Abstract

One of the directions of using piezoelectric elements in modern technology is related to their use for controlling the shape of a structure under the influence of operational loads. The issue of a change in the shape (geometry) of a structure can be caused, for example, by the need for minimization of displacements in certain regions or, vice versa, for maximization of displacements to ensure the stability of a structural shape under operational loads. Due to the presence of the inverse piezoelectric effect in piezoelectric materials, this problem can be solved by applying a predetermined electric voltage to the electroded surfaces of piezoelectric elements. Elastic structures with elastic piezoelectric elements attached to their surfaces become electroelastic. It is necessary to first assess the abilities of piezoelectric elements to have an effect on deformations caused by external actions of different types in order to use different strategies of control over their mechanical behavior. This means that piezoelectric elements must provide a controlled form change depending not only on the characteristics of the elements themselves (the size, physico-mechanical properties of the material, and position) but also on the parameters of the structure (its geometry, size, boundary conditions, and physico-mechanical characteristics) and acting loads. The influences of different factors on the deformation of an electroelastic structure under the action of an electric voltage applied to the piezoelectric elements in this work was established numerically based on mathematical modeling by solving the static problem of electroelasticity. The numerical implementation was carried out by the finite-element method in the ANSYS software package. The possibilities for using piezoelectric elements for changing the shape of a structure for different numbers of elements and different options of their layout on the surface are demonstrated based on the example of a cantilevered fixed plate.

中文翻译：

---

使用位于其表面的压电元件对板的变形进行建模

摘要

在现代技术中使用压电元件的方向之一与它们在操作负载的影响下控制结构形状的用途有关。结构形状（几何形状）变化的问题可能是由于，例如，某些区域需要最小化位移，或者反之亦然，这是因为需要最大化位移以确保结构形状在操作中的稳定性。负载。由于压电材料中存在逆压电效应，因此可以通过向压电元件的电极表面施加预定电压来解决该问题。具有附着在其表面的弹性压电元件的弹性结构变为电弹性的。首先必须评估压电元件对由不同类型的外部作用引起的变形产生影响的能力，以便对它们的机械行为采用不同的控制策略。这意味着压电元件必须提供受控的形状变化，不仅取决于元件本身的特性（尺寸，材料的物理机械特性和位置），还取决于结构的参数（其几何形状，尺寸，边界条件，物理力学特性）和作用载荷。在数学模型的基础上，通过解决电弹性的静态问题，数值建立了在压电元件上施加电压的作用下，不同因素对电弹性结构变形的影响。数值实现是通过ANSYS软件包中的有限元方法进行的。基于悬臂固定板的示例，展示了使用压电元件改变不同数量的元件的结构形状以及在表面上布局的不同选择的可能性。