夹芯梁结构有效性能的多尺度变分渐近模型  

A multi-scale variational asymptotic model for the effective performance of sandwich beams

作　　者：罗丹 钟轶峰[1,2] 李帛书[1,2] 李奕豪 LUO Dan;ZHONG Yifeng;LI Boshu;LI Yihao(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：《复合材料学报》2019年第4期1029-1035,共7页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金(51778088);重庆市自然科学基金项目(cstc2016jcyjA0426;cstc2017jcyjBX00036)

摘　　要：为有效分析夹芯梁结构性能,基于变分渐近法建立多尺度变分渐近模型。首先基于旋转张量分解概念建立三维夹芯梁几何非线性的能量方程;利用梁结构细长和非均质较小的特征,将三维夹芯梁结构各向异性、非均质问题严格分解为宏观层面的梁轴线的一维非线性分析和细观层面的单胞本构分析。基于最小势能原理,通过对单胞应变能泛函变分主导项最小化得到有效属性和波动函数解,代入梁的一维模型进行全局非线性响应分析。利用得到的全局响应、波动函数解重构局部场。由于变分特性,构建多尺度模型可以很容易通过有限元数值实现。通过三类夹芯梁结构算例表明:构建模型得到的全局位移和局部应力场与三维有限元具有很好的一致性,但计算成本和建模工作量明显减少,为结构设计人员在初始设计阶段对夹芯梁结构性能评估提供了一种简洁的途径。In order to effectively analyze the properties of sandwich beams,a multi-scale variational asymptotic model was established based on the variational asymptotic method.Firstly,the geometrical nonlinear equations of the original 3D sandwich beam were established based on the concept of rotation tensor decomposition.By using the characteristics of slender and heterogeneous,the anisotropy and heterogeneity problems of sandwich beams were strictly decomposed into 1D nonlinear analysis along the beam reference line at the macroscopic level and unit cell constitutive analysis at the microscopic level.Based on the principle of minimum potential energy,the effective stiffness and fluctuation function solution were obtained by minimizing the variational leading items in the strain energy functional,and substituted into the 1D model of beam to perform the global response analysis.Then,the resulting global response and fluctuation function solution were used to recover the local fields.Due to the variational characteristics,the constructed multiscale model can be easily numerical implemented by finite element method.The example results of three kinds of sandwich beams show that the global displacements and local stress fields obtained by the constructed model are in good agreement with the 3D finite element method,but the computational cost and modeling workload are significantly reduced,which provides a simple way for the structural designer to evaluate the performance of the sandwich beams at the initial design stage.

关 键 词：夹芯梁 几何非线性 本构关系 变分渐近法 模型 

分 类 号：TB330.1[一般工业技术—材料科学与工程]