预先满足层间应力连续的C0型整体-局部高阶理论

The C1-type global-local higher-order theories satisfying continuity conditions of interlaminar stresses are successfully used to construct lower-order elements whereas it is difficult to construct the higher-order displacement elements in terms of these theories. Up to date, the higher-order displacement elements satisfying continuity conditions of interlaminar stresses have never been reported in the published papers. To improve the present higher-order theories, this project aims at developing the C0-type global-local higher-order theories a priori satisfying continuity conditions of interlaminar stresses. Based on the proposed models, it is convenient to construct the higher-order elements for the analysis of free edge problems, hygrothermal problems and piezoelectric laminated structures. To achieve this goal, the following contents will be studied: 1) An enhanced C0-type global-local higher-order theory is to be developed for analysis of multilayer composite plates containing arbitrary shape of hole. The proposed theory a priori satisfies the continuity conditions of interlaminar stresses whereas the first derivates of transverse displacement can be taken out from in-plane displacement fields. Based on the proposed theory, the higher-order finite elements will be developed to predict the interlaminar stresses around the hole of multilayer composite plates as well as dynamic and buckling problems. 2) To avoid improving the order number of transverse displacement component of the higher-order theory for hygrothermal expansion problems of laminated composite structures, a C0-type global-local higher-order theory is to be proposed by introducing the transverse normal thermal deformation in the transverse displacement field. The proposed model is extended to study the effects of temperature on the stiffness and the strength of laminated composite structures. 3) A C0-type global-local higher-order theory satisfying continuity conditions of interlaminar stresses will be developed to refine the prediction of 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 global-local higher-order theories can be further improved.

已有满足层间应力连续的层合板C1型整体-局部高阶理论成功地用于建立低阶单元，但是难以构造多节点高阶单元，以致国内外至今没有给出此类多节点高阶单元。本项目将发展适于分析不同类型问题的预先满足层间应力连续C0型整体-局部高阶理论，用于构造多节点高阶单元分析孔边、湿热及压电问题。研究内容概括为：1）建立适于分析含任意孔形多层大厚度复合材料的满足层间应力连续增强C0型整体-局部高阶理论，并构造多节点高阶单元分析多层大厚度层合结构孔边附近层间应力、动力及稳定等问题；2）发展适于分析温湿耦合作用下复合材料的预先满足层间应力连续的C0型高阶理论，解决分析复合材料湿热膨胀问题时，必须提高横向位移阶数的问题，研究温度对复合材料层合结构刚度和强度等影响；3）建立能准确分析力电耦合作用下压电层合结构的预先满足层间应力连续的C0型高阶理论，考虑电场对横向剪切应力影响。通过本项目的实施，完善整体-局部高阶理论。

复合材料结构准确数值分析，需要发展新的理论模型和有限元方法并进行实验验证。在国家自然科学基金（No.11272217）资助下，申请人针对新型复合材料结构开展系列理论研究和实验验证，并取得如下学术成果：（1）创新性提出预先满足层间应力连续的C0型高阶理论，我们提出的适于分析复合材料结构力学问题的预先满足层间应力连续C0型高阶理论兼具已有C0型高阶理论和C1型高阶理论优点。同行专家在国际期刊撰写学术论文评价我们发展的C0型高阶锯齿理论比同类理论模型更好（Better）更准确（More accurate），且非常罕见（Very few）。（2）已有研究不得不使用更为复杂的三维弹性理论分析复合材料软核夹层结构动力和稳定问题。为提高计算效率，在保证精度前提下我们提出能够对复合材料软核夹层结构动力和稳定响应精确计算的等效单层板理论。在此之前，没有看到国内外相关报道。此项研究为泡沫夹层结构复合材料可靠设计提供理论支持，国外同行撰写学术期刊论文评价我们开展了卓越的研究工作，进一步评价我们此项研究工作为其他数值方法和实验提供标准；（3）在国际上率先提出在Hu-Washizu变分原理框架内准确分析复合材料层合结构静力和动力问题。对于静力问题解决了等效单层板理论不满足层间应力连续问题（相应成果发表在Composite Structures），对于复合材料自由振动和强迫振动问题误差从30%降至6%以内（相应成果已被AIAA J接受发表）。在国家自然科学基金资助下，发表及正式接受学术论文28篇，其中SCI期刊论文21篇（第一作者17篇，中科院分区表2区文章8篇），编写英文书籍《Encyclopedia of Thermal Stresses》章节2章（均为第一作者）