应力分布,且计算效率大为提高,为结构设计人员在初步设计阶段对FRP层合板性能评估提供了一种简洁的途径。In order to accurately predict the free-edge stress caused by the different elasticity of adjacent layers and to avoid premature delamination or transverse cracking,a multiscale model for FRP laminates was established based on the variational asymptotic method.The original 3D anisotropic elastic problem was strictly decomposed into the unit cell analysis and the macroscopic analysis of 2D plate by taking advantage of the thickness to width ratio.The former could provide the constitutive relationship and 3D recovery relationship needed for macroscopic plate analysis.Based on the principle of minimum potential energy,a series of solution of fluctuation functions were obtained by asymptotic analysis of the leading variational items in the energy functional of 2D plates.Finally,the local 3D stress field distribution near the free-edge was recovered by using the constitutive relation and the obtained warping functions.Numerical examples of symmetrical laminates subjected to tensile,bending and torsion show that the proposed dimensional reduced model can accurately predict the through-the-thickness stress distribution along the free-edge and the interface interlaminar stress distribution,and the computational efficiency can be greatly improved.It can provide a simple way for the structural designer to evaluate the performance of the FRP laminates at the initial design stage.

关 键 词：FRP层合板 自由边效应 变分渐近法 降维模型 本构关系 

分 类 号：TU31[建筑科学—结构工程] TB332[一般工业技术—材料科学与工程]