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A Static Analysis of Three-dimensional Functionally Graded Beams through Hierarchical One-dimensional Finite Elements

机译:通过分层一维有限元对三维功能梯度梁的静态分析

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In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements' stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements' family.
机译:在本文中,通过一系列分层一维有限元素研究了由功能梯度材料制成的三维光束的静态响应。通过运动制剂和沿梁轴的每个元件的节点数量不同,提出了各种各样的元件。元件'刚度矩阵和负载向量以统一的核形式导出,其不依赖于横截面上的先验膨胀顺序,也不沿着梁轴线逼近。结果符合三维有限元模型以及等效的Navier型分析解决方案。数值研究表明,可以通过拟议的分层一维元素的家庭获得准确和有效的解决方案(与完整的三维FEM解决方案相比)。

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