Liviu Librescu

Elastostatics and Kinetics of Anisotropic and Heterogeneous Shell-Type Structures

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Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: Part II—Buckling and free vibration

Abstract Using the higher-order plate theory developed in the first part of this paper, as well as the technique based on the state space concept, the free vibration and buckling problems of rectangular cross-ply laminated plates are analyzed. In this context a variety of boundary conditions is considered and comparisons with the existing literature are made.

Recent developments in the modeling and behavior of advanced sandwich constructions: a survey

A general overview of some recent developments related with the modeling and stability of sandwich structures is presented in this paper. The survey covers a number of issues related with the geometrically linear and non-linear formulations of curved and flat sandwich constructions featuring laminated anisotropic face sheets, and associated stability problems. Issues related with the enhancement of the load carrying capacity of sandwich panels resulting in the increase of the buckling strength, the reduction of the intensity of a snap-through buckling and even of its removal are also addressed. The provided list of references is not exhaustive, in the sense that it is mainly connected with topics of sandwich constructions in which the first author of this paper has been involved during a good part of his research activity. Moreover, the displayed results illustrating some basic trends concern not only the ones previously obtained by the authors of this survey-paper, but also several others, presented here for the first time.

A shear deformable theory of laminated composite shallow shell-type panels and their response analysis. I - Free vibration and buckling

SummaryThis paper deals with the substantiation of a shear deformable theory of cross-ply laminated composite shallow shells. While the developed theory preserves all the advantages of the first order transverse shear deformation theory it succeeds in eliminating some of its basic shortcomings. The theory is further employed in the analysis of the eigenvibration and static buckling problems of doubly curved shallow panels. In this context, the state space concept is used in conjunction with the Lévy method, allowing one to analyze these problems in a unified manner, for a variety of boundary conditions. Numerical results are presented and some pertinent conclusions are formulated.

Thin-Walled Beams Made of Functionally Graded Materials and Operating in a High Temperature Environment: Vibration and Stability

ABSTRACT In this study, problems related to the thermoelastic modeling and behavior of thin-walled beams made of functionally graded materials (FGMs) are addressed. In this context, two structural systems are considered: (i) rotating turbomachinery blades, and (ii) thin-walled beam structures spinning about their longitudinal axis. In all these cases, the structures operate in a high temperature environment. Under the spinning speed, gyroscopic forces are generated. Although conservative in nature, under their influence, as in nonconservative systems, instabilities by flutter and divergence can occur. In this context, the implications on their vibration and instability of conservative and gyroscopic forces considered in conjunction with a temperature field that yields the degradation of elastic properties are investigated. A continuously graded variation in composition of the ceramic and metal phases across the beam wall thickness in terms of a simple power law distribution is implemented. Results highlighting the effects of the volume fraction, temperature gradient, considered in conjunction with the temperature degradation of materials properties, compressive axial load and rotational/spinning speed on vibration, and instability are presented and pertinent conclusions are drawn. The thin-walled structural beam model considered in this study is an advanced one. In this sense, in addition to the transverse shear and the secondary warping, the effect of the pretwist and nonuniformity of the beam cross-section along its span are considered. Both box-beams and circular cross-section spinning beams are considered in the analysis. Validation of the obtained results against those obtained via the Mori–Tanaka scheme is carried out, and excellent agreements are reported. In addition, issues related to the foundation and behavior of geometrically nonlinear rotating/spinning thin-walled beams build-up of FGMs and operating in a temperature field are addressed. It should be stressed that the supplied results are based entirely on the research by these authors, and that there are no parallel works in the specialized literature on rotating/spinning systems made of functionally graded materials.

Control of cantilever vibration via structural tailoring and adaptive materials

A dual approach integrating structural tailoring and adaptive materials technology and designed to control the dynamic response of cantilever beams subjected to external excitations is presented. Whereas structural tailor- ing uses the anisotropy properties of advanced composite materials, adaptive materials technology exploits the actuating capabilities of piezoelectric materials bonded or embedded into the host structure. A control law relat- ing the piezoelectrically induced boundary bending moment with the velocity at given points of the structure is implemented and its effect on the closed-loop frequencies and dynamic response to harmonic excitations is inves- tigated. The combination of structural tailoring and control by means of adaptive materials proves very effective in damping out vibration. I. Introduction A Sthe requirements for higherexibility on high-speed aircraft increase, so do the challenges of developing innovative de- sign solutions. Whereas the increasedexibility is likely to provide enhanced aerodynamic performance, the aircraft also must be able to ful® ll a multitude of missions in complex environmental condi- tions and to feature an expanded operational envelope and longer operational life. To achieve such ambitious goals- advanced con- cepts resulting in the enhancement of static and dynamic response of the multimission- highlyexible aircraft must be developed and implemented. One way of achieving such goals consists of the in- tegration of advanced composite materials in the aircraft structure. 1 In this regard, the directionality property featured by anisotropic composite materials is capable of providing the desired elastic cou- plings through the proper selection of the ply angle. However, such a technique is passive in nature in the sense that, once the design is in place, the structure cannot respond to the variety of conditions in which it must operate. The situation can be mitigated by incorporating into the host structure adaptive materials able to respond actively to changing conditions. In a structure with adaptive capabilities, the natural fre- quencies, damping, and mode shapes can be tuned to reduce the vibration so as to avoid structural resonance andutter instability, and in general toenhance the dynamic response characteristics.The adaptivecapabilityisachievedthroughtheconversepiezoelectricef- fect,whichconsistsofthegenerationoflocalized strainsinresponse to an applied voltage. This induced strain ® eld produces, in turn, a change in the dynamic response characteristics of the structure. It is proposedheretoenhancethefreevibrationanddynamicresponseto externalexcitationsofwing structures by incorporating theadaptive capabilityreferredtoasinduced strain actuationinconjunctionwith structural tailoring. Under consideration is a cantilevered aircraft wing, modeled as a thin/thick-walled closed cross-section beam of anisotropic material. Implementation of a control law relating the applied electric ® eld to one of the mechanical quantities charac- terizing the response of the wing according to a prescribed func- tional relationship results in eigenvalue/boundary-value problems. The solution consists of closed-loop eigenvalues/dynamic response characteristics, which are functions of the applied voltage, i.e., of the feedback control gain. Investigation of static and dynamic control of aircraft wing structures via the simultaneous implementation of induced strain

On the static aeroelastic tailoring of composite aircraft swept wings modelled as thin-walled beam structures

Abstract The sub-critical static aeroelastic response and the divergence instability of swept-forward aircraft wing structures constructed of anisotropic composite materials is analyzed. The new element distinguishing this study from the previous, existing ones is the structural model in which framework this problem is treated. In this sense, in contrast to the classical plate-beam or solid-beam models traditionally used in the study of these problems, the thin-walled anisotropic composite beam model is adopted here. The model used incorporates a number of non-classical effects. Among these are the anisotropy of the material of the constituent layers, the transverse shear deformation and the primary and secondary warping effects. Within the framework of this study, in addition to an assessment of the influence of the previously mentioned effects, the aeroelastic tailoring technique is applied and as a result, a series of conclusions concerning the enhancement of the static aeroelastic response characteristics of aeronautical wing structures made of advanced composite materials are outlined.

On a shear-deformable theory of anisotropic thin-walled beams: further contribution and validations

Within the framework of an existing anisotropic thin-walled beam model, a number of non-classical effects are further incorporated and the model thereby developed is validated. Three types of lay-ups, namely, the cross-ply, circumferentially uniform stiffness, and circumferentially asymmetric stiffness are investigated. The solution methodology is based on the Extended Galerkins Method and the non-classical effects on the static responses and natural frequencies are investigated. Comparisons of the predictions by the present model with experimental data and other analytical as well as numerical results are conducted and pertinent conclusions are drawn. This work is the first attempt to validate a class of refined thin-walled beam model that has been extensively used towards the study, among others, of dynamic response, static aeroelasticity and structural/aeroelastic feedback control.

Aeroelastic response of 2-D lifting surfaces to gust and arbitrary explosive loading signatures

Abstract The aeroelastic response to time-dependent external excitation of a two-dimensional rigid/elastic-lifting surface in incompressible flow field featuring plunging – pitching coupled motion is addressed in this paper. The expressions of the unsteady aerodynamic lift and moment in the time domain are given in terms of the Wagners function, while the gust loads are given in terms of the Kussners function. Numerical simulations of the aeroelastic response to gust and blast pressure signatures and comparisons with the solution obtained for an airfoil featuring plunging motion alone, are supplied. The concepts of the alleviation factor envelope and of the one- and two-degrees-of-freedom rigid/elastic-lifting surfaces, considered in conjunction with the aeroelastic response, are investigated and pertinent conclusions are outlined.

A general linear theory of laminated composite shells featuring interlaminar bonding imperfections

This paper is devoted to the foundation of a general linear theory of laminated composite anisotropic shells of arbitrary shape and curvature, in which the effect of the interfacial damage induced by the imperfect bonding between the constituent laminae is incorporated. In this context, the imperfect interface conditions are described in terms of linear relations between the interface tractions in the normal and tangential directions, and the respective displacement jumps. In addition to the effects of imperfectly bonded interfaces, the theory incorporates the effects of transverse shear and transverse normal strain, the dynamic effects, as well as the anisotropy of constituent material layers. Due to its general character, this theory can contribute to a more reliable prediction in the linear range of the load carrying capacitiy and failure of laminated composite shell structures featuring imperfectly bonded interfaces.