Vyacheslav N. Burlayenko, R. Kouhia, Svetlana Dimitrova
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In the procedures, material heterogeneity was assigned to each material integration point of appropriate standard one- and three-dimensional finite elements, eliminating the need to design graded finite elements via user-defined element subroutine. Frequencies and mode shapes of free vibrations of one- and three-dimensional axially functional graded beams with non-uniform cross-sections were found using the Lanczos method in Abaqus. An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. 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An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. 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引用次数: 0
摘要
有限元软件包 Abaqus 用于对横截面不均匀的轴向功能分级梁的自由振动进行建模和分析。由于几何形状对梁作为结构组件的行为有重大影响,因此对这方面的问题给予了极大关注。针对指定梁的一维和三维模型,以统一的方式开发了用户自定义材料模型子程序(UMAT),以便在每个有限元中对功能材料梯度进行数值计算。UMAT 程序是在 MS Visual Studio 环境下用 FORTRAN 编写的,并使用英特尔 Fortran 编译器与主程序包一起编译。在程序中,材料异质性被分配到适当的标准一维和三维有限元的每个材料积分点,从而无需通过用户定义的元素子程序来设计梯度有限元。使用 Abaqus 中的 Lanczos 方法计算了具有非均匀横截面的一维和三维轴向功能分级梁的自由振动频率和模态振型。通过将获得的结果与文献中已知的数据进行比较,对所提出的建模方法的准确性和有效性进行了分析。所提出的基于用户定义材料子程序的建模技术为从事功能梯度材料结构组件动态分析的科学家和工程师提供了宝贵的机会,这些结构组件沿轴向具有可变的几何形状。关键词:轴向功能梯度梁;非均匀截面梁;自由振动;梯度有限元;Abaqus 用户自定义子程序
FINITE ELEMENT MODELLING AND ANALYSIS OF FREE VIBRATIONS OF AXIALLY FUNCTIONALY GRADED BEAMS WITH NON-UNIFORM CROSS-SECTIONS
The finite element package Abaqus is used for modeling and analysis of free vibrations of axially functional graded beams with non-uniform cross-sections. Considerable attention has been paid to this aspect of the geometry, as it has a significant effect on the behavior of the beam as a structural component. User-defined material model subroutines (UMAT) were developed in a unified way for one- and three-dimensional models of the specified beams to provide numerical implementation of functional material gradients within each finite element. UMAT procedures were programmed in FORTRAN in the MS Visual Studio environment and compiled with the main program package using the Intel Fortran Compiler. In the procedures, material heterogeneity was assigned to each material integration point of appropriate standard one- and three-dimensional finite elements, eliminating the need to design graded finite elements via user-defined element subroutine. Frequencies and mode shapes of free vibrations of one- and three-dimensional axially functional graded beams with non-uniform cross-sections were found using the Lanczos method in Abaqus. An analysis of the accuracy and effectiveness of the proposed modeling approach was carried out, comparing the obtained results with data known in the literature. The presented modeling technique based on user-defined material subroutines provides valuable opportunities for scientists and engineers engaged in the dynamic analysis of structural components made of functionally gradient materials and having variable geometry along the axial direction. Keywords: axially functionally graded beams; non-uniform cross-section beams; free vibrations; graded finite element; Abaqus user defined subroutines