Corotational Finite Element Formulation for Static Nonlinear Analyses with Enriched Beam Elements
Corotational Finite Element Formulation for Static Nonlinear Analyses with Enriched Beam Elements
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DOI：
10.2514/1.j058441
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发表时间：
2020-05-01
期刊：
影响因子：
2.5
通讯作者：
Pirrera, A.
中科院分区：
文献类型：
--
作者：
Macquart, T.;Scott, S.;Pirrera, A.
航空航天结构对数值分析的依赖日益增加，这鼓励了精确且计算效率高的模型的发展。特别是，有限元（FE）梁模型在初步设计阶段和研究新概念（例如气动弹性裁剪）时已成为广泛使用的近似方法。在过去的50年里，基于变大小元素(h)和多项式度(p)的hp-FE方法的发展有助于降低数值分析的计算成本。同时，许多结构，包括飞机机翼和风力涡轮机叶片，在长度、细度和复杂性方面逐渐增加。因此，现代的叶片和机翼经常超出线性变形范围，需要进行非线性分析，而hp-FE方法往往不容易适用。因此，本文的目的是推导出一种适用于非线性hp-FE精化的富三、四、五节点梁单元的旋转有限元公式。为此，推导了数学公式，以在同向FE梁框架内纳入富集元素。然后，针对多个非线性基准问题和实验案例研究验证了所提出的公式。
The increasing reliance of aerospace structures on numerical analyses encourages the development of accurate, yet computationally efficient, models. Finite element (FE) beam models have, in particular, become widely used approximations during preliminary design stages and to investigate novel concepts, for example, aeroelastic tailoring. Over the last 50 years, developments in hp-FE methods based on elements of variable size (h) and polynomial degree (p) have helped reduce the computational cost of numerical analyses. Concurrently, many structures, including aircraft wings and wind turbine blades, have gradually increased in length, slenderness, and complexity. As a result, modern blades and wings regularly operate beyond the range of linear deformation, requiring nonlinear analyses for which hp-FE methods are often not readily applicable. The aim of this paper is, therefore, to derive a corotational FE formulation for enriched three-, four-, and five-noded beam elements, suitable for nonlinear hp-FE refinement. To this end, the mathematical formulation is derived to incorporate enriched elements within the corotational FE beam framework. The proposed formulation is then validated against multiple nonlinear benchmark problems and an experimental case study.