In the present work, the static and the dynamic analysis of intelligent advanced beams structures with piezoelectric actuators have been studied. The structure substrate is made of isotropic and/or anisotropic materials, subjected to axial and transverse mechanical loads as well as electrical load. The actuators’ layers are made of piezoelectric material of PZT type. The model is able to solve the structure with piezoelectric actuators either patches or completely covers the structure; in the upper or lower surface or impeded in the structure. The classical laminate theory is used to represent the deformation of the lamination for each considered structure. The ID isoperimetric Hermit cubic shape functions and the Lagrange interpolation functions are used to formulate the finite element model for the distributed coupled electromechanical behavior. The equations of motion of each structure system is obtained by using the principle of total potential energy considering the Euler-Bernoulli beam assumptions. A Matlab code is prepared to perform the analysis of such beams. The results of the proposed finite element model for each structure are compared to the available finite element and analytical results of other investigators, good agreement is generally obtained.

In the current work, a finite element formulation is developed for modeling and analysis of isotropic as well as orthotropic composite beams with distributed piezoelectric actuators subjected to both mechanical and electrical loads. The proposed model is developed based on a simple higher order shear deformation theory where the displacement field equations in the model account for a parabolic distribution of the shear strain and the nonlinearity of in-plane displacements across the thickness and subsequently the shear correction factor is not involved. The virtual displacement method is used to formulate the equations of motion of the structure system. The model is valid for both segmented and continuous piezoelectric elements, which can be either surface bonded or embedded in the laminated beams. A two-node element with four mechanical degrees of freedom in addition to one electrical degree of freedom for each node is used in the finite element formulation. The electric potential is considered as a function of the thickness and the length of the beam element. A MATLAB code is developed to compute the static deformation and free vibration parameters of the beams with distributed piezoelectric actuators. The obtained results from the proposed model are compared with the available analytical results and the finite element results of other researchers.

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In the present work, a finite element model is developed to analyze the response of isotropic and orthotropic beams, a common structural element for aeronautics and astronautic applications. The assumed field displacements equations of the beams are represented by a first order shear deformation theory, the Timoshenko beam theory. The equations of motion of the beams are derived using Hamilton’s principle. The shear correction factor is used to improve the obtained results. A MATLAB code is constructed to compute the natural frequencies and the static deformations for both types of beams with different boundary conditions. Numerical calculations are carried out to clarify the effects of the thickness-to-length ratio on both the Eigen values and the deflections of the beams due to the applied mechanical load. The obtained results of the proposed model are compared to the available results of other investigators, good agreement is generally obtained.

This paper concerns the shape control of composite material plates using piezoelectric actuators. A finite element formulation is developed for modeling a laminated composite plate that has piezoelectric actuators and sensors. To improve the accuracy of the prediction of the plate deformation, a simple higher-order deformation theory is used. The electrical potential is treated as a generalized coordinate, allowing it to vary over the element. For the shape control, an optimization algorithm, based on finite element techniques, is developed to determine optimal actuator voltages to minimize the surface error between the desired shape and actual deformed shape. The error function for a plate element is determined by calculating the mean square of the surface error over the surface, instead of determining it only at the node points of the element. Based on these techniques, Matlab codes were developed. Analyses were performed to determine optimum actuator voltages. The analytical results demonstrate the feasibility of using piezoelectric actuators for the active shape control of spacecraft reflectors.

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In the present work, a modified higher-order shear deformation theory is developed to analyze isotropic and composite plates to obtain the static response as well as dynamic characteristics using Ritz solution technique. The displacement-field equations of Lo's higher order shear deformation theory are modified by representing the total rotation of the normal to the mid-plane by two components, bending and shear rotations. The model is valid for thin and thick plates. The plates are subjected to mechanical loads with different types of boundary conditions. A Mathematica code is developed to analyze different plate problems. The obtained results are compared to the available studies solved by different theories and finite element methods. It is shown that the obtained results are accurate using less number of degrees of freedom.

A finite element formulation is presented for modeling the dynamic as well as static response of a compressor blades subjected to extension, bending and torsional loads. The formulation is derived from the variational principle with the consideration for the total potential energy of the structure based on the classical lamination theory. The compressor blade is modeled as an advanced beam with idealized rectangular cross-section that takes the warping effect into consideration. The bending-torsion coupling is introduced in the stiffness and mass matrices. A one dimensional linear isoparametric element with hermit cubic shape function is used. A two end nodes and one intermediate node as well is implemented for the finite element formulation. A Matlab interactive code was developed to solve a blade with a multi action loads. The results obtained are compared to the available analytical and finite element results.