弹性柔性板的动量-膜理论作为石墨烯薄片的连续几何非线性理论

IF 0.6 4区物理与天体物理 Q4 MECHANICS

Doklady Physics Pub Date : 2023-12-26 DOI:10.1134/S1028335823040055

S. H. Sargsyan

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引用次数: 0

摘要

摘要在三维几何非线性弹性力矩理论的基础上，建立了弹性板的几何非线性力矩-膜理论，作为柔性石墨烯变形的连续理论，该理论假定板元素的变形、弯曲-扭转特性和旋转角度（包括自由角度）都很小，只保留了来自法向位移（挠度）及其导数的非线性项。对于这种非线性弹性板理论，通过引入应力函数，解析方程也以混合形式呈现：这是一个在板变形状态下编制的横向弯曲变形平衡方程组，以及由应力和挠度函数表示的变形连续性方程组。为弹性板的几何非线性力矩-膜理论建立了拉格朗日型变分原理。

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The Moment-Membrane Theory of Elastic Flexible Plates as a Continual Geometrically Nonlinear Theory of a Graphene Sheet

A geometrically nonlinear moment-membrane theory of elastic plates has been built as a continual theory of deformations of flexible graphene under the assumption of smallness of deformations, bending-torsional characteristics, and angles of rotation (including a free one) of plate elements on the basis of the 3D geometrically nonlinear moment theory of elasticity with preservation of only the nonlinear terms that come from normal displacement (deflection) and its derivatives. For this nonlinear theory of elastic plates, the resolving equations are presented also in mixed form by introducing stress functions: this is a system of equilibrium equations for the transverse bending deformation compiled in the deformed state of the plate and the deformation continuity equations expressed by the stress and deflection functions. The Lagrangian-type variational principle for the geometrically nonlinear moment-membrane theory of elastic plates has been established.

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来源期刊

Doklady Physics 物理-力学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

4-8 weeks

期刊介绍： Doklady Physics is a journal that publishes new research in physics of great significance. Initially the journal was a forum of the Russian Academy of Science and published only best contributions from Russia in the form of short articles. Now the journal welcomes submissions from any country in the English or Russian language. Every manuscript must be recommended by Russian or foreign members of the Russian Academy of Sciences.