Modeling Of Composite Plates Research Articles

A load reconstruction model for advanced grid-stiffened composite plates

This paper presents a practical method for load reconstruction on an advanced grid-stiffened (AGS) composite plate. With this method, separate AGS ribs are smeared onto a continuous unsymmetrical plate. A forward response approximate model is then built to describe the dynamic response of the plate. Numerical verification indicates that the proposed model can simulate the structure with reasonable accuracy and high computing speed. We also adopted an optimization technology to recover the load history and location. The load history is recovered with a smoothing/filter algorithm and the load location is estimated with a linear search for the lowest value of a defined figure of merit J, which measures the difference between the calculated response and the measured response. The feasibility of the reconstruction technology has been verified by numerical experiments in which good agreements were obtained. Since it calculates rapidly, it is possible to use the proposed method to develop an automatic system to monitor environmental conditions causing emergency in real time.

Orthotropic material properties of the gerbil basilar membrane

Material properties of the cochlear partition play an important role in understanding the cochlear hydrodynamics. In this paper, two sets of experimental results are analyzed to extract the orthotropic material properties of the gerbil cochlear partition at different longitudinal locations. In order to accomplish this, a geometrically nonlinear composite orthotropic plate model is employed. The model is used to predict both out‐of‐plane and in‐plane motion of the partition under a static finite area distributed load. Both in‐plane and out‐of‐plane motion are needed for comparison with recent experimental results. It is shown that the spatial decay rate (the space constant) for the in‐plane deflection is different from the out‐of‐plane deflection, which has a significant effect on the derived partition properties. The size of the probe tip is shown to have little influence on the results. Results are presented for two types of boundary conditions. Orthotropy ratios (the ratio of the two elastic moduli) determined from the experimental data are found to vary with longitudinal position and choice of boundary conditions. Orthotropy ratios vary from 65 close to the base to 10 in the upper middle turn of the cochlea.

Development of an acoustical energy harvester

This paper presents the development of one component of a miniature acoustical energy harvesting system that is designed to convert acoustical energy into electrical energy. This component consists of a composite circular membrane containing a circular piezoelectric ring near the clamped boundary. An acoustic pressure fluctuation leads to a deflection of the membrane. This deflection generates a strain concentrated near the clamped boundary. The piezoelectric material, strategically placed in this region of high strain, converts the strain into an electrical voltage that can then be utilized in an electrical circuit or stored in a battery. The energy harvester was designed by combining a linear piezoelectric composite plate model with a lumped-element, electroacoustic model. Characterization was performed via acoustic excitation in a plane-wave tube. Preliminary results indicate a maximum generated output voltage of 18.2 mV across a 78.3−kΩ resistive load, resulting in 4.2 μW of generated power for an incident sound pressure level of 153.4 dB.

A simple thermopiezoelastic model for smart composite plates with accurate stress recovery**Presented at the 44th Structures, Structural Dynamics and Materials Conference, Norfolk,VA, 7–10 April 2003.

A Reissner–Mindlin model for analyzing laminated composite plates including piezoelectriclayers under mechanical, thermal and electric loads has been constructed using thevariational-asymptotic method. The present work formulates the original nonlinear,three-dimensional, one-way coupled, thermopiezoelasticity problem allowing for arbitrarydeformation of the normal line and using a set of intrinsic variables defined on the referenceplane. The variational-asymptotic method is used to rigorously split the three-dimensionalproblem into two problems: a nonlinear, two-dimensional, plate analysis over the referenceplane to obtain the global deformation, and a linear analysis through the thickness toprovide both the two-dimensional generalized constitutive model and recovery relations toapproximate the original three-dimensional results. The obtained asymptoticallycorrect second-order electric enthalpy is cast into the form of the commonly usedReissner–Mindlin model to account for transverse shear deformation. The present theory isimplemented into the computer program VAPAS (variational-asymptotic plate and shellanalysis). Results for several cases obtained from VAPAS are compared with theexact thermopiezoelasticity solutions, classical lamination theory and first-ordershear–deformation theory for the purpose of demonstrating the advantages of the presenttheory and the use of VAPAS. The proposed theory can achieve an accuracy comparableto higher-order layerwise theories at the cost of a first-order shear–deformationtheory.

Equivalent Finite Element Modeling of Thick Composite Structures for Analysis of Composite Hingeless Hub System

Finite element analysis for thick composite structures is rather complicated. Two-dimensional modeling, which is relatively easy to make, can cause inaccurate result since the plane stress condition cannot be applied, while three-dimensional modeling is hard to make. In the three- dimensional modeling, it is difficult to model all the layers with different material properties and ply orientation in the structure. In this paper, an equivalent modeling is proposed and numerically tested for analysis of thick composite structures. The method has been verified for the modeling of composite plate and circular composite tube in order to find their bending deflection and natural frequency. MSC/NASTRAN and PATRAN are used for the calculation. It has been confirmed that three-dimensional analysis must be conducted for thick structures and the equivalent modeling is proven to be accurate when layers with same characteristics are properly grouped. The proposed modeling technique has been applied to analyze hingeless composite rotor hub system designed by Korea Aerospace Research Institute (KARI). Detailed three-dimensional modeling for this structure is almost impossible to make due to its complex geometry of thick composite structures. Using the proposed equivalent modeling technique, failure analysis was performed based on stress/strain criterion and the safety of each part was checked. Deflection of the hub system was validated comparing with the result from the simple analytical beam model, and the numerical result will be used for the next design cycle of the composite hub system.

Experimental Validation of Refined Models of Composite Plates

Experimental Validation of Refined Models of Composite Plates

Dynamic stability analysis of finite element modeling of piezoelectric composite plates

The dynamic stability of negative-velocity feedback control of piezoelectric composite plates using a finite element model is investigated. Lyapunov’s energy functional based on the derived general governing equations of motion with active damping is used to carry out the stability analysis, where it is shown that the active damping matrix must be positive semi-definite to guarantee the dynamic stability. Through this formulation, it is found that imperfect collocation of piezoelectric sensor/actuator pairs is not sufficient for dynamic stability in general and that ignoring the in-plane displacements of the midplane of the composite plate with imperfectly collocated piezoelectric sensor/actuator pairs may cause significant numerical errors, leading to incorrect stability conclusions. This can be further confirmed by examining the complex eigenvalues of the transformed linear first-order state space equations of motion. To overcome the drawback of finding all the complex eigenvalues for large systems, a stable state feedback law that satisfies the second Lyapunov’s stability criteria strictly is proposed. Numerical results based on a cantilevered piezoelectric composite plate show that the feedback control system with an imperfectly collocated PZT sensor/actuator pair is unstable, but asymptotic stability can be achieved by either bonding the PZT sensor/actuator pair together or changing the ply stacking sequence of the composite substrate to be symmetric. The performance of the proposed stable controller is also demonstrated. The presented stability analysis is of practical importance for effective design of asymptotically stable control systems as well as for choosing an appropriate finite element model to accurately predict the dynamic response of smart piezoelectric composite plates.

A new asymptotic model for a composite piezoelastic plate

A new asymptotic homogenization piezoelastic composite plate model is obtained. Derivation is based on a modified two-scale asymptotic homogenization technique applied to a rigorously formulated piezoelectric problem for a three-dimensional thin composite layer of a periodic structure. The obtained model makes it possible to determine both local fields and the effective properties of piezoelectric plate by means of solution of the obtained three-dimensional local unit cell problems and a global two-dimensional piezoelastic problem for a homogenized anisotropic plate. It is shown, in particular that the effective stiffnesses generally depend on the local piezoelectric constants of the material. The general symmetry properties of the effective stiffnesses and piezoelectric coefficients of the homogenized plate are derived. The general model is applied to a practically important case of a laminated anisotropic piezoelastic plate, for which the analytical formulas for the effective stiffnesses, piezoelectric and dielectric coefficients are obtained. Theory is illustrated by a numerical example of a piezoelectric laminated plate of a specific structure.

Contribution to the nonlinear theory of multilayered composite shells featuring damaged interfaces

Based on a displacement field which: (i) accounts for an arbitrary distribution of the tangential displacements through the shell thickness; (ii) fulfills a priori the continuity conditions on the transverse shear stresses at the interfaces between the layers; (iii) fulfills the zero transverse shear conditions on the top and bottom surfaces; and (iv) allows for jumps in the tangential displacements when interlayer slips are present, the equations governing the geometrically nonlinear elastodynamic behavior of multilayered composite shallow shells are derived by using the virtual work principle. First-order and third-order shallow shells models are obtained as special cases. The work is an extension of the multilayered composite shallow shells of a recently developed model for multilayered composite plates featuring damaged interfaces [AIAA J, 35(11) (1997) 1753].

Modeling Segmented Active Constrained Layer Damping Using Hybrid Displacement Field

A finite element model for composite plates with active constrained layer (ACL) damping is developed using hybrid displacement fields. The higher order displacement field is used in the composite plate to capture the transverse shear deformations. Since viscoelestic and piezoelectric layers are made from certain isotropic material, the first and the second order displacement fields are employed in these layers to maintain computational efficiency in problem solution. The refined displacement fields defined in different material layers are derived by applying the displacement and transverse shear stress continuity conditions at interfaces of different materials and the traction-free boundary conditions at the top and the bottom surfaces of the structure. The anelastic displacement field method is used to implement the viscoelastic material model to enable time domain finite element analysis. The- finite element model is validated by comparison with NASTRAN 3D finite element modal analysis. The developed technique isused to investigate the dynamic responses of a cantilever composite plate with ACLs. Numerical results are presented with both the open and closed loop control. Significant improvements are observed with the use of active control treatment.

A Method for Establishing Hybrid Piezoelectric Composite Plate Theories with Continuous Interlaminar Stresses

In the present paper, a regular method is proposed to establish approximate piezoelectric composite plate theories with continuous interlaminar stresses. As an application of the treatment, a hybrid piezoelectric composite plate model with eight unknown displacement and electric potential parameters is developed. The theory satisfies the continuity conditions of transverse shear stresses at layer interfaces and is adequate for both global and ply level analysis. Furthermore, for a composite plate with any number of piezoelectric and fiber-reinforced layers, the number of unknown displacement and electric potential parameters in the governing equations is fixed for a specific approximate model. The methodology suggested in the paper can be used to construct approximate piezoelectric composite plate theories with various degrees of accuracy and unknown parameters.

A mixed model for adaptive composite plates with piezoelectric for anisotropic actuation

A theoretical formulation for modelling composite smart structures, in which the piezoelectric actuators and sensors are treated as constituent parts of the entire structural system, is presented. The mathematical model is based on a High Order Displacement field coupled with a Layerwise Linear electric potential. This model is developed for a composite laminated plate structure using Hamilton’s variational principle with the Finite Element (FE) formulation. The performance of the 8 node element was found to be superior to the four node element for very thin structures. This formulation was verified using existing FE software and results from literature. Investigation into the effects of different actuator locations, orientations and electric field directions illustrate anisotropic actuation capabilities. Then the variation in mechanical and piezoelectric anisotropy was also examined.

Damage Analysis of Honeycomb Core Composite Sandwich Plate Subjected Low Velocity Impact

A systematic study on the impact process and damage characteristics of honeycomb core composite sandwich plates were completed on the basis of the ex-study on laminated composite plates. A series of quasi-static transverse indentation tests of composite sandwich plates are carried out to study the contact law of honeycomb core sandwich composites. An analysis program of the transient dynamic finite element analysis was developed to calculate the impact characteristics of the impactor and the composite sandwich plate, and to predict the damage to the composite sandwich plate during the low velocity impacts process. For estimating the occurrence and the extension of the damage to the composite sandwich plate subjected impact, an impact damage model of the honeycomb core composite sandwich plates was set up and applied in the program. This model consisted of the damage occurring criterion and the damage extension criterion. A simplified criterion of the damage to honeycomb core was proposed in this paper. The results of numerical calculation showed that the impact energy had significant effect on the impact contact face and the damage process of sandwich plates, and the impact characteristics of composite sandwich plate were different from laminated composite plate. Finally, a series of standard low velocity tests on honeycomb core composite sandwich plates were carried out to demonstrate the analysis results. The comparison between both showed that the predictions agree with the test data fairly well.

Delamination Modeling and Detection in Smart Composite Plates

A refined model for smart composite plates with delamination is developed. The modeling is based on a third order refined displacement field, which satisfies the stress free boundary conditions at all free surfaces including delamination interfaces. The displacement field also accounts for the presence of distributed piezoelectric actuators. The mathematical model is implemented using the finite element method. The dynamic strain is analyzed for smart composites with and without delamination. Next, a new approach is investigated for the detection of delamination in smart composites based on the Root-Mean Square (RMS) values of the plate response subject to disturbances. Numerical results presented show accurate location of the delamination and its size.

Thermoelastic Fracture Mechanics for Nonhomogeneous Material Subjected to Unsteady Thermal Load

This article provides a comprehensive treatment of cracks in nonhomogeneous structural materials such as functionally graded materials. It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using a laminated composite plate model to simulate the material nonhomogeneity, we present an algorithm for solving the system based on the Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problems in the functionally graded materials with arbitrarily varying material properties. The algorithm can be applied to steady state or transient thermoelastic fracture problem with the inertial terms taken into account. As a numerical illustration, transient thermal stress intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of nonhomogeneous material with properties varying in the thickness direction. [S0021-8936(00)01601-9]

Coevolutionary Approaches to Structural Optimization

The numerical results on the shape control of laminated plates with piezoelectric actuators demonstrate that even if the plate is unconstrained the piezoelectrically induced in-plane stresses may signie cantly affect the mechanical behavior of the plate. Therefore, for the case of combined in-phase and out-of-phase piezoelectric actuation, accurate modeling of composite plates with piezoelectric elements should account for the stress-stiffening effects. The importance of the stress-stiffness effect depends on the magnitude of the in-phase actuation and geometric arrangement of the piezoelectric actuators, boundary conditions, geometry of the problem, and material properties. The ability of controlling the plate stiffness has potentially interesting applications in smart structures. For example, piezoelectric actuationsystemsmay be designed to tune the vibrationfrequencies of composite plates. Also, the problem of buckling control of composite plates with piezoelectric elements can be properly modeled using the present formulation.

MIXED VARIATIONAL FORMULA FOR THE THERMAL BENDING OF LAMINATED PLATES

A mixed variational formula based upon Hamilton's principle is obtained including the thermomechanical action of composite structures. Based on this formula, a linear thermomechanical composite plate model is presented. The model accounts for a Mindlin-type assumption on displacements and stresses in consistence with general surface conditions. So the rationale for the shear correction factor is obviated. Governing equations of orthotropic composite plates subjected to thermal and mechanical loading are derived. A wide variety of results are presented. The validity of the model is demonstrated by comparison with solutions available in the literature. The present results are in good agreement with the results of others.

MULTI-MODAL VIBRATION CONTROL OF SMART COMPOSITE PLATES

In this paper, multi-modal vibration control of smart composite plates has been studied. Piezoelectric films and ceramics have been used as sensors and actuators in surface bonded forms. For modeling and analysis of smart composite plates, an efficient finite element method based on the layerwise plate theory has been used. The effect of thickness changes due to bonded piezoelectric materials and variable in-plane displacement fields on the dynamic, actuating and sensing characteristics have been considered in the finite element formulation. This study includes an optimization method based on genetic algorithms to select appropriate locations of piezoelectric sensors and actuators of a smart composite plate for maximization of control performance. The cost function used in the optimization is based on degrees of controllability, observability, and spillover prevention. Experimental multi-modal vibration control has been also performed. A smart composite plate is prepared according to the optimization results for the experimental works. Coupled positive position feedback algorithms have been implemented in digital signal processing (DSP) system. The control results show that vibration level of the controlled modes has been significantly reduced with negligible effect on the residual modes.

Second-approximation shear theory for shallow layered shells and plates

Analysis of a second-approximation refined shear model for shallow layered composite shells and plates with a substantially inhomogeneous structure over the thickness is presented. The tangential displacements and corresponding normal stresses are expressed in the form of a polynomial of the fith degree in the transverse coordinate and contain squared rigidity characteristics. In this way, the accuracy of results and practical coincidence with the 3D solutions is ensured. Based on the refined model, a theory of shallow layered shells is developed. A system of resolving equations of sixteenth power together with appropriate boundary conditions was obtained and solved analytically. It is shown that the area of application of the formed model is extended as compared with the model of the first approximation. The model proposed allows us to examine the stress-strain state of layered composite structures of substantially different thickness and physical-mechanical characteristics of the layers, including the possibility of simulating relatively large shear deformations of rigid layers separated by a low-modulus thin interlayer pliable to transverse shear.

On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element

In the analysis of composite beams and plates, a higher-order shear deformation theory can lead to finite elements having the same number of nodal variables but giving solutions with different accuracy. By studying the interpolation order of the element bending strain, this paper discusses the efficient finite element modeling of composite beams and plates based on higher-order shear deformation theories i.e. how to choose the proper strain expressions to formulate accurate elements under the same number of nodal degrees of freedom. As an example, a simple and accurate third-order composite beam element is presented, which possesses a linear bending strain as opposed to the constant bending strain in existing higher-order composite beam elements. The numerical examples show that the present composite beam element is more accurate than the higher-order beam elements which are based on the same higher-order theory and having the same number of nodal variables but using a different bending strain expression.