Abstract

In this work, we consider the problem of finite deformations of a dielectric tube under the action of an electric field. The tube consists of two layers, each of which is helically reinforced with fibers. The winding angles of the fibers in each layer are different. Flexible electrodes are deposited onto the inner and outer surfaces of the tube and between the layers. An electric field is induced by applying a voltage to the first or second layer, i.e., either to the electrodes of the inner surface and between the layers or to the electrodes between the layers and the outer surface. In the analysis, a simple model of an incompressible electroactive anisotropic material is considered. The potential-energy function is represented by the sum of the energy of an isotropic matrix in the Gent form, the simplest electrical component and the energy of the reinforcing fibers. Using a semi-inverse representation, the problem of the statics of a three-dimensional body is reduced to integral equations for the tube-deformation parameters: the radius of the outer layer, the multiplicity of the longitudinal elongation, and the angle of twist. The effect of the layer thickness on the deformation of the tube under a quasi-static increase in the electric voltage is studied. The aim of this study is to determine such ratios of the layer thicknesses, at which applying a voltage to different layers will lead to twisting of the tube in different directions.

中文翻译：

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电场作用下双层介电非线性弹性各向异性管的有限变形

摘要

在这项工作中，我们考虑了电场作用下介电管的有限变形问题。该管由两层组成，每一层都用纤维螺旋增强。每层纤维的缠绕角度不同。柔性电极沉积在管的内表面和外表面以及层之间。通过将电压施加到第一层或第二层，即施加到内表面和层之间的电极或者施加到层和外表面之间的电极来感应电场。在分析中，考虑了不可压缩电活性各向异性材料的简单模型。势能函数由根特形式的各向同性矩阵的能量之和表示，最简单的电气元件和增强纤维的能量。使用半逆表示法，三维体的静力学问题被简化为管变形参数的积分方程：外层半径、纵向伸长率的重数和扭曲角。研究了在准静态电压增加下层厚度对管变形的影响。本研究的目的是确定这样的层厚比，在该比值下，向不同层施加电压将导致管在不同方向上扭曲。外层半径、纵向伸长倍数、扭转角。研究了在准静态电压增加下层厚度对管变形的影响。本研究的目的是确定这样的层厚比，在该比值下，向不同层施加电压将导致管在不同方向上扭曲。外层半径、纵向伸长倍数、扭转角。研究了在准静态电压增加下层厚度对管变形的影响。本研究的目的是确定这样的层厚比，在该比值下，向不同层施加电压将导致管在不同方向上扭曲。