MFC纤维压电智能结构几何和迟滞非线性有限元建模方法

Macro-fiber composite (MFC) is made of piezoceramic fibrous phase embedded in epoxy matrix phase, which improves significantly the flexibility and actuation ability, remedies many of the limitations in conventional piezoelectric materials, like brittle nature of lead zirconium titanate (PZT) and weak actuation forces of polyvinylidene fluoride (PVDF). Concerning the difficulty in computation and simulation of MFC laminated thin-walled smart structures undergoing large displacements and rotations, as well as subjected to high electric voltages, the project intends to study on the geometrically nonlinear and hysteresis modeling for MFC laminated smart structures. The project first investigates on homogenization of MFC patches to obtain the overall material constants for the constitutive equations of MFC patches. Second, study the fundamental mathematics for geometrically nonlinear and hysteresis analysis of MFC to obtain the strain field matrix, electric field matrix, elastic constant matrix, piezoelectric coupled matrix, dielectric matrix and hysteresis matrix, respectively, which include arbitrary piezo fiber and electric field orientations. Third, through the finite element method, Newton-Raphson and Newmark iteration methods, one obtains the static and dynamic equations for MFC laminated thin-walled structures, and the solution for solving the nonlinear static and dynamic equations. Finally, the proposed model is validated by the simulation and experimental results. Through this project, MFC laminated thin-walled smart structures can be calculated and simulated.

纤维压电材料（Macro-fiber composite）采用普通压电陶瓷纤维与环氧树脂交错排列的复杂结构形式，极大提高了其柔韧性和致动能力，有效克服了普通压电陶瓷和聚合物脆弱易碎、致动能力弱的缺陷。针对纤维压电层合板壳智能结构发生大转角大应变变形和加载强致动电压的计算与仿真难题，拟开展纤维压电智能结构几何和迟滞非线性建模方法研究。首先开展纤维压电材料参数等效方法的研究，获得建模所需的等效材料参数和迟滞非线性本构方程；其次，研究几何和迟滞非线性建模基理，获得建模所需的应变场和电场矩阵，以及弹性、压电耦合、介电和迟滞等系数矩阵，并且考虑压电纤维和电场任意方向；再次，通过采用有限元、牛顿迭代和Newmark等方法，实现对纤维压电层合板壳静力学和动力学建模及其后处理；最后通过数值仿真和实验对所建模型进行验证和修正。通过本项目的实施，最终实现纤维压电智能结构大转角变形和强致动电压加载的计算与仿真。

薄壁结构广泛存在于航空、航天、船舶等领域。由于薄壁结构弱刚性、低阻尼，使得结构极易发生形变与振动。一方面振动降低航空航天产品性能与结构可靠性，另一方面振动往往引发额外噪声，造成腔内空间舒适度下降，并大大减弱产品的隐身性能。在薄壁结构中嵌入智能材料，如压电材料、磁致伸缩材料、形状记忆合金等，作传感与致动，形成智能结构，为减振降噪提供很好的解决方案。相比传统压电材料，粗纤维压电复合材料MFC采用压电陶瓷纤维与环氧树脂交错排列的复杂结构形式，形成高柔性、强制动的特点，具有强大的应用前景。.本项目围绕MFC压电智能结构，首先，研究了MFC的组成结构与变形机理，构建了机电耦合非线性的材料参数等效模型，获得了建模所需的应变场和电场矩阵，以及弹性、压电耦合、介电和迟滞等系数矩阵，并且考虑压电纤维和电场任意方向；其次，推导了几何非线性的“应变-位移”关系，包括大转角几何全非线性、中等转角几何非线性和冯卡门几何非线性，从理论层面上进行了对比分析；然后，构建了几何和机电耦合双重非线性的有限元模型，建立了非线性静力学/动力学模的求解算法，实现了对纤维压电层合板壳静力学和动力学建模及其后处理；最后，对文献典型的压电结构进行了数值计算与仿真，验证了本模型的准确性，实现了纤维压电智能结构大转角变形和强致动电压加载的计算与仿真。.通过本项目研究，提出了一套MFC压电智能结构几何和机电耦合非线性建模方法，为高性能壁板结构在极端环境下的准确计算提供理论基础，如发生大变形、处在强电场环境下。最终可以较好帮助设计人员准确计算结构性能，提高研发速度、降低研发成本。