Haozhong Gu

New higher-order plate theory in modeling delamination buckling of composite laminates

A new higher order plate theory for modeling delamination buckling and postbuckling of composite laminates is developed. Delaminations between layers of composite plates are modeled by jump discontinuity conditions, in both lower and higher order terms of displacements, at the delaminated interfaces. Some higher order terms are identified at the beginning of the formulation by using the conditions that shear stresses vanish at all free surfaces including the delaminated interfaces. Therefore, all boundary conditions for displacements and stresses are satisfied in the present theory. Geometric nonlinearity is included in computing layer buckling. The general governing equations, along with all boundary and continuity conditions of plates, are derived for predicting the delamination buckling and postbuckling behavior. The associated delamination growth problem is also examined by the use of Griffith-type fracture criterion. A numerical example is presented to validate the theory. The results are also compared with experimentally obtained data.

Dynamic Responses of Smart Composites Using a Coupled Thermo-Piezoelectric -Mechanical Model

A completely coupled thermo-piezcelectricmechanical theory is developed to model the dynamic response of composite plates with surface bonded piezoelectric actuators. A higher order laminate theory is used to describe the displacement fields of both composite laminate and piezoelectric actuator layers to accurately model the transverse shear deformation which is significant in moderately thick constructions. A higher order temperature field is used to accurately describe the temperature distribution through the thickness of composite plates subjected to a surface heat flux. A finite element model is developed to implement the theory. The results obtained using this model are correlated with those using an uncoupled model. Numerical analysis reveals that the thermo-piezoelectricmechanical coupling has a significant effect on the dynamic response of composite plates. It also affects the control authority of piezoclectric actuators.

A higher order temperature theory for coupled thermo-piezoelectric-mechanical modeling of smart composites

A higher order temperature field that satisfies the thermal surface boundary conditions, necessary for accurate modeling of temperature distribution through the thickness of laminated structures, is developed. The theory is implemented in the coupled thermo-piezoelectric-mechanical analysis of composite laminates with surface bonded piezoelectric actuators. A higher order displacement theory is used to define the mechanical displacement field. Therefore, transverse shear effects are modeled accurately and the developed procedure is applicable to both thin and moderately thick laminates. The mathematical model is implemented using finite element technique. Numerical results are presented for a composite laminated plate, with one edge fixed, subjected to thermal loading. Correlations with ANSYS, for both the temperature field and the displacement field, are presented to validate the higher order temperature theory. Composite laminates of various stacking sequences are studied to investigate the effects on temperature field and displacement field. The results obtained using the coupled theory are compared with those obtained using the standard uncoupled theory. It is shown that thermal coupling affects plate deflection and control authority due to actuation.

Coupled Thermo-Piezoelectric-Mechanical Model for Smart Composite Laminates

A coupled thermo ‐piezoelectric ‐mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied loads, isdeveloped. The governing differential equationsare obtained by applying the principleof freeenergy and variational techniques. A higher-order displacement e eld is used to accuratelycapturethetransversesheareffectsinlaminatedcompositeplatesofarbitrarythickness.Adoubletriangular function expansion that satise es the boundary conditions is used as a solution. Both thermal and mechanical loads are considered, and the effect of actuation is studied. Composite laminates of various thickness and lengths are analyzed.Thethermalcouplingisshowntohavesignie canteffectsinbothquasi-staticandactiveresponseanalyses. Nomenclature aT = cE=T0 bij = dielectric permittivity cE = heat capacity cijkl = elastic constants Di = electric displacement vector di = thermal‐piezoelectric coupling constants Ei = electric e eld eijk = piezoelectric constants kij = thermal‐mechanical coupling constants L1 = displacement operator matrix L2 = piezoelectric operator matrix l1 = thermal operator vector N1

An experimental investigation of delamination buckling and postbuckling of composite laminates

The mechanics and mechanisms of delamination buckling and postbuckling of composites have been studied. Compression tests were carried out on HYE-3574 OH graphite/epoxy composites with built-in delaminations in order to evaluate the critical load and the actual postbuckling load-carrying capacity. The variation in structural configurations, such as ply stacking sequence and the location and the length of the delamination, were considered. It is observed that, in general, composite laminates can retain their load-bearing capacity by carrying higher loads after buckling. For particular cases, the ultimate load is found to be as high as three times the critical load. The delamination buckling mode is found to be closely related to the location and the length of the delamination. Excellent agreement is observed between the experimental values of critical load and those predicted by the previously developed new higher-order theory. Good comparisons are also presented for the initial postbuckling behavior.

Dynamics of Delaminated Composite Plates with Piezoelectric Actuators

A ree ned higher-order-theory-based e nite element model is developed for modeling the dynamic response of delaminated smart composite plates. The theory assures an accurate description of displacement e eld and the satisfaction of stress-free boundary conditions at all free surfaces including delamination interfaces. A nonlinear induced strain model is used. Vibration control is obtained through piezoelectric layers bonded on the composite plate. The theory is implemented using a e nite element technique, which allows the incorporation of practical geometries and boundary conditions, various sizes, and locations of delaminations, as well as discrete sensors and actuators. The resulting model is shown to agree well with published experimental data. Signie cant changes in dynamic properties are observed due to the presence of delamination.

Dynamics of delaminated smart composite cross-ply beams

A refined higher order theory-based finite element model is presented for modeling the dynamic response of delaminated smart composite cross-ply beams. The refined displacement field accurately accounts for transverse shear deformations through the thickness, and all traction-free boundary conditions are satisfied at all free surfaces including delamination interfaces. The developed theory provides an accurate, computationally efficient analysis tool for the study of smart composite cross-ply beams with piezoelectric sensing and actuation in the presence of delamination. The theory is implemented using the finite element method to allow the incorporation of practical geometries, boundary conditions and the presence of discrete piezoelectric transducers. A new formulation is presented to include nonlinear induced strain effects. Vibration control is accomplished by piezoelectric layers incorporated in the composite beam. The resulting finite element model is shown to agree well with published experimental data, and the results show significant improvements compared to existing analytical solutions. Numerical results presented in the paper indicate changes in natural frequencies, mode shapes and dynamic responses due to delaminations.

Exact elasticity solution for buckling of composite laminates

Abstract An exact elasticity solution is presented for the buckling of a simplysupported orthotropic plate whose behavior is referred to as cylindrical bending. The general class of problems involving the geometric configuration of any number of orthotropic layers bonded together and subjected to an inplane compressive load is also analyzed by making use of the uniform prebuckling stress assumption which is equivalent to the membrane assumption used in plate theories. The closed-form expressions for the displacements and stresses are derived and the nonlinear eigenvalue equations are presented which are used to solve for critical loads. The results obtained from the exact solution are compared with the critical loads furnished by the classical laminate theory, the first order and the refined third order shear deformation theory. The solution provides a means of accurate assessment of existing two-dimensional plate theories.

Modeling of smart composite box beams with nonlinear induced strain

A new smart composite box beam model is developed to investigate the behavior of helicopter rotor blades built around the active box beam. Piezoelectric actuators and sensors are surface bonded on the walls of the composite box beam. The new theory, based on a refined higher order displacement field of a plate with eccentricity, is a three-dimensional model which approximates the elasticity solution so that the box beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both in-plane and out-of-plane warpings are included automatically in the formulation. The formulations also include nonlinear induced strain effects of piezoelectric actuators. The procedure is implemented using finite element method. The developed theory is used to model the load carrying member of helicopter rotor blades with moderately thick-walled sections. Static analysis of the smart box beam under varying degrees of actuation has been performed. Very good overall agreement is observed with available experimental data for thin-walled sections without embedded actuators. The results show that piezoelectric actuation significantly reduces the deflection along the box beam span and therefore can be used to control the magnitude of rotor blade vibrations. The nonlinear actuation effect is found to be closely related to the material stiffness of the primary structure.

Three dimensional elasticity solution for buckling of composite laminates

Three-dimensional elasticity solutions are presented for the buckling of simply supported orthotropic and laminated composite plates. A uniform prebuckling stress assumption is made for composite laminates, which is equivalent to the membrane assumption used in plate theories. The closed-form expressions for the displacements and stresses are derived and a nonlinear eigenvalue problem is constructed which is used to solve for the critical load. The results obtained from the elasticity solution are compared with the critical loads furnished by the classical laminate theory and the refined third-order shear deformation theory. The solution provides a means of accurate assessment of existing two-dimensional plate theories.