Strain gradient and generalized continua obtained by homogenizing frame lattices

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2018-07-26 DOI:10.2140/MEMOCS.2018.6.213

H. Abdoul-Anziz, P. Seppecher

引用次数: 142

Abstract

We determine the effective behavior of periodic structures made of welded elastic bars. Taking into account the fact that flexural and torsional stiffnesses are much smaller than the extensional one we overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.

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均质化框架格得到应变梯度和广义连续体

我们确定了由焊接弹性杆组成的周期结构的有效性能。考虑到挠曲刚度和扭转刚度比拉伸刚度小得多的事实，我们超越了经典的均匀化公式，得到了完全不同类型的有效能量。我们在线性弹性的框架下工作。我们给出了二维或三维微观结构的不同例子，这些结构导致广义的1D, 2D或3D连续体，如Timoshenko梁，Mindlin-Reissner板，应变梯度，Cosserat或微态连续体。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.