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Geometrically exact micropolar Timoshenko beam and its application in modelling sandwich beams made of architected lattice core

机译:几何精确的微极性季莫申科梁及其在建模格构芯夹层梁建模中的应用

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摘要

With a view towards modelling nonlinear elastic response of sandwich beams made of architected lattice core, a geometrically exact formulation for micropolar Timoshenko beam is developed. Starting with the assumed deformation field that reflects the classical hypothesis of shear deformable Timoshenko beam theory, a systematic dimensional reduction is carried out without any further approximation in the definition of strain measures and thus follows the phrase geometrically exact. Proposed beam model is then used to investigate the mechanics of sandwich beams made of architected lattice core. We establish that the new beam formulation is capable of representing the nonlinear mechanical behaviour of such sandwich structures through an equivalent single layer beam theory. Two-scale computational homogenization approach based on the FE2 formalism is adopted to obtain the constitutive behaviour of the proposed single layer beam. A set of numerical simulations is carried out to investigate the nonlinear behaviour of the proposed beam as well as to attest to the effectiveness of the homogenized beam formulation. While the present theory is applicable for planar deformation alone, it has no restriction over the finiteness of deformation and micro/macro-rotation of the beam.
机译:为了建模由结构化的晶格芯制成的夹心梁的非线性弹性响应,开发了微极性季莫申科梁的几何精确公式。从反映剪切可变形季莫申科梁理论的经典假设的假定变形场开始,进行系统的尺寸缩减,而无需进一步近似应变测量的定义,因此遵循了几何精确的说法。然后,使用拟议的梁模型研究由建筑格芯制成的夹心梁的力学。我们建立了新的梁公式能够通过等效的单层梁理论来表示此类夹层结构的非线性力学行为。采用基于FE2形式主义的两尺度计算均质化方法来获得所提出的单层梁的本构行为。进行了一组数值模拟,以研究所提出的梁的非线性行为,并证明了均质梁公式的有效性。尽管本理论仅适用于平面变形,但它对梁的变形和微/宏观旋转的有限性没有限制。

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