【作者】 高妍；

【导师】 周立明；

【作者基本信息】 吉林大学 ， 力学， 2024， 硕士

【摘要】 磁电弹材料可以实现磁能、电能和机械能之间的快速转化,可用于传感器、俘能器等电子元器件的制造,在航空航天、通信工程、生物医疗等高新技术领域中发挥着关键作用。由磁电弹材料设计而成的智能元器件的工作环境中,常受到电场、磁场、热场等影响,为了提高设备的整体性能和服役寿命,采取准确有效的研究方法对磁电弹结构的力学特性进行分析必不可少,对智能器械的发展有着重要意义。多物理场耦合问题涉及的变量很多,解析法难以求解,实验法存在诸多限制。随着计算设备的不断发展,有限元法(FEM)作为一种体系完善的数值方法,兼顾准确性和成本较低的优势,被广泛应用于各种工程领域。然而,有限元法存在刚度矩阵偏“硬”、对单元离散质量要求高等诸多问题,其求解精度往往依赖于求解域的精确离散化,增加人工成本,影响计算效率。磁电弹结构在热场中的力学特性更为复杂,要考虑到热电、热磁效应等因素,如果采用FEM,需要对结构进行精细的离散。Enriched有限元法(EFEM)是一种新型FEM,其在有限元形函数中引入了节点插值覆盖函数来计算求解域,本质上是用更高阶的插值函数代替FEM形函数进行求解,降低了单元离散质量的要求,在分析磁电弹结构的多场耦合力学特性问题上,提高了计算精度。本文基于磁电弹材料基本方程和EFEM基本理论,从热力学原理出发,提出力电磁热耦合Enriched有限元法(MP-EFEM),求解热场中磁电弹结构的静力学响应;并基于MP-EFEM基本理论,构建热场中磁电弹结构的动力学模型,采用子空间迭代法,分析磁电弹结构的固有频率;采用Wilson-θ法,实现MPEFEM动力学问题瞬态响应的求解。通过磁电弹悬臂梁结构、含孔磁电弹结构和含两种材料的磁电弹双层结构等数值算例的分析,研究磁电弹结构在力电磁热多场耦合作用下的力学特性。结论表明,在满足给定的精度要求时,与FEM相比,MP-EFEM可以通过采用节点数目较少的单元离散方案获得精确的结果,验证了MP-EFEM在求解磁电弹结构力电磁热耦合问题上具有良好的精度,能有效地分析磁电弹结构多场耦合作用下的力学特性,为智能元件的设计和应用提供了新思路。更多还原

【Abstract】 Widely used in the fields of electronics,aerospace,and smart devices,magnetoelectro-elastic(MEE)materials can exhibit rapid conversion between mechanical,magnetic and electric energy,which can be used in the manufacturing of sensors,storage devices,and other devices.Magneto-electro-elastic materials have magnetostriction,piezoelectric,and magnetoelectric effects,influenced by electric,magnetic field,and thermal field in their working environment.Investigating the mechanical characteristics of MEE-based structures influenced by the coupled of multiple physical fields is of vital importance for improving the structures and application of MEE-based structures.The coupling mechanism of multi-physical fields is complex,and analytical methods are difficult to solve complex problems,while experimental methods have many limitations.With the progress of computational devices,FEM,as a wellstructured numerical method with the advantages of efficiency and cost,is widely used in various engineering fields.However,the standard FEM has some limitations that the stiffness matrix is relatively stiff and the elements are required to be discretized sufficiently with solution accuracy depending on the precise discretization of the solution domain,increasing manual effort,and impacting computational efficiency.The mechanical characteristics of MEE-based structures influenced by the thermal field are even more complex,requiring consideration of thermo-electric and thermo-magnetic effects.The standard FEM would demand a refined discretization of the structure.Enriched Finite Element Method(EFEM)is the derivative of FEM that introduces the interpolation functions of nodal additional degrees into the FEM shape functions.Essentially,it uses higher-order interpolation functions instead of standard FEM shape functions for solving,reducing the requirements for element discretized mass and improving computational accuracy in analyzing multi-physics coupling mechanical characteristics of MEE-based structures.This paper,constructed on the basic equations of MEE-based structures and the fundamental notion of multi-physics coupling EFEM,proposed the multi-physics coupled Enriched Finite Element Method(MP-EFEM).Starting with the fundamentals of thermodynamics,it aims to solve the static behaviors of MEE-based structures in thermal field.In addition,on the basis of the fundamental theory of MP-EFEM,the dynamic model for multi-physics coupled of MEE-based structures is constructed.The Subspace Iteration Method is utilized to analyze the natural frequencies of MEE-based structures,and the Wilson-θ method is employed to analyze the transient characteristics of the MP-EFEM dynamic problems.Through numerical examples,including analysis of MEE-based cantilever beams,MEE-based structures with holes,and double-layer structures with two different materials,the mechanical characteristics of MEE-based structures influenced by the multi-physics coupled effect are investigated.The conclusions indicate that,when it comes to the given accuracy,MP-EFEM can obtain the precise solution with fewer node discretization schemes compared to standard FEM,which validates the high accuracy of MP-EFEM in solving the multiphysics coupled problem of MEE-based structure.MP-EFEM has the potential to analyze the mechanical properties of MEE-based structures under mechanical-electricmagnetic-thermal coupled issues,providing new insights for the design and application of intelligent components.更多还原