细观尺度复合材料层合板偶应力工程理论及细观有限元

In this object,we will establish the engineering theory of composite laminated beam/plate on new modified couple stress theory which is invented by the applicant, and will develop finite elements satified strictly convergence condition and morover experimental study of the modified couple stress for indentical the material length scale parameter. Unlike classical elastic theory, the study of the couple stress theory is limited in the 2-D and 3-D elasticity, especially there is a lack of practical beam/plate theory. Previous researchers focused on the beam/plate theory for size effects are based on a C0 theory (Cosserat-type theory) in which rotation and displacement are independent variables especially they contain more than two length constants. Recently, various isotropic beam and plate models based on the C1 modified couple stress theory with only one type of the displacement and one miro-material parameter have been proposed, and result in the governing equations of these models are isomorphic with the classical beam and plate models. However, the anisotropic composite laminated beam and plate models based on the C1 modified couple stress theory still not appear. Objective of this study is that to establish a new anisotropic modified couple-stress theory in general，and then a constitutive relation of composite laminated beam/plate on modified couple stress theory is defined. In this object, for composite laminated beam/plate based on the global or global-local high order theory, we will establish the engineering theory of composite laminated beam/plate on new modified couple stress theory,and will develop strictly variational principle to derive the governing equations and boundary conditions and the continuum condition of inter-player stresses. All present models will be used to study the scale effects of composite laminated beam/plate.

本项目将开展各向异性细观尺度层合板修正偶应力理论，细观有限元法和细观材料工程参数标定的试验研究。该理论为申请者首创。目前细观尺度偶应力理论研究多限于平面和三维理论，没有像经典弹性理论那样建立了完整的工程梁、板壳理论。早期建立的细观尺度偶应力板理论多限于各向同性C0偶应力模型（含两类位移和至少含两个材料细观参数），与经典梁、板模型差异很大。近期推出的各向同性梁、板的C1对称修正偶应力模型含一类位移和一个材料细观参数，建立的模型与经典梁、板模型同构，尺度效应直观，但是，修正偶应力理论只能用于各向同性材料。本项目将深化首次提出的新的各向异性修正偶应力一般理论。系统建立C1修正偶应力层合梁、板工程理论体系，建立满足层间应力连续的高阶细观尺度复合材料层合板偶应力工程理论和层间应力的尺度效应研究。有限元法研究将建立收敛检验函数和保证收敛的单元。同时开展基于修正偶应力理论细观材料长度参数标定的试验研究。

目标：系统建立细观尺度修正偶应力复合材料层合梁、板工程理论，特别是满足层间连续条件的整体-局部高阶理论；建立可靠的偶应力层合板有限元方法,以往都限于位移法，本项目开展基于广义变分原理的偶应力层合板有限元方法研究。.本项目独立创新建立了各向异性层合板的偶应力本构方程和相应的修正偶应力理论。理论完善和工程应用集中解决了如下的关键问题.1修正偶应力模型中合理引入z向转动参数的假设。.2修改现有的整体_局部理论满足层间剪应力和偶应力矩的连续条件。关键解决偶应力矩（位移二阶导数）连续性..3首次建立了满足增强型分片检验的偶应力层合板的单元。推出复合材料层合板和夹层板新模型，C0模型和有限元方法；振动和稳定性尺度效应分析基于修正偶应力理论;一个重要的进展从位移法发展为基于广义变分原理的杂交法，其优势表现在如下几个方面:.1) 平衡前处理可以提高特征值计算精度,例如:动力和稳定性分析.2) 基于广义变分原理的杂交法可以改进位移法的单元性能：实现满足层间预平衡；解除横向剪切闭锁。层合板的杂交法不仅仅满足层间剪力连续，而且满足层间的平衡。经典的杂交法是放松单元间的连续性。满足z向的平衡，可能会提高传统有限元的性能（剪切奇变，剪切闭锁）；3) 可以解除位移法计算完全固定点横向剪切应力的问题,例如,位移法计算悬臂梁的固定端的横向剪力为零.. 本项目对标定试验的理论和层合梁标定试验的问题做了初步探讨。结论是与经典连续体力学不同，细观本构方程中材料细观长度常数的标定不仅与材料有关，还与采用那种细观理论有关。. 发表论文24篇（其中SCI收录12篇，国内核心期刊12篇）