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Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads

均匀热载荷和机械载荷共同作用下具有温度依赖材料特性的层合梁的弹性力学解

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Abstract

An exact solution for simply-supported laminated beams with material properties variable with temperature under a combination of uniform thermo-load and mechanical loads was investigated, based on the two-dimensional (2-D) thermo-elasticity theory. Firstly, the beam was divided into a series of layers with uniform material properties along the interfaces of the beam. The uniform thermo-load acted on each layer was transformed into a combination of the normal surface forces acted at the two ends and the transverse thermo-load. Secondly, the state space method was employed to obtain the general solutions of displacements and stresses in an arbitrary layer. Thirdly, based on the interfacial continuity conditions between adjacent layers, the relations of displacement and stress components between the top and bottom layers of the beam were recursively derived by use of the transfer-matrix method. The unknowns in the solutions can be solved by the mechanical loads acted on the top and bottom surfaces. The convergence of the present solutions was checked. The comparative study of the present solutions with the Timoshenko’s solutions and the finite element (FE) solutions was carried out. The effects of material properties variable with temperature on the thermo-elastic behavior of laminated beams were discussed in detail.

摘要

本文基于二维热弹性力学理论, 考虑材料物性参数的温度依赖性, 研究了均匀热荷载和机械荷载联合作用下简支叠层梁的精确解。 首先将叠层梁沿各组分材料的界面划分为一系列单层, 以保证每一单层材料的物理性能均匀。 利用等效模型, 将作用在单层内的均匀热荷载转化为作用于层两端的法向面力和横向热荷载。 其次, 利用状态空间法求得任一层内位移和应力的一般解。 第三, 根据相邻层界面的连续性条件, 使用传递矩阵法递推得到顶层和底层位移和应力的关系, 由作用于梁上下表面的机械荷载确定未知系数。 研究了本文解的收敛性, 并给出了与 Timoshenko 的解和有限元解的比较。 最后通过数值算例, 详细分析了随温度变化的材料物理参数对叠层梁力学性能的影响。

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Authors and Affiliations

  1. College of Civil Engineering, Nanjing Tech University, Nanjing, 211816, China

    Zhong Zhang  (张忠), Ding Zhou  (周叮), Rui-li Huo  (霍瑞丽) & Xiu-li Xu  (徐秀丽)

  2. Flood Control and Drought Relief Rescue Center of Jiangsu Province, Nanjing, 211500, China

    Wen-ling Zhou  (周文领)

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  1. Zhong Zhang  (张忠)
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  3. Ding Zhou  (周叮)
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Correspondence to Ding Zhou  (周叮).

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Foundation item: Project(2012CB026205) supported by the National Basic Research Program of China; Projects(51608264, 51778289) supported by the National Natural Science Foundation of China; Project(2014Y01) supported by the Transportation Science and Technology Project of Jiangsu Province, China

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Zhang, Z., Zhou, Wl., Zhou, D. et al. Elasticity solution of laminated beams with temperature-dependent material properties under a combination of uniform thermo-load and mechanical loads. J. Cent. South Univ. 25, 2537–2549 (2018). https://doi.org/10.1007/s11771-018-3934-1

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