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This paper presents a detailed treatment of the formulation of static, bucking and vibration analysis of non-prismatic thin-walled composite spatial members of generic section. The theory is limited to small strains, moderate deflections and small rotations. The torsional shear strain on the middle surface of the beam wall is zero for an open contour while it corresponds to constant shear flow for a closed contour. Rigorous expressions for strains based on membrane theory of shells are obtained through which the effect of nonlinear tapering is considered. Solutions for classical buckling and vibration analysis by the finite element method are discussed. Numerical integration by using Gaussian quadrature on the cross-sections for the computation of sectorial properties and stress resultants and over the length for the computation of flexural, geometric and mass matrices is suggested. Some examples are solved and critical bucking loads, natural frequencies and the corresponding buckled and mode shapes are obtained by the Jacobi iteration procedure.

The present study deals with the dynamic stability of laminated composite pre-twisted cantilever panels. The effects of various parameters on the principal instability regions are studied using Bolotin's approach and finite element method. The first-order shear deformation theory is used to model the twisted curved panels, considering the effects of transverse shear deformation and rotary inertia. The results on the dynamic stability studies of the laminated composite pre-twisted panels suggest that the onset of instability occurs earlier and the width of dynamic instability regions increase with introduction of twist in the panel. The instability occurs later for square than rectangular twisted panels. The onset of instability occurs later for pre-twisted cylindrical panels than the flat panels due to addition of curvature. However, the spherical pre-twisted panels show small increase of nondimensional excitation frequency.

The steady increase of composite parts in civil aircraft over the last three decades has recently been followed by a radical increase of weight percentage composites in the structure. In the most recent long range aircraft under development by both Boeing and Airbus, most major structure components, not only of the wings but also of the fuselage, now consist of composites. This necessitates an increased use of efficient structural simulation capabilities.

One important aspect of this is the virtual testing of shear compression panels at Airbus, which will be presented here. Having served well for Glare during the A380 development, it is currently undergoing considerable development to extend its capacity to composites. Summarized under the designation "Simulation of Panels in AirCraft", (SIMULPAC), this platform is here introduced and described in terms of functioning and methodology. It has played a major role in the initial A350 developments: in the first designs, during virtual testing of the configuration of new components and for predictions of the first real shear compression panels.

In this paper, closed-form approximate solutions for the geometrically nonlinear behaviour of rectangular laminated plates with flexural orthotropy under longitudinal compression are presented. Based on the governing Marguerre-type differential equations postulated for imperfect plates, two plate configurations are discussed in detail, representing important application cases in practical engineering work. The first configuration is a laminated plate that is simply supported at all four edges (the so-called SSSS plate), while for the second configuration clamped unloaded longitudinal edges are considered (denoted as the SSCC plate). For both plate configurations, rather simple closed-form approximations in the form of trigonometric shape functions are employed for the description of the out-of-plane postbuckling plate deflections. Based on the chosen shape functions, the compatibility condition with respect to the in-plane strains is fulfilled exactly, while the out-of-plane equilibrium condition for a deflected plate element is not, but is solved using a Galerkin-type formulation instead. Eventually, very simple closed-form solutions for all postbuckling state variables (deflections, in-plane edge displacements, and effective widths) are derived that can be used very conveniently in engineering practice. The high accuracy of the presented analysis methods is established by comparison with the results of other authors.

Modern fiber placement machines allow laminates with spatially varying stiffness properties to be manufactured. In earlier research, the authors optimized variable stiffness plates for maximum buckling load, demonstrating significant improvements in load-carrying capacity. In aerospace applications, panel structures are often permitted to enter the postbuckling regime during service. It is, therefore, not only important to understand their postbuckling behavior, but also to develop fast analysis methods that can subsequently be used in a design optimization framework. The aim of the present research is to study the postbuckling behavior of the optimized plates using a perturbation method that has been developed earlier within a general-purpose finite element environment. The perturbation approach is used to compute postbuckling coefficients, which are used to make a quick estimate of the postbuckling stiffness of the panel and to establish a reduced-order model. In the present work, the postbuckling analysis of variable stiffness plates is carried out using the reduced-order model, and the potential of the approach for incorporation within the optimization process is demonstrated.

Understanding the mechanical behaviors of graphene under different stress states is crucial to their applications. Comparing with the bucking behavior of free standing graphene under compression, the monolayer graphene embedded in the polymer matrix has a higher critical buckling load and smaller atomic length scale wavelengths as well as buckling amplitudes. In this paper, the molecular dynamics (MD) method is adopted to study the buckling behaviors of embedded graphene under uniaxial compression. Two MD models are built, namely the hybrid MD/continuum nanomechanics model and the full MD model. Periodical boundary conditions are applied in the MD simulations. Graphene sheets with different aspect ratios are considered and it is observed that the critical buckling strain of graphene sheets embedded in polymer matrix is independent of their aspect ratios. The current simulation results match well with the reported experimental results. Furthermore, it is demonstrated that the current simulation method can produce clear buckling shapes, which are difficult to observe in nanoscale experiments.

The present paper describes a numerical modeling approach to predict impact resistance and residual Shear Strength After Impact (SSAI) of fiber reinforced polymer composites subjected to bird strike loading. An improved damage mechanics based on material model, previously developed by the authors, is combined with an equation of state to simulate the progressive failure in composite aerostructures subjected to bird strike loading. A series of bird strike impacts on flat panels fabricated from low cost woven glass composite materials are used to validate the material model for practical composite component applications. A numerical study on the residual SSAI of a typical composite shear web is also presented. The panels are modelled with shell elements only. The proposed material model formulation accounts for the strain rate enhancement to strength and shear nonlinearities observed in composite materials. A hydrodynamic model for the bird, based on 90% water and 10% air, is derived to represent the behavior of the bird for all impact scenarios considered. The bird is heterogeneous in nature. However, a uniform material behavior is assumed with a geometry based on a 2:1 length to diameter ratio with a cylindrical body and spherical end caps using Lagrangian mesh. Appropriate contact definitions are used between the bird and the composite panel. The simulations results are compared to experimental results and conclusions drawn.

Glass-fiber reinforced polymer (GFRP) composite materials have an undisputed dominance over conventional metallic materials. However, susceptibility to barely visible or invisible internal damage due to impact has increased the demand for these composite materials in robust real-time structural health monitoring (SHM) system since they are capable of localizing the source of impact. Thus, in this paper, an in situ FBG sensor was embedded in a GFRP beam, providing an online real-time monitoring system and with the knowledge of cross-correlation linear source location (CC-LSL) algorithm, the impact location was capable of being determined in a split second. The consistency of cross-correlation function in providing repeatable results for all trials estimated a consistent time difference for all the impact points. The CC-LSL algorithm also revealed that the highest percentage of error was only 4.21% away from the actual hit. In the meantime, FBGs also showed good results as a dynamic strain measuring device in capturing frequency response at certain orientations compared to the AE sensor.

Multistable laminates have been actively studied in recent years due to its potential applications in morphing and energy harvesting devices. Variable stiffness (VS) bistable laminates provide opportunities for further improvements in design space in comparison with constant stiffness bistable laminates. The snap-through process involving shape transition between the stable configurations is highly nonlinear in nature and exhibits rich dynamics. Exploiting the dynamic characteristics during the snap-through transition is of considerable interest in designing the morphing structural components. In this paper, we present a semi-analytical model based on Rayleigh–Ritz approach in conjunction with Hamilton’s principle to predict the natural frequencies of bistable VS laminates. The obtained results are compared with the results from the full geometrically nonlinear finite element (FE) model. The proposed FE model is further extended to study the dynamics of VS laminates subjected to external forces with different amplitudes. Subsequently, a parametric study is performed to explore the effect of different curvilinear fiber alignments on natural frequencies, mode shapes, free vibration characteristics and forced vibration characteristics (single-well and cross-well vibrations).

A nonlinear rate dependent constitutive model for fiber-reinforced composites is presented. Through the use of a plastic potential function, effective stress and effective plastic strains are introduced, with which a single equation is established for the orthotropic and nonlinear rate dependent behavior of composites. This viscoplasticity constitutive model is employed together with a microbuckling model to predict compressive strength of composites for different strain rates. Results of qasi-static and high strain rate compression tests using off-axis composite specimens of S2/8552 glass/epoxy are reported and compared with model predictions. Excellent agreement between experimental data and predictions is found. From the experimental results as well as model predictions, it is noted that the longitudinal compressive strength of a composite is significantly influenced by the presence of shear stresses.

This paper presents a new coupled electro-mechanical dynamics model of piezoelectric actuator-sensors. The new model takes the bonding layer between piezoelectric patches and host structures into account in the coupled electro-mechanical analysis by treating the bonding layer as a spring-mass-damper system. Numerical simulations are performed to reveal the effect of bonding layers as well as to demonstrate the application of the new model to debonding detection of composite repair patches.

This paper presents a computational approach for composite materials subjected to ballistic impact. The composite materials are composed of layers of fabric embedded in a matrix material. The fabric is represented by bar elements and the matrix material is represented by solid elements. The geometric characteristics of these composite materials are three dimensional, which in turn requires a three dimensional analysis. The strength and failure characteristics of the fabric are determined directly from the actual fiber characteristics. For the matrix material it is necessary to modify the solid elements, because much of the volume of the solid elements is occupied by the volume of the fabric. The resulting modifications include the determination of effective density, stiffness, strength and failure characteristics for the solid elements. This approach has been shown to provide good agreement with experimental ballistics data. Because this approach treats each of the component materials individually (instead of blending them into a homogeneous anisotropic material), it is possible to examine the effects of individual material properties for both the fabric and the matrix material. This includes the capability to allow for failure of the fabric material and/or the matrix material. Parametric computational results are included to illustrate some of these effects.