六参数一般约束FGM夹层梁的弯曲特性  

BENDING BEHAVIOR OF FUNCTIONALLY GRADED MATERIAL SANDWICH BEAMS UNDER GENERALLY RESTRAINED BOUNDARY CONDITIONS WITH SIX-PARAMETER

作　　者：蒲育 周凤玺[2] 史拴虎 滕兆春[4] 任永忠 刘君 PU Yu;ZHOU Feng-xi;SHI Shuan-hu;TENG Zhao-chun;REN Yong-zhong;LIU Jun(College of Civil Engineering,Lanzhou Institute of Technology,Lanzhou,Gansu 730050,China;School of Civil Engineering,Lanzhou University of Technology,Lanzhou,Gansu 730050,China;School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou,Gansu 730070,China;School of Science,Lanzhou University of Technology,Lanzhou,Gansu 730050,China)

机构地区：[1]兰州工业学院土木工程学院,甘肃兰州730050 [2]兰州理工大学土木工程学院,甘肃兰州730050 [3]兰州交通大学机电工程学院,甘肃兰州730070 [4]兰州理工大学理学院,甘肃兰州730050

出　　处：《工程力学》2025年第3期262-272,共11页Engineering Mechanics

基　　金：国家自然科学基金项目(51978320,11962016);甘肃省自然科学基金项目(20JR5RA379);甘肃省青年博士基金项目(2023QB-050);甘肃省青年科技基金项目(21JR1RA251)。

摘　　要：构建六参数模型研究功能梯度材料(Functionally Graded Material,FGM)夹层梁在一般约束下的静力弯曲特性。考虑由上面板层、夹芯层和下面板层组成三明治梁,其中芯层分别为陶瓷单相(硬芯)、陶瓷-金属复合(FGM芯)、金属单相(软芯)材料这三类夹芯,基于Voigt混合幂率模型来表征FGM层的材料属性沿梁厚的梯度连续变化,由横向、轴向和转动这三组线性弹簧支撑来模拟梁两端的一般弹性约束。基于Timoshenko梁理论和能量变分原理建立FGM夹层梁静力弯曲的控制微分方程并推导出一般弹性约束边界方程;采用位移法求解问题,通过编写微分求积法的MATLAB计算程序获得结构的弯曲响应;通过算例着重分析约束弹簧刚度、层厚比、夹芯类型、材料组分梯度指标、跨厚比等诸多因素对FGM夹层梁静态弯曲输出响应特性的影响。研究表明:该分析方法切实可行,数值结果可靠精确;与各种经典梁约束相比,该六参数约束模型具有明显的普适优越性;该结果可供FGM夹层梁的强度和刚度设计提供理论依据和参考。A constraint model with six-parameter is presented to study the static bending behavior of functionally graded material(FGM)sandwich beams with general boundary conditions.The beams are assumed to be composed of an upper panel layer,a sandwich layer and a lower panel layer,in which the core layers are ceramic single-phase(hard core),ceramic-metal composite(FGM core)and metal single-phase(soft core)materials,respectively.The effective material properties for FGM layer across the depth of sandwich beams are described by the mixture power-law distributions according to Voigt model.The general elastic constraints at both ends of a beam is simulated by two sets of translational springs and one set of rotational springs.Based on Timoshenko beam theory,the governing differential equations and general elastic boundary conditions can be obtained by energy variational principle for the structure.The displacement method is used to solve the problem,and the bending response of the structure is obtained by writing the MATLAB calculation program of differential quadrature method.The significant influences of constraining spring stiffness,layer thickness ratio,sandwich type,material graded index,and slenderness ratios on the static bending characteristic of FGM sandwich beams are mainly discussed by several numerical examples.The results show that the method is feasible and the numerical results are reliable and accurate.Moreover,the universality and superiority for the constraint model with six-parameter are demonstrated by comparing with those of various classical boundary conditions.This research can provide theoretical basis and reference for both strength and stiffness design of FGM sandwich beam.

关 键 词：功能梯度材料 夹层梁 一般弹性约束 静力弯曲 微分求积法 

分 类 号：O343[理学—固体力学] TB34[理学—力学]