Analysis of adaptive shell structures using a refined laminated model

This work presents the development of a shell conical panel finite element model, which has the possibility of having embedded piezoelectric actuators and/or sensors patches. A mixed laminated theory is used, which combines an equivalent single layer higher order shear deformation approach for the mechanical behavior with a layerwise representation in the thickness direction to describe the distribution of the electric potential in each of the piezoelectric layers of the finite element. The electrical potential function is represented through a linear variation across the thickness with two electric potential nodes for each piezoelectric layer. Based in this model an active damping scheme applied to laminated shell structures is presented and discussed.     

Analysis of laminated conical shell structures using higher order models

In this paper is presented a numerical method for the structural analysis of laminated conical shell panels using a quadrilateral isoparametric finite element based on the higher order shear deformation theory. The displacement expressions used for the longitudinal and circumferential components of the displacement field are given by power series of the transversal coordinate and the condition of zero stresses in the top and bottom surfaces of the shell is imposed. The shape functions used for the transversal displacement are C¹ conforming and the finite element is a conical/cylindrical panel with 8 nodes and 40 degrees of freedom. The model presented performs static analysis with arbitrary boundary conditions and loads, as well eigenvalue problems (free vibration and buckling). Illustrative examples are presented and discussed.     

Analyses of magneto-electro-elastic plates using a higher order finite element model

In this paper is presented a higher-order model for static and free vibration analyses of magneto-electro-elastic plates, which allows the study of thin and thick plates. The finite element model is a single layer triangular plate/shell element with 24 degrees of freedom for the generalized mechanical displacements. Two degrees of freedom are introduced per each element layer, one corresponding to the electrical potential and the other for magnetic potential. Solutions are obtained for different laminations of the magneto-electro-elastic plate, as well as for the purely elastic plate as a special case. Results are compared with alternative models for static and free vibrations situations.     

Refined theory for the analysis of laminated orthotropic structures

A new higher-order theory for the analysis of laminated orthotropic plates and shells subject to both mechanical and thermal loads is developed. Using the variational approach the system of governing differential equations and corresponding boundary conditions are derived. Two refined models of the stress and strain state are considered, their application and accuracy are discussed. The analytical solution is obtained for plates and shells with the Navier boundary conditions on the side surfaces. The results of calculations are given and compared with an exact three-dimensional solution available in the literature. The influence of the laminated structure upon the exactness of results and the characteristics of stress–strain state is studied and discussed.     

Nonlinear vibration of an initially stressed laminated plate according to a higher-order theory

The nonlinear behavior of laminated plates in a general state of non-uniform initial stress was studied at large vibration amplitudes. The nonlinear governing equations of this study were derived using a higher-order theory approach. The results were compared with the Mindlin plate theory’s results. The results showed that the higher-order shear deformation terms had a significant influence on the plate in a large amplitude vibration when the thickness ratio decreases and the plate was stacked with less layers. In addition, the effect of Young’s modulus in the thickness direction on the frequency ratio was significant for the two-layered plate. However, the results of the four-layered plates were not affected too much.     

Optimal design of piezolaminated structures

This paper presents refined finite element models based on higher-order displacement fields to study the mechanical and electrical behavior of laminated composite plate structures with embedded and/or surface bonded piezoelectric actuators and sensors. Sensitivity analysis and optimization techniques are also applied in order to maximize the piezoelectric actuator efficiency, improve the structural performance and/or minimize the weight of the structure. The application of structural optimization to the static shape control of adaptive structures is also addressed. To show the performance of the proposed models, several illustrative and simple examples are presented.     

Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory

Geometrically nonlinear vibrations of functionally graded (FG) doubly curved shells subjected to thermal variations and harmonic excitation are investigated via multi-modal energy approach. Two different nonlinear higher-order shear deformation theories are considered and it is assumed that the shell is simply supported with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities which is truncated based on solution convergence. A pseudo-arclength continuation and collocation scheme is employed to obtain numerical solutions for shells subjected to static and harmonic loads. The effects of FGM power law index, thickness ratio and temperature variations on the frequency–amplitude nonlinear response are fully discussed and it is revealed that, for relatively thick and deep shells, the Amabili–Reddy theory which retains all the nonlinear terms in the in-plane displacements gives different and more accurate results.     

Shape control and damage identification of beams using piezoelectric actuation and genetic optimization

This paper deals with the shape control of beams under general loading conditions, using piezoelectric patch actuators that are surface bonded onto beams to provide the control forces. The mathematical formulation of the model is based on the shear deformation beam theory (Timoshenko theory) and the linear theory of piezoelectricity. The numerical solution of the model is based on the development of superconvergent (locking-free) finite elements using the form of the exact solution of the Timoshenko beam theory and Hamilton’s principle. The optimal values for the locations of the piezo-actuators are determined and optimal voltages for shape control are obtained for cantilever beams by using a genetic optimization procedure. Finally, a simplified related damage identification problem is formulated and solved using static data and genetic optimization.     

Post-buckling analysis of composite plates containing embedded delaminations with arbitrary shape by using higher order shear deformation theory

The compressive post-buckling behavior of composite laminates containing embedded delamination with arbitrary shape is investigated analytically. For modeling the embedded delamination, the laminate is divided into three smaller regions. The higher order shear deformation theory is implemented and the formulation is based on the Rayleigh-Ritz approximation technique by the application of the simple/complete polynomial series for each region. The nonlinear equilibrium equations, which are achieved through the application of the principle of Minimum Potential Energy, are solved by employing the Newton-Raphson iterative procedure. Some interesting results are obtained and compared with those achieved by the finite element method of analysis using ANSYS commercial software. A good agreement is seen to exist between the results. This is while for a given level of accuracy in the results, ANSYS requires a markedly larger number of degrees of freedom compared to that needed by the developed method. Moreover, a considerable reduction in the load carrying capacity of laminate is noticed due to the presence of delamination.     

Hygrothermal effects on multilayered composite plates using a refined higher order theory

A four-node quadrilateral plate element based on the global–local higher order theory (GLHOT) is proposed to study the response of laminated composite plates due to a variation in temperature and moisture concentrations. C⁰$C^0$ and C¹$C^1$ continuities are required in the transverse displacement functions as the first and the second derivatives are involved in the computation of the strain components in GLHOT [Int J Mech Sci, 2007; 49:1276–1288]. In this paper, a displacement function satisfying C⁰$C^0$ continuity is constructed by using the refined element method, and the discrete Kirchhoff quadrilateral thin plate element DKQ is employed for satisfying the requirement of C¹$C^1$ continuity. The effects of temperature and moisture concentrations on the material properties and the hygrothermal response of multilayered plates are studied, in contrast to most of the previous investigations in which the material properties are assumed to be independent of temperature. Hygrothermal response due to a variation in temperature and moisture concentrations has been studied for different material types sensitive to changing hygrothermal environment conditions. Numerical results suggest that temperature-dependent material properties ought to be used in the analysis of laminated plates subjected to hygrothermal loads.     

Geometrically non-linear analysis of composite structures with integrated piezoelectric sensors and actuators

This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuators or sensors layers and/or patches. The motivation for the present developments is the lack of studies in the behavior of adaptive structures using geometrically non-linear models, where only very few published works were found in the open literature.

The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings.

The finite element model is a non-conforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric layer or patch.

An updated Lagrangian formulation associated to Newton–Raphson technique is used to solve incrementally and iteratively the equilibrium equations.

The model is applied in the solution of four illustrative cases, and the results are compared and discussed with alternative solutions when available.     

基于降阶模型的水下结构振动主动控制仿真及实验研究

基于降阶模型对水下结构振动的主动控制进行了仿真及实验研究,并取得了较好的抑制振动的效果。基于结构在可压缩流体加载下的无阻尼实模态矩阵建立了水下结构的降阶模型,由于维数的降低,进而能够设计出相对简化的主动控制系统,减少传感器和作动器的数量。通过线性二次型最优控制和结构主动变刚度控制两种方法对水下结构振动进行了主动控制仿真,均使结构振动有所下降。仿真结果显示线性二次型最优控制能够降低结构振动的峰值,而结构主动变刚度控制能够将结构的固有频率按照需要进行改变。还通过水下平板振动主动控制模型实验,验证了主动控制技术对水下结构的减振效果。     

Active control of nonlinear forced vibration in a flexible beam using piezoelectric material

Geometric nonlinearities of the beam and piezoelectric patch are considered. Velocity feedback control algorithm is implemented applying piezoelectric materials. The equation of motion of the system is established using Hamilton's principle. The effects of control gains on primary resonance properties of the beam are studied. It is observed that, with the amplitude of external excitation increasing, the amplitude of resonance curve increases. The velocity feedback control can improve unstable resonance of the beam. When the control gain is increased to a certain value, the unstable regions in the resonance and amplitude-frequency curves disappear.     

Modeling of hybrid vibration control for multilayer structures using solid-shell finite elements

A self-control method of vibrations is presented in this paper. This method combines the passive damping capabilities afforded by viscoelastic materials with the active control properties associated with piezoelectric materials. Active control is introduced, using the piezoelectric properties, in order to improve the reduction in vibration amplitudes that can be obtained by viscoelastic passive damping alone. To this end, a filter has been mounted between the sensors and the actuators. The resulting nonlinear problem is discretized using the recently developed solid-shell finite element SHB20E, due to the advantages it offers in terms of accuracy and efficiency as compared to standard finite elements with the same geometry and kinematics. In order to solve the discretized problem, a resolution method using DIAMANT approach is developed. A set of selective and representative numerical tests are performed on multilayer plates to demonstrate the interest of the proposed damping model.     

A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates

A new 4-node quadrilateral finite element is developed for the analysis of laminated composite plates containing distributed piezoelectric layers (surface bonded or embedded). The mechanical part of the element formulation is based on the first-order shear deformation theory. The formulation is established by generalizing that of the high performance Mindlin plate element ARS-Q12, which was derived based on the DKQ element formulation and Timoshenko’s beam theory. The layerwise linear theory is applied to deal with electric potential. Therefore, the number of electrical DOF is a variable depending on the number of plate sub-layers. Thus, there is no need to make any special assumptions with regards to the through-thickness variation of the electric potential, which is the true situation. Furthermore, a new “partial hybrid”-enhanced procedure is presented to improve the stresses solutions, especially for the calculation of transverse shear stresses. The proposed element, denoted as CTMQE, is free of shear locking and it exhibits excellent capability in the analysis of thin to moderately thick piezoelectric laminated composite plates.     

Using Krylov‐Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain

In many engineering problems, the behavior of dynamical systems depends on physical parameters. In design optimization, these parameters are determined so that an objective function is minimized. For applications in vibrations and structures, the objective function depends on the frequency response function over a given frequency range, and we optimize it in the parameter space. Because of the large size of the system, numerical optimization is expensive. In this paper, we propose the combination of Quasi‐Newton type line search optimization methods and Krylov‐Padé type algebraic model order reduction techniques to speed up numerical optimization of dynamical systems. We prove that Krylov‐Padé type model order reduction allows for fast evaluation of the objective function and its gradient, thanks to the moment matching property for both the objective function and the derivatives towards the parameters. We show that reduced models for the frequency alone lead to significant speed ups. In addition, we show that reduced models valid for both the frequency range and a line in the parameter space can further reduce the optimization time. Copyright © 2012 John Wiley & Sons, Ltd.     

A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core

A new finite element (FE) model has been developed based on higher order zigzag theory (HOZT) for the static analysis of laminated sandwich beam with soft core. In this theory, the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to vary quadratically within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. A C₀ quadratic beam finite element is implemented to model the HOZT for the present analysis. Numerical examples covering different features of laminated composite and sandwich beams are presented to illustrate the accuracy of the present model. Many new results are also presented which should be useful for future research.     

Optimal shape control of functionally graded smart plates using genetic algorithms

This paper deals with optimal shape control of functionally graded smart plate containing patches of piezoelectric sensors and actuators. The genetic algorithm (GA) is designed to search for optimal actuator voltage and displacement control gains for the shape control of the functionally graded material (FGM) plates. The work extends the earlier finite element formulations of the two leading authors, so that it can be readily treated using genetic algorithms. Numerical results have been obtained to study the effect of the shape control of the FGM plates under a temperature gradient by optimising (i) the voltage distribution for the open loop control, and (ii) the displacement control gain values for the closed loop feedback control. The effect of the constituent volume fractions of zirconia, through varying the volume fraction exponent n, on the optimal voltages and gain values has also been examined.     

Dynamic analysis of laminated composite plates subjected to a moving oscillator by FEM

This paper presents a finite element model based on the first order shear deformation theory to investigate the dynamic behavior of laminated composite plates traversed by a moving oscillator. The oscillator model is assumed to be consisting of two nodal masses that are connected by means of a spring-damper unit. The governing equations of motion of two sub-systems are separately integrated by applying the Newmark’s time integration procedure. Then, the obtained equations are coupled and the responses of system components are calculated in each time step. The accuracy of algorithm is verified by comparing the numerical results of static, free vibration and simplified moving force problems analysis with the available exact solutions and other numerical results in the literature. Also, the effects of mass ratio, damping ratio of system components, stiffness of suspension system, velocity and eccentricity of moving oscillator on dynamic responses is parametrically studied. This algorithm can be applied to various boundary conditions, lamination schemes and fiber angels.