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Active systems have attracted a great deal of attention in the last few decades due to the potential benefits they offer over the conventional passive systems in various applications. Dealing with active systems requires the possibility of modeling and simulation of their behavior. The paper considers thin-walled active structures with laminate architecture featuring fiber reinforced composite as a passive material and utilizing piezoelectric patches as both sensor and actuator components. The objective is the development of numerically effective finite element tool for their modeling. A 9-node degenerate shell element is described in the paper and the main aspects of the application of the element are discussed through a set of numerical examples.

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The article considers thin-walled active structures, which utilize the piezoelectric patches as both sensor and actuator components. Most of the developed models for this type of application make an assumption of a constant electric field and, consequently, a linear distribution of the electric potential over the thickness of the piezopatches. Some recent papers use higher-order functions to model the mentioned electric quantities. In the study, it is demonstrated through an analytical deduction that a quadratic distribution of the electric potential and a linear distribution of the electric field are adequate for the piezoelectric patch that exhibits kinematics described by a first-order two-dimensional theory. A degenerated shell element is developed for modeling purposes and a set of numerical analyses is performed in order to demonstrate the additional stiffening effect caused by the refined functions for the electric quantities. The significance of the effect is discussed in detail.

The piezoelectric effect is studied for bending and traction tests for two types of structure configurations: homogeneous and composite structures. Mechanical displacements are calculated for traction and bending tests, using FEM for the homogeneous body, where the input material properties are taken from the overall coefficients reported by the Asymptotic Homogenization Method (AHM). A brief theoretical description about the basics of the piezoelectric finite elements and the AHM is given. On the other hand, the calculations of the mechanical displacements are done for the composite structure using FEM where the real data of the material parameters for cylindrical fibers (PZT-5) embedded in a matrix (elastic isotropic polymer) were taken from reported references. A comparison between the results obtained using AHM + FEM and FEM for the homogeneous and the composite structures respectively is reported and shows a favorable result.