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Isogeometric dynamic analysis of shells based on the nonlinear micropolar theory
International Journal of Non-Linear Mechanics ( IF 3.2 ) Pub Date : 2021-05-21 , DOI: 10.1016/j.ijnonlinmec.2021.103750
A. Norouzzadeh , R. Ansari , M. Darvizeh

Studying the large-amplitude forced vibration characteristics of micropolar shell-type structures is the main objective of this paper. In order to obtain the full geometrically nonlinear model of micropolar theory, the micromorphic seven-parameter shell kinematic is first developed. Via a nonlinear micro-motion map, the extracted formulation is fitted for the micropolar continuum. As a result, possessing three stress–strain fields with eighteen independent elastic parameters of a linear material, the proposed micropolar shell theory is able to capture the inhomogeneity and size-effects. On the basis of Hamilton’s principle, the variational form of governing equations of motion is determined. The finite element isogeometric solution approach is then utilized to produce the geometry and approximate the displacement field in mid-surface area of shell. This would be helpful for resolving the locking and instability issues of the traditional low-order standard finite element shell models. By discretizing the period of harmonic vibration, a numerical method is also implemented in time domain. To demonstrate the microstructural effects, dynamic behavior of micropolar plate- and shell-type structures are investigated in several parametric studies. Since the classical strain and stress tensors are retained in present micropolar elasticity, both the large macro- and micro-deformations are captured for the first time.



中文翻译:

基于非线性微极理论的壳等几何动力分析

研究微极壳型结构的大振幅受迫振动特性是本文的主要目的。为了获得微极理论的完整几何非线性模型,首先开发了微晶七参数壳运动学。通过非线性微运动图,提取的公式适用于微极连续体。因此,具有线性材料的 18 个独立弹性参数的三个应力 - 应变场,所提出的微极壳理论能够捕获不均匀性和尺寸效应。根据哈密顿原理,确定了运动控制方程的变分形式。然后利用有限元等几何解法来产生几何形状并近似壳中表面区域的位移场。这将有助于解决传统低阶标准有限元壳模型的锁定和不稳定问题。通过对谐波振动周期进行离散化,在时域中也实现了一种数值方法。为了证明微结构效应,在几个参数研究中研究了微极板和壳型结构的动态行为。由于经典应变和应力张量保留在目前的微极弹性中,因此首次捕获了大的宏观和微观变形。在几个参数研究中研究了微极板和壳型结构的动态行为。由于经典应变和应力张量保留在目前的微极弹性中,因此首次捕获了大的宏观和微观变形。在几个参数研究中研究了微极板和壳型结构的动态行为。由于经典应变和应力张量保留在当前的微极弹性中,因此首次捕获了大的宏观和微观变形。

更新日期:2021-06-05
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