复合材料层合结构锯齿型高阶厚板理论

New composite structures are widely used in aerospace engineering. In order to improve efficiency of such structures, the accurate theories are required to reasonably analyze the mechanical behaviors of these structures. Due to their accuracy and efficiency, the zig-zag theories are widely studied and used. In the latest study, however, we found that the maximum percentage errors of previous zig-zag theories are more than 50% for mechanical analysis of thick composite structures. As these zig-zag theories are used to analyze composite structures, incorrect conclusions may be drawn, which will mislead design of engineering structures. Therefore, following contents will be studied: 1) The reasons of inaccuracy of zig-zag theories will be studied in this work. Moreover, a C0-type zig-zag higher-order theory is to be developed for accurate analysis of thick composite plates. 2) A C0-type higher-order zig-zag theory is proposed for thermomechanical analysis of laminated composite structures. If transverse displacement field is assumed to be smooth parabolic distribution through the thickness, the derivarives of transverse displacement will be involved in the displacement fields of the previous zig-zag theories, which will be solved in this project. The proposed model is extended to study the effects of temperature on the mechanical behaviors of laminated composite structures. 3) A C0-type zig-zag higher-order theory will be developed to accurately predict the mechanical and electric behaviors coupled of piezoelectric composite structures. In the proposed model, the effects of electric field on transverse shear stresses will be taken into account as continuity conditions of interlaminar stresses are used. If the project is to be finished, the C0-type zig-zag higher-order theories can be further improved to accuately analyze thick composite structures.

新复合材料结构广泛应用于航空航天工程，对高阶理论精度提出新的要求，需要准确高效的理论对其精细分析以提高其结构效率。由于兼具精度和效率优势，锯齿理论被广泛研究和应用。然而，我们最新研究发现，对于较厚复合材料层合结构静力分析，已有锯齿理论最大误差超过50%。基于这些锯齿理论分析较厚复合材料工程结构问题，可能得出错误结论误导工程结构设计。基于此，本项目开展如下研究：1）研究已有锯齿理论高误差原因，并发展能准确分析复合材料层合结构弯曲问题的C0型锯齿厚板理论；2）发展适于分析复合材料热力耦合问题的C0型锯齿高阶理论。解决发展锯齿型高阶理论时，如果横法向位移沿厚度方向非线性分布，横法向位移高阶参数导数进入位移场的关键问题。研究温度对复合材料层合结构力学性能影响；3）建立能准确分析力电耦合作用下压电层合结构的C0型锯齿高阶理论。本项目将完善C0型锯齿高阶厚板理论以适应较厚复合材料结构精细分析。

新复合材料结构广泛应用于航空航天工程，对高阶理论精度提出新的要求，需要准确高效的理论对其精细分析以提高其结构效率。由于兼具精度和效率优势，锯齿理论被广泛研究和应用。然而，我们最新研究发现，对于较厚复合材料层合结构静力分析，已有锯齿理论最大误差超过50%。基于这些锯齿理论分析较厚复合材料工程结构问题，可能得出错误结论误导工程结构设计。基于此，本项目开展如下研究：1）研究已有锯齿理论高误差原因，并发展了能准确分析复合材料层合结构弯曲问题的C0型锯齿厚板理论；2）发展适于分析复合材料热力耦合问题的C0型锯齿高阶理论。解决发展锯齿型高阶理论时，如果横法向位移沿厚度方向非线性分布，横法向位移高阶参数导数进入位移场的关键问题。研究温度对复合材料层合结构力学性能影响；3）发展了预先满足层间应力连续并考虑横法向应变的高阶整体-局局部理论，构造三节点三角形单元分析在湿热力载荷作用下复合材料力学行为，并研究湿热膨胀系数对湿热行为影响；4）发展了考虑横法向热应变的五自由度高阶理论分析功能梯度板热力耦合问题。发展的理论模型虽然考虑了横法向应变，但不增加额外位移变量。进一步发展了适于分析复合材料热力耦合问题的五自由度高阶理论；5）发展了新预先满足自由表面条件的正弦高阶理论。基于发展的新正弦高阶理论，分析了功能梯度板和复合材料板热力耦合问题。本项目将完善高阶厚板理论以适应较厚复合材料结构精细分析。