Dineshkumar Harursampath

Aeroelastic Response of Composite Helicopter Rotor with Random Material Properties

This study investigates the effect of uncertainty in composite material properties on the cross-sectional stiffness properties, natural frequencies, and aeroelastic responses of a composite helicopter rotor blade. The elastic moduli and Poisson’s ratio of the composite material are considered as random variables with a coefficient of variation of around 4%, which was taken from published experimental work. An analytical box beam model is used for evaluating blade cross-sectional properties. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in forward flight. The stochastic cross-sectional and aeroelastic analyses are carried out with Monte Carlo simulations. It is found that the blade cross-sectional stiffness matrix elements show a coefficient of variation of about 6%. The nonrotating rotor blade natural frequencies show a coefficient of variation of around 3%. The impact of material uncertainty on rotating natural frequencies varies from that on nonrotating blade frequencies because of centrifugal stiffening. The propagation of material uncertainty into aeroelastic response causes large deviations, particularly in the higher-harmonic components that are critical for the accurate prediction of helicopter blade loads and vibration. The numerical results clearly show the need to consider randomness of composite material properties in the helicopter aeroelastic analysis.

Non-classical effects in non-linear analysis of pretwisted anisotropic strips☆

Abstract The literature on classical analysis of anisotropic beams assumes that all 1D “moment strain” measures (i.e. twist and bending curvatures) are of the same order of magnitude, resulting in a linear cross-sectional analysis. The present paper treats the situation in which one or more of the 1D moment strain measures may be larger than the other(s), resulting in a non-linear cross-sectional analysis. This type of non-classical analysis is needed, for example, in problems where the trapeze effect is important, such as in rotor blades. As a precursor to complicated non-linear sectional analysis of arbitrary cross sections, a non-linear sectional analysis is presented for an anisotropic strip with small pretwist, based on the dimensional reduction of laminated shell theory to a non-linear one-dimensional theory using the variationalasymptotic method. Results obtained from this strip-beam analysis are compared with available theoretical and experimental results for a problem in which the trapeze effect is important. In order to demonstrate the usage of the results in the analysis of structures made of an arbitrary geometrical combination of pretwisted generally anisotropic strips, a closed-form expression is derived for the torsional buckling of a column with a cruciform cross section.

Material uncertainty propagation in helicopter nonlinear aeroelastic response and vibration analysis

The effect of uncertainty in composite material properties on the nonlinear aeroelastic response and vibratory loads of a four-bladed composite helicopter rotor is studied. The aeroelastic analysis is done using a finite element method in space and time, and the composite cross section is analyzed using a variational asymptotic approach. The effective material properties of composite laminas are first considered as random variables with a coefficient of variation of 5%. The material uncertainty is propagated to cross-sectional stiffness,rotating natural frequencies, aeroelastic response, and vibratory loadsof the composite helicopter rotor. The stochastic cross-sectional and aeroelastic analyses are carried out with Monte Carlo simulations. The stochastic stiffness values are scattered up to 15% around the baseline stiffness values and show a Gaussian distribution with a coefficient of variation of about 4%. The uncertainty impact on rotating natural frequencies depends on the level of centrifugal stiffening for different modes. The stochastic rotating natural frequencies indicate a possibility of their coincidence with the integer multiples of rotor speed. The propagation of material uncertainty into aeroelastic response causes large deviations from the baseline predictions and affects the crucial higher harmonics content, which is critical for vibration predictions. The magnitudes of 4/rev vibratory loads show a scattering up to 300% from the baseline value,and their probability density functions show non-Gaussian-type distributions. Further, the uncertainty results for a coefficient of variation of 10% in the material properties are obtained. The uncertainty impact on the aeroelastic response is found to be proportional to the coefficient of variation of the composite material properties.

Asymptotic analysis of the non-linear behavior of long anisotropic tubes

Abstract An asymptotically correct beam model is obtained for a long, thin-walled, circular tube with circumferentially uniform stiffness (CUS) and made of generally anisotropic materials. By virtue of its special geometry certain small parameters cause unusual non-linear phenomena, such as the Brazier effect, to be exhibited. The model is constructed without ad hoc approximations from 3D elasticity by deriving its strain energy functional in terms of generalized 1D strains corresponding to extension, bending, and torsion. Large displacement and rotation are allowed but strain is assumed to be small. Closed-form expressions are provided for the 3D non-linear warping and stress fields, the 1D non-linear stiffness matrix and the bending moment–curvature relationship. In bending, failure could be caused by limit-moment instability, local buckling or material failure of a ply. A procedure to determine the failure load is provided based on the non-linear response, neglecting micro-mechanical failure modes, post-failure behavior, and hygrothermal effects. Asymptotic considerations lead to the neglect of local shell interlaminar and transverse shear stresses for the thin-walled configuration. Results of the theory are illustrated for a few symmetric, antisymmetric angle-ply and unsymmetric layups and show that some previously published theories are not asymptotically correct.

Effect of Asymptotically Correct Nonlinear Cross-Sectional Analyses on Dynamics of Anisotropic, Flexible Four-Bar Mechanisms

This work intends to demonstrate the importance of geometrically nonlinear crosssectional analysis of certain composite beam-based four-bar mechanisms by using dierent stacking sequences in all component bars in predicting better system dynamic characteristics. All component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the four beam reference curves. For thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict multi-body dynamic responses, more quickly and accurately than would otherwise be possible. With the model, tools and procedure in place, we shall attempt to identify and investigate a few problems where the cross-sectional nonlinearities are significant. This will be carried out by arranging the beams in distinctly dierent orientations, varying stacking sequences and material properties, and speculating on the dominating diagonal and coupling terms in the closedform nonlinear beam stiness matrix. Noticeable dierence in system dynamic parameters can be achieved through lay-up optimization. In the sensitivities evaluation of the design variable considered is the layer orientation in the lay-ups of the component bars to find the optimal lay-ups which are suitable for practical applications. The goal of this optimization process is to improve the system dynamic characteristics through searching for the optimal values for the fiber orientation of all component bars in the mechanism, which relies on ecient and accurate calculation of the system sensitivities. These important parameters not only indicate the importance of the non-linear non-classical terms in the 1-D stiness matrix of the beams but can also help to achieve the specified performance of the mechanism for practical applications. A numerical example is presented which illustrates not only the importance of 2-D cross-sectional nonlinearities on system dynamics but also shows the advantages of selecting the well-known stacking sequence of Winckler’s system through the behavior of the system as observed by using commercial software (I-DEAS + NASTRAN + ADAMS).

Effects of Structural Uncertainty on Aeroelastic Response of Composite Helicopter Rotor

The efiect of uncertainty in composite material properties on the cross-sectional stifiness properties, natural frequencies and aeroelastic response of a composite helicopter rotor blade is investigated using numerical simulations. The elastic modulii and Poisson’s ratio of the composite material are considered as random variables with co-e‐cient of variation around 5 percent. A flnite element method based on variational asymptotic procedure is used for evaluating the blade cross-sectional properties. Aeroelastic analysis based on flnite element in space and time is used to evaluate the helicopter blade response in forward ∞ight. The stochastic cross-sectional and aeroelastic analysis are carried out with Monte Carlo simulations. It is found that the blade cross-sectional stifiness show a co-e‐cient of variation of about 12 percent. The fundamental rotating natural frequencies of the rotor blade show a co-e‐cient of variation of 0.63, 5.62 and 5.07 percent for ∞ap, lag and torsion, respectively. The impact of material uncertainty on rotating natural frequencies varies with the in∞uence of centrifugal stifiening over structural stifiness for ∞ap, lag and torsional motions. Further, the stochastic rotating natural frequencies show a chance of coinciding with the integer multiples of the rotor speed. The propagation of material uncertainty into aeroelastic response cause large deviations from the baseline response. The vibratory 4/rev loads acting on the rotor hub show a considerable deviation from the baseline predictions because of the material uncertainty. The numerical results clearly show the need to consider randomness of composite material properties in the helicopter aeroelastic analysis, design and optimization.

Modal analysis of delaminated plates and shells using Carrera Unified Formulation - MITC9 shell element

ABSTRACT The present paper considers the modal analysis of delaminated composite shell structures with double-curvature geometry. The finite element for shell with variable through-the-thickness kinematic is adopted for the analysis. The refined models are grouped in the Unified Formulation by Carrera (CUF) and they permit the distribution of displacements along the thickness of the multilayered shell to be accurately described. The shell element has nine nodes and the Mixed Interpolation of Tensorial Components (MITC) method is used to alleviate the membrane and shear locking phenomenon. The governing equations are derived from the Principle of Virtual Displacement (PVD) and the Finite Element Method (FEM) is employed to solve them. From the analysis, one can conclude that the shell element based on the CUF is very efficient and the results obtained match closely with three-dimensional finite element simulations. The effect of delamination size, curvature, stacking sequence, and boundary conditions is studied. The results from different ordered theories are tabulated and compared. It is observed that there is reduction in frequencies in the presence of delamination; however, for a given size of delamination, stacking sequence, and boundary conditions, the effect of delamination on shell structure is more predominant in comparison with respect to the plates structures.

Radial Deformation of Cylinders Due to Torsion

Classical literature on solid mechanics claims existence of radial deformation due to torsion but there is hardly any literature on analytic solutions capturing this phenomenon. This paper tries to solve this problem in an asymptotic sense using the variational asymptotic method (VAM). The method makes no ad hoc assumptions and hence asymptotic correctness is assured. The VAM splits the 3D elasticity problem into two parts: A 1D problem along the length of the cylinder which gives the twist and a 2D cross-sectional problem which gives the radial deformation. This enables closed form solutions, even for some complex problems. Starting with a hollow cylinder, made up of orthotropic but transversely isotropic material, the 3D problem has been formulated and solved analytically despite the presence of geometric nonlinearity. The general results have been specialized for particularly useful cases, such as solid cylinders and/or cylinders with isotropic material. DOI: 10.1115/1.4006803]

Non-classical Non-linear Effects in Thin Walled Open Section Composite Beams

This work describes the development of a comprehensive and reliable tool for analysis of the most commonly used geometries of open section thin walled composite beams. This tool, being based on the mathematically rigorous variational asymptotic method, automatically incorporates all the relevant non-linear and non-classical effects that arise in an arbitrary thin walled open section composite beam. Further, the closed form solutions for all the variables enable an effective transformation to a reliable and computationally effecient probabilistic model. With the inclusion of an easy-to-use and portable graphics user interface we now have an effective aid for composite tailoring of open section beams.

Analytical Solutions for Dynamic Behavior of Pretwisted Anisotropic Strip-like Beams

In this paper, we propose a “marching method” to iteratively solve the nonlinear one-dimensional (1-D) problem in strip-like beams obtained from dimensional reduction using the Variational Asymptotic Method (VAM). We discuss closed-form analytical solutions describing both quasi-static and dynamic behavior in strip-like beams. Themethod hasbeen shown tobeapplicableduringapplication ofboth conservative and non-conservative system of forces and moments.