Timoshenko梁的变形场重构及传感器位置优化

针对KO位移理论仅适用于重构单方向位移场问题,提出一种适用于六自由度位移场重构的新方法,称之为"多维积分法"。依据Timoshenko梁的静力学平衡方程,建立了位移、转角与外载荷之间的数学模型。并针对不同的外载荷环境,推导出相应的应变场函数和位移场函数,建立了表面应变与截面应变之间的转换关系。为了提升该方法的容差性,以重构位移场的精确性和稳定性为优化目标,建立了关于应变传感器位置的多目标粒子群优化模型。以机翼框架为试验平台,对其进行有限元分析,建立优化目标模型,给出优化后的应变传感器的布置方案。并以此方案为依据,分别利用有限元分析结果和实测梁表面应变值来重构位移场。试验结果表明,提出的"多维积分法"在两种不同形式的外载荷作用下均呈现出较高的重构精度。

Deformation Field Reconstruction of Timoshenko Beam and Optimization of Sensor Placement

For the problem that KO displacement theory can be only applicable to the reconstruction of the one-dimensional deformation field, a new method is presented for reconstructing six degree of freedom displacement field, which is known as “multidimensional integration method”. According to the static equilibrium equation of Timoshenko beam, the mathematical model is established between displacement, rotation and external load. And the corresponding strain field functions and displacement field functions are deduced and the translation relation between section strain and surface strain is established for different external load. In order to improve the tolerance of the presented method, the accuracy and the robustness of the reconstruction displacement are taken as the optimization objective function to established multi-objective particle swarm optimization model for strain sensor placement. The wing frame is taken as the experimental platform to perform the finite element analysis, establish optimization objection model, and give the optimized strain sensor distribution scheme. And on the basis of this scheme, the displacement field is reconstructed by using the results of finite element analysis and the measured surface strain. The experimental results show that the proposed “dimensional integration method” presents a high reconstruction accuracy under the action of two different forms of external loads.