Dynamic buckling of a laminated composite stringer–stiffened cylindrical panel

The present study deals with the “dynamic buckling” of a laminated composite stringer–stiffened curved panel. The “dynamic buckling”, in the present study, is concerned with the unbounded lateral response of the panel, which is subjected to an axial impact load.In reinforced panels with widely spaced adequately stiff stringers, the structure may pass through two major states before its total collapse: buckling of the panel skin between stiffeners and buckling of the stiffeners themselves. This study focuses on the lowest buckling load of the stringer–stiffened panel, which is, buckling of the panel skin between stiffeners.The analysis of the laminated composite stringer–stiffened cylindrical panel was performed by using the commercial ANSYS finite element software. The model simulates the structure and its associated boundary conditions. The boundary conditions simulate the stringer–stiffened cylindrical panel as a part of a fuselage. The static buckling analysis was performed using the eigenvalue buckling approach to determine the static critical load. Modal analysis was used to calculate the first natural frequency and corresponding mode shape of the structure. Nonlinear transient dynamic analysis was used to determine the dynamic critical load. In the transient dynamic analysis the Newmark method with the Newton–Raphson scheme were used.In the present study, the equation of motion approach was applied. By this approach, the equations of motion were numerically solved for various load parameter values (loading amplitude and loading duration) to obtain the system response. Special attention was given to the neighborhood of loading durations corresponding to the period of the lowest bending frequency of the skin.For each load duration, the dynamic buckling load was calculated using a load versus lateral displacement curve generated by the ANSYS code.The results were plotted on a dynamic load amplification factor (DLF) graph. The DLF is defined, as the ratio of the dynamic buckling to the static buckling of the panel. For loading periods in the neighborhood of the lowest natural frequency of the panel, the DLF was less than unity. It means that, for those particular loading periods, the dynamic buckling load is lower than the static one.     

State vector approach of free-vibration analysis of magneto–electro-elastic hybrid laminated plates

In this paper, state variable formulation for free vibration of the laminated structures bonded and embedded actuators and sensors (piezoelectric and/or piezomagnetic) is established. The present mixed type formulation has the great advantage that the size of the system to be solved is independent of the number of layers and is of order three for free vibration of the laminate with bonded and embedded piezoelectric and/or piezomagnetic layers. Analytical solutions of 3D free vibration of simply supported piezoelectric and piezomagnetic composite plates have been presented. The transfer matrices for either closed circuit or open circuit piezoelectric and piezomagnetic layers are derived. The special case of elastic layer is also treated. The assembly procedure is described for the different electric and magnetic surface conditions. Numerical examples are analyzed to study the vibration characteristics of smart laminate plates with different stacking sequence and different span to thickness ratio.     

Active constrained layer damping of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of sandwich plate with laminated composite faces. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. Several honeycomb core materials like HEREX honeycomb and honeycomb with foam fill separated by different facing materials have been studied and a three-dimensional finite element model has been developed considering first order shear deformation theory individually for each layer of the sandwich plate. The effect of the ratio between the face sheet thickness and the core thickness of the sandwich plate on the frequency response has been studied. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Smart control of nonlinear vibrations of doubly curved functionally graded laminated composite shells under a thermal environment using 1–3 piezoelectric composites

This paper addresses the active control of geometrically nonlinear vibrations of doubly curved functionally graded (FG) laminated composite shells integrated with a patch of active constrained layer damping (ACLD) treatment under the thermal environment. Vertically/obliquely reinforced 1-3 piezoelectric composite (PZC) and active fiber composite (AFC) are used as the materials of the constraining layer of the ACLD treatment. Each layer of the substrate FG laminated composite shell is made of fiber-reinforced composite material in which the fibers are longitudinally aligned in the plane parallel to the top or bottom surface of the layer and the layer is assumed to be graded in the thickness direction by way of varying the fiber orientation angle across its thickness according to a power law. The novelty of the present work is that, unlike the traditional laminated composite shells, the FG laminated composite shells are constructed in such a way that the continuous variation of material properties and stresses across the thickness of the shell is achieved. The Golla-Hughes-McTavish (GHM) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. Based on the first-order shear deformation theory (FSDT), a finite element (FE) model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite shell under a thermal environment. Both symmetric and asymmetric FG laminated composite doubly curved shells are considered for presenting the numerical results. The analysis suggests that the ACLD patch significantly improves the damping characteristics of the doubly curved FG laminated composite shells for suppressing their geometrically nonlinear transient vibrations. It is found that the performance of the ACLD patch with its constraining layer being made of the AFC material is significantly higher than that of the ACLD patch with vertically/obliquely reinforced 1-3 PZC constraining layer. The effects of variation of piezoelectric fiber orientation in both the obliquely reinforced 1-3 PZC and the AFC constraining layers on the control authority of the ACLD patch have also been investigated.     

3D non-linear time domain FEM–BEM approach to soil–structure interaction problems

Dynamic soil–structure interaction is concerned with the study of structures supported on flexible soils and subjected to dynamic actions. Methods combining the finite element method (FEM) and the boundary element method (BEM) are well suited to address dynamic soil–structure interaction problems. Hence, FEM–BEM models have been widely used. However, non-linear contact conditions and non-linear behavior of the structures have not usually been considered in the analyses. This paper presents a 3D non-linear time domain FEM–BEM numerical model designed to address soil–structure interaction problems. The BEM formulation, based on element subdivision and the constant velocity approach, was improved by using interpolation matrices. The FEM approach was based on implicit Green's functions and non-linear contact was considered at the FEM–BEM interface. Two engineering problems were studied with the proposed methodology: the propagation of waves in an elastic foundation and the dynamic response of a structure to an incident wave field.     

Shell–tensionless foundation interaction and nonlinear thermoelastic stability analysis of laminated composite cylindrical panels

In this paper, the thermal buckling behavior of composite laminated curved panels on one-sided foundation is addressed. Governing equations of shell stability are derived based on classical shell theory (CST) and minimum total potential energy. They are solved by a hierarchical Rayleigh–Ritz technique. A part of the contribution is formulating effects of curvature and composite materials in nonlinear analysis of stability for cylindrical panels surrounded by one-sided foundations subjected to thermal loading. The other part is related to the results from parametric studies. In this work, the effects of parameters such as panel aspect ratio thickness, central angle, degree of material orthotropy, and foundation stiffness are investigated. It is observed that with an increase in panel aspect ratio the influence of one-sided constraint on the critical temperature is reduced for a flat panel, while it is magnified for a curved panel. The effect of nonlinear foundation on one-sided buckling of curved panels is highly dependent on parameters such as central angle, aspect ratio, thickness, and degree of foundation stiffness, such that any change in each parameter might have direct influence and severe change on the penetration of the panel into the foundation. The results for simpler case studies are compared and validated with those available in the literature.     

Active constrained layer damping of geometrically nonlinear vibrations of smart laminated composite sandwich plates using 1–3 piezoelectric composites

This paper deals with the analysis of active constrained layer damping (ACLD) of geometrically nonlinear vibrations of sandwich plate with orthotropic laminated composite faces separated by a flexible core. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1?C3 piezoelectric composites. The Golla?CHughes?CMcTavish method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The first-order shear deformation theory and the Von Kármán type nonlinear strain displacement relations are used for analyzing this coupled electro-elastic problem. A three dimensional finite element model of smart laminated composite sandwich plate integrated with ACLD patches has been developed to investigate the performance of these patches for controlling the geometrically nonlinear vibrations of the plates. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the sandwich plates with laminated cross-ply and angle-ply facings for suppressing their geometrically nonlinear vibrations. Particular emphasis has been placed on investigating the effect of the variation of piezoelectric fiber orientation angle on the performance of the ACLD treatment.     

Improvement in dynamic properties of laminated MWCNT-polystyrene composite beams via an integrated numerical–experimental approach

A new concept for the optimization of dynamic behavior of laminated nanocomposites is introduced where fiber orientation factor in continuous fiber-reinforced composites is replaced by different wt.% of carbon nanotubes (CNTs) in each layer. First, at a design concept level, an optimum distribution of multi-walled CNTs (MWCNTs) through the thickness of a typical cantilever beam is sought to achieve its highest fundamental natural frequency for a given weight percent of MWCNTs. This is done using a finite element (FE) model in ABAQUS along with a user-defined Python code. Next, based on the obtained optimum distribution, actual laminated MWCNT/polystyrene (PS) composite beams were fabricated and their effective stiffness, fundamental natural frequencies and damping ratios were measured through static deflection and free vibration tests. It was found that the optimum distribution of MWCNTs resulted in an increase of 21.9% and 10.4% in the effective Young’s modulus and the fundamental damped natural frequency values, respectively, which were almost two-fold higher than those of a beam with a uniform MWCNT distribution. In addition, compared to a pure polymer beam, 38.9% and 27.8% improvements in the damping ratio of the uniformly and optimally distributed MWCNT polymer composite beams were achieved.     

Nanoindentation measurement of core–skin interphase viscoelastic properties in a sandwich glass composite

Mechanics of Time-Dependent Materials - Debonding at the core–skin interphase region is one of the primary failure modes in core sandwich composites under shear loads. As a result, the...     

Behavioural analysis of a time series–A chaotic approach

Out of the various methods available to study the chaotic behaviour, correlation dimension method (CDM) derived from Grassberger-Procaccia algorithm and False Nearest Neighbour method (FNN) are widely used. It is aimed to study the adaptability of those techniques for Indian rainfall data that is dominated by monsoon. In the present study, five sets of time series data are analyzed using correlation dimension method (CDM) based upon Grassberger-Procaccia algorithm for studying their behaviour. In order to confirm the results arrived from correlation dimension method, FNN and phase randomisation method is also applied to the time series used in the present study to fix the optimum embedding dimension. First series is a deterministic natural number series, the next two series are random number series with two types of distributions; one is uniform and another is normal distributed random number series. The fourth series is Henon data, an erratic data generated from a deterministic non linear equation (classified as chaotic series). After checking the applicability of correlation dimension method for deterministic, stochastic and chaotic data (known series) the method is applied to a rainfall time series observed at Koyna station, Maharashtra, India for its behavioural study. The results obtained from the chaotic analysis revealed that CDM is an efficient method for behavioural study of a time series. It also provides first hand information on the number of dimensions to be considered for time series prediction modelling. The CDM applied to real life rainfall data brings out the nature of rainfall at Koyna station as chaotic. For the rainfall data, CDM resulted in a minimum correlation dimension of one and optimum dimension as five. FNN method also resulted in five dimensions for the rainfall data. The behaviour of the rainfall time series is further confirmed by phase randomisation technique also. The surrogate data derived from randomisation gives entirely different results when compared to the other two techniques used in the present study (CDM and FNN) which confirms the behaviour of rainfall as chaotic. It is also seen that CDM is underestimating the correlation dimension, may be due to higher percentage of zero values in rainfall data. Thus, one should appropriately check the adaptability of CDM for time series having longer zero values.     

Postbuckling behavior of a pressurized stiffened composite panel – Part II: Numerical analysis. Effect of the geometrical imperfections

Numerical simulations of the experimental tests performed with a pressurized composite stiffened panel are presented in this paper. As a consequence of the high slenderness of this structural typology, pressure caused the panel to enter the postbuckling regime. Previous experimental tests showed that the panel had a large safe postbuckling range, the experimental collapse pressure being over four times the first buckling load. Due to the relevant influence of the geometric imperfections on the global response, a procedure for taking into account actual imperfections in the development of the models is proposed. This procedure can be used as a tool to facilitate the modeling of the actual geometry of the panel, mainly the zone of the skin located between the stringers. A satisfactory agreement with experimental results has been reached using the proposed procedure.     

Coupling FEM and symmetric BEM for dynamic interaction of dam–reservoir systems

A numerical model coupling boundary and finite elements suitable for dynamic dam–reservoir interaction is presented herein. This model involves standard finite element idealization of the dam structure displacements and a new symmetric boundary element formulation of the unbounded reservoir domain leading to an equivalent symmetric stiffness matrix for the discretized pressure field. These two basic parts of the computation are directly coupled by imposing an equilibrium condition at the fluid–structure interface, then the resulting algebraic system is reduced by localizing the coupled terms in the global mass matrix such as usually achieved in the added-mass formulation. Finally, the performance and the accuracy of this model are examined by comparing its results to those obtained from three other numerical models.     

Postbuckling behaviour of a pressurized stiffened composite panel – Part I: Experimental study

Results of an experimental study of the buckling and postbuckling behaviour until the collapse of a cylindrical stiffened composite panel are presented. The specimen is subjected to a uniform pressure on one of its faces using a combination of gas and liquid inside a hermetic box. The present analysis shows the postbuckling load carrying capacity of elements of this kind without developing failure mechanism. Due to the high sensitivity to geometric imperfections of these structures, a simple procedure to obtain their measurements once the specimen is placed in the experimental device is set out. The data registered in these tests will be used for the subsequent validation of the numerical model in order to develop more accurate solutions. This will produce a significant increment in the fidelity of those predictions, making possible a reduction in the number of tests to be performed in real applications.     

Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach

This paper presents the Kriging model approach for stochastic free vibration analysis of composite shallow doubly curved shells. The finite element formulation is carried out considering rotary inertia and transverse shear deformation based on Mindlin’s theory. The stochastic natural frequencies are expressed in terms of Kriging surrogate models. The influence of random variation of different input parameters on the output natural frequencies is addressed. The sampling size and computational cost is reduced by employing the present method compared to direct Monte Carlo simulation. The convergence studies and error analysis are carried out to ensure the accuracy of present approach. The stochastic mode shapes and frequency response function are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results using Kriging model and its performance.     

Nonlinear thermomechanical dynamic buckling analysis of imperfect viscoelastic composite/sandwich shells by a double-superposition global–local theory and various constitutive models

Almost no dynamic buckling analysis has been performed so far for the sandwich/multilayer viscoelastic shells. Even the vibration analyses of the mentioned shells have been restricted to the harmonic loads ignoring the transverse stresses and their continuity at the mutual interfaces of the layers, and the transverse flexibility of the shell. In the present paper, a high-order double-superposition global–local theory inherently suitable for nonlinear analyses is proposed and employed for nonlinear dynamic buckling and postbuckling analyses of imperfect viscoelastic composite/sandwich cylindrical shells subjected to thermomechanical loads. Depending on the nature of the applied loads, both complex modulus and hierarchical constitutive models are used for the viscoelastic materials. Results reveal that as the time duration of the suddenly applied loads decreases beyond the first natural period of the shell, the dynamic buckling load becomes much higher than the static buckling load, especially for the rectangular load–time histories. Furthermore, the relaxation behavior of the viscoelastic material may decrease the dynamic buckling load.     

Structural performance of composite sandwich bridge decks with hybrid GFRP–steel core

This paper presents the static and fatigue performance of composite sandwich bridge decks with hybrid GFRP–steel core. The composite sandwich bridge deck system is comprised of wrapped hybrid core of GFRP grid and multiple steel box cells with upper and lower GFRP facings. Its structural performance under static loading and fatigue loading with a nominal frequency of 5 Hz was evaluated. The responses from laboratory testing were compared with the ANSYS finite element predictions. The failure mode of the proposed composite sandwich bridge deck was more favourable because of the yielding of the steel tube when compared with that of all-GFRP decks. The ultimate failure of the composite sandwich deck panels occurs by shear of the bonded joints between GFRP facings and steel box cells. Results from fatigue load test indicated no loss in stiffness, no signs of de-bonding and no visible signs of deterioration up to 2 million load cycles. The thickness of the composite sandwich deck retaining the similar stiffness may be decreased to some extent when compared with the all-GFRP deck. This paper also presents design of a connection between composite sandwich deck and steel girder.     

Fractional Fourier transform of a higher-order cosh–Gaussian beam

A higher-order cosh–Gaussian beam is an appropriate model to describe the flattened laser beam. The fractional Fourier transform (FRFT) is applied to treat the propagation of higher-order cosh–Gaussian beams. An analytical expression for a higher-order cosh–Gaussian beam passing through a FRFT system has been derived. By using the derived expression, the properties of a higher-order cosh–Gaussian beam in the FRFT plane are graphically illustrated with numerical examples.     

Thermal postbuckling analysis of fiber–metal laminated plates including interfacial damage

Considering the effects of interfacial damage, geometric nonlinearity and transverse shear deformation, thermal postbuckling of fiber–metal laminated plates including interfacial damage is analyzed in detail. Firstly, the Heaviside step function and higher order shear deformation functions are introduced into displacement field so that the damage degree can be characterized. Then, the shape functions can be determined by using the stress continuity conditions between interfaces and the stress boundaries on surfaces. By using the generalized variational principle, the thermal postbuckling equilibrium equations of fiber–metal laminated plates including interfacial damage are established. Finally, the thermal postbuckling problem is solved by adopting finite difference method and iteration method. In numerical examples, the effects of interfacial damage, width-to-thickness ratio and thermal load on the thermal postbuckling of fiber–metal laminated plates including interfacial damage are investigated.