Aditi Chattopadhyay

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 instability of composite laminates using a higher order theory

Abstract A higher order shear deformation theory is used to investigate the instability associated with composite plates subject to dynamic loads. Both transverse shear and rotary inertia effects are taken into account. The procedure is implemented using the finite element approach. The natural frequencies and the critical buckling load are computed and compared with the results based on the classical laminate plate theory and the first-order shear deformation theory. The first two instability regions are determined for various loading conditions using both first- and second-order approximations. These results are also compared with the other approaches. Significant deviations are observed for thick plates due to the presence of shear deformation.

Characterization of delamination effect on composite laminates using a new generalized layerwise approach

Abstract A dynamic analysis method has been developed to investigate and characterize the effect due to presence of discrete single and multiple embedded delaminations on the dynamic response of composite laminated structures with balanced/unbalanced and arbitrary stacking sequences in terms of number, placement, mode shapes and natural frequencies. A new generalized layerwise finite element model is developed to model the presence of multiple finite delamination in laminated composites. The new theory accurately predicts the interlaminar shear stresses while maintaining computational efficiency.

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 theory for modeling composite laminates with induced strain actuators

A refined higher order laminate theory is developed to analyze smart materials, surface bonded or embedded, in composite laminates. The analysis uses a refined displacement field which accounts for transverse shear stresses through the thickness. All boundary conditions are satisfied at the free surfaces. Non-linearities are introduced through the strain dependent piezoelectric coupling coefficients and the assumed strain distribution through the thickness. The analysis is implemented using the finite element method. The procedure is computationally efficient and allows for a detailed investigation of both the local and global effects due to the presence of actuators. The finite element model is shown to agree well with published experimental results. Numerical examples are presented for composite laminates of various thicknesses and the results are compared with those obtained using classical laminate theory. The refined theory captures important higher order effects which are not modeled by the classical laminate theory, resulting in significant deviations.

Dynamic analysis of composite laminates with multiple delamination using improved layerwise theory

A procedure has been developed to investigate the dynamic response of composite structures, with embedded multiple delaminations. A recently developed improved layerwise composite laminate theory is extended to model composite laminates of moderately large thickness with delamination. The theory accurately predicts interlaminar shear stresses while maintaining computational efficiency. Natural frequencies and mode shapes are computed for cross-ply laminates with delaminations placed at different locations. Experiments are conducted to validate the developed theory. Numerical results indicate excellent correlation with analytical solutions and experimental results. Parametric studies are conducted to investigate the effect of delamination location, both through the thickness and in plane, and number of delaminations on the dynamic response. A potential application of the developed procedure is in structural health monitoring where accurate predictions of dynamic response in the presence of delamination are important issues.

Modeling of adaptive composites including debonding

Abstract Debonding of piezoelectric actuators for use in composite structures can result insignificant changes to the static and dynamic response. This important issue is studied in thecurrent work. The refined higher order theory for composite laminates with embedded⧹surfacebonded piezoelectric sensors and actuators is extended to incorporate debonding of transducersby partitioning the laminate into debonded and nondebonded regions. The stress free boundaryconditions at the free surfaces are satisfied in the analytical formulation. Continuity conditionsbetween the debonded and the nondebonded regions, which are nontrivial for the higher ordertheory, are formulated and implemented using a penalty approach in the finite element model.The computational model is efficient and correlation with experimental results is very good.Numerical results are presented which indicate significant changes in the natural frequencies andmode shapes due to debonded transducers.

Experimental investigation of composite beams with piezoelectric actuation and debonding

Piezoelectric transducers can be used as sensors and actuators for vibration reduction in composite structures. Debonding at the transducer-laminate interface results in significant changes to the dynamic response and control authority. This important issue is studied in the current work. Composite specimens with surface bonded piezoelectric transducers were constructed with varying stacking sequences and debonding lengths. Closed loop control was implemented using an analog circuit. Experimental results were obtained for both open and closed loop frequencies and damping ratios. The results correlate well with a newly developed higher order based theory for modeling composites with debonded piezoelectric transducers. Significant changes are observed in the open and closed loop frequencies and damping ratios as a result of debonding.

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.

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

Abstract A refined higher order shear deformation theory is used to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modeling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Delamination is modeled through the multi-point constraint approach using the transformation matrix technique. For validation purposes, the natural frequencies and the critical buckling loads are computed and compared with three-dimensional NASTRAN results and available experimental data. The effect of delamination on the critical buckling load and the first two instability regions is investigated for various loading conditions and plate thickness. As expected, the natural frequencies and the critical buckling load of the plates with delaminations decrease with increase in delamination length. Increase in delamination length also causes instability regions to be shifted to lower parametric resonance frequencies. The effect of edge delamination on the static and dynamic stability as well as of delamination growth is investigated.