Large Deflection Beam Theory Research Articles

Nonlinear vibration responses of lattice sandwich beams with FGM facesheets based on an improved thermo-mechanical equivalent model

An investigation on the nonlinear vibration behaviors of a lattice sandwich beam with pyramidal truss core and functionally graded material (FGM) facesheets under thermo-mechanical loads is performed with consideration of the temperature-dependency of material properties. In present work, an improved equivalent methodology is proposed to determine the transverse shear modulus of pyramidal core subjected to a non-uniform thermal field across thickness direction and makes lattice truss core transformed to a continuous layer. Finally, the lattice sandwich beam is modeled as a three-layered sandwich structure. The facesheets are made of FGMs with mixture of ceramics and metals in a pow-law form. The outer surfaces of facesheets are ceramic-rich, while the inner surfaces are metal-rich. The nonlinear strain–displacement relations are established based on the von Kármán large deflection and classical beam theory. The Lagrange method are implemented to yield equations governing the free and forced vibration behaviors. With the help of Newton-Raphson iteration technique as well as the Newmark-β method, the nonlinear time-independent responses of the sandwich beam under thermal environment are solved. A comprehensive parameter study is directed to address the effects of non-uniform thermal environment, FMG facesheets, external load, and lattice core on the nonlinear vibrations of the beams.

Large deflection stability of axially functionally graded tapered cantilever column

This article studies the large deflection stability of axially functionally graded (AFG) cantilever column for analyzing post-buckling behavior. Consideration is given to a nonlinearly tapered column with a regular polygon cross section, whose volume is constant. The governing differential equations of the problem are derived based on the large deflection beam theory. To calculate the elastica and buckling load of the AFG column, the differential equations are solved with the direct integration method together with the nonlinear solution method. The computed results are compared with those reported in literature and obtained from finite element method. Numerical examples are provided to ascertain the effects of the geometric and material parameters on the elastica and buckling load. The elastica shape is shown to depend on applied load and column properties, and the optimal shape such that the AFG column with fixed volume enables to bear the maximum buckling load is discussed.

Mechanical behaviors of 3D re-entrant honeycomb polyamide structure under compression

In this study, a total of five 3D re-entrant honeycomb (RH) specimens made of polyamide were fabricated with various configurations by using additive manufacturing (AM) technique. Uniaxial quasi-static compressive tests were conducted on the RH specimens. The damage modes, the stress-strain curves and Poisson’s ratios were recorded and analysed. The five specimens exhibited negative Poisson’s ratios between -0.105 and -0.193. The effects of geometric parameters on the mechanical properties were analysed and discussed. In addition, 3D finite element (FE) models were established by using a commercial finite element software (ANSYS), and verified by comparing the predicted stress-strain curves and deformation patterns with the experimental results. Furthermore, an analytical model of 3D RH unit cell under uniaxial compression was proposed based on Timoshenko beam theory and large deflection beam theory. The proposed analytical model can well predict the mechanical properties of 3D RH unit under compression.

The effect of graphene on the deflections of multiscale composites under thermo-mechanical loading

The present investigation aims to shed light on an important aspect of graphene reinforced multiscale composites that may appear in the form of reduced dimensional stability of the structure when exposed to thermal gradients. The study consists of two main parts: an extensive review of the related literature and a thermo-mechanical analysis of a laminated composite beam made of three-phases: arbitrary oriented Graphene Nanoplatelets (GNPs) embedded in an epoxy resin (ER) polymer matrix, reinforced with E-Glass fibers.The review of related literature reveals that the problem of finding the equivalent coefficient of thermal expansion (CTE) for multiscale composites is not as easy as the conventional composites, the trend is different, and more complicating parameters are involved. The analysis includes the predictions of the effective thermo-elastic properties of the multiscale composite laminate, based on Halpin-Tsai theory and hierarchy modeling, and the formulation of the beam deflection governing equation, based on Timoshenko nonlinear (large deflection) beam theory. Different GNPs weight fractions, different E-glass fiber volume fractions, and three lamination layups are investigated. It is found that the addition of GNPs increases the beam deflections when exposed to temperature gradients and that the laminate longitudinal CTE is the main factor responsible for this effect.

A new physical model for empirical fiber snubbing effect in cementitious composites based on large deflection beam theory

A single fiber crosses a crack in Strain-Hardening Cementitious Composites (SHCC) can be either perpendicular or inclined to the crack surface. When the single fiber pullout test is performed on inclined polymeric fibers, the peak pull-out load is commonly observed to increase with the inclination angle. Usually the fiber is modeled as a flexible string passing over a frictional pulley, and the observed phenomenon is explained by the high local friction (or snubbing effect) near the fiber exiting point. However, such an explanation is not perfectly satisfactory because the bending stiffness of the fiber is not necessarily negligible and the pulley does not physically exist. In this study, a new model which treats the fiber as a beam and emphasize on the large deflection effect of the fiber is developed. The entire fiber bridging stress vs crack opening relationship can be derived and the empirical snubbing effect is also revealed, even without assuming the presence of a frictional pulley. Moreover, at small crack opening, the predicted trend of bridging force with inclination angle from the new model is in better agreement with test results than the snubbing friction model.

Study of Large Deflection in Nano-Beams Using the Nonlocal Elasticity Theory

A nonlocal elastic beam model is developed by incorporating Eringen’s nonlocal constitutive equation into the large deflection beam theory for a nano-cantilever Euler–Bernoulli beam. The equilibrium equations are solved in an iterative manner using the shooting method. Deformed configurations of beam for different values of nonlocal parameter are plotted, and the final length of the beam after deflection is obtained. It is demonstrated that the beam scale has a significant impact on its flexural behavior under the large deflection, such that the nano-beam deflection can be either larger or smaller than the classical theory, depending on the loading level.

Dynamic Gust Load Analysis for Rotors

Dynamic load of helicopter rotors due to gust directly affects the structural stress and flight performance for helicopters. Based on a large deflection beam theory, an aeroelastic model for isolated helicopter rotors in the time domain is constructed. The dynamic response and structural load for a rotor under the impulse gust and slope-shape gust are calculated, respectively. First, a nonlinear Euler beam model with 36 degrees-of-freedoms per element is applied to depict the structural dynamics for an isolated rotor. The generalized dynamic wake model and Leishman-Beddoes dynamic stall model are applied to calculate the nonlinear unsteady aerodynamic forces on rotors. Then, we transformed the differential aeroelastic governing equation to an algebraic one. Hence, the widely used Newton-Raphson iteration algorithm is employed to simulate the dynamic gust load. An isolated helicopter rotor with four blades is studied to validate the structural model and the aeroelastic model. The modal frequencies based on the Euler beam model agree well with published ones by CAMRAD. The flap deflection due to impulse gust with the speed of 2m/s increases twice to the one without gust. In this numerical example, results indicate that the bending moment at the blade root is alleviated due to elastic effect.

Analysis on J lay of SCR based on catenary and large deflection beam theory

This paper mainly focuses on J lay of Steel Catenary Riser, and proposes a new model using Sectional Mechanics Model, by iterating and composing catenary method and large deflection method. First the initial deformation and reaction force are evaluated by simple catenary model. For the pipe section with large deformation, asymptotic expansion in singular perturbation techniques pursues the solutions of second-order nonlinear governing equation. Comparison between these three methods shows that the new model displays very close results with high-accuracy large deflection model. This new model is also performed to evaluate the sensitivity of top tension, wet weight, and stiffness on the riser.

A nonlinear mechanical model for deepwater steel lazy-wave riser transfer process during installation

To meet the increasing applications of the deepwater steel lazy-wave riser (SLWR), its installation is a great challenge for SLWR which affects its service performance. This paper is focused on the transfer process during the SLWR installation which is of great importance to the installation feasibility and analysis. A comprehensive mechanical model based on the nonlinear large deflection beam theory for the deepwater SLWR transfer process is developed. The presented model is able to deal with three different stages analysis of the transfer process and the length and tension of the two cables used to lift the riser's pull-head: A&R cables of installation vessel and pull-in cable of production platform. Numerical analysis is conducted to investigate the riser configurations and some important mechanical parameters which exert influences on the riser's performance. The proposed model can be a basic reference to the design and dynamic analysis of deepwater SLWR installation.

Investigation of Wake Effects on Aeroelastic Responses of Horizontal-Axis Wind-Turbines

Wake effects of a horizontal-axis wind-turbine blade on aeroelastic characteristics were investigated under normal operational conditions. A structural analysis was performed employing a nonlinear beam model based on the large deflection beam theory. For inflow analysis on rotor blades, a free-vortex wake method was employed. An advantage of the present approach is its ability to calculate directly the induced velocities from the wake. Also, for the predictions of aerodynamic loads, a fully turbulent flow solution is invoked in FLUENT, where the SST turbulent model of two-dimensional airfoils is adopted for transient analysis. To verify and validate the aerodynamic model for wind turbines, the wake geometry and the aerodynamic coefficients from the present simulation are compared with measurements and numerical results of previous studies. Finally, an analysis of the tightly coupled fluid–structure interaction phenomena of a wind-turbine blade has been carried out to investigate aeroelastic characteristics, such as steady-state blade deflections and dynamic stability. The present results are compared with the numerical results obtained using a uniform inflow model, which clearly confirms the importance of wake effects on the blade aeroelastic characteristics.

Research on mechanical model for the J-lay method

The J-lay method is regarded as the most feasible way to lay pipeline in ultra-deep water; however, the time required to compute the forces generated is considerable. In this article, a new and simple mechanical model is developed in order to reduce the calculation time required. It comprises two parts: the first is a pipe–soil interaction model based on the linear beam theory and the Winkler foundation model, and the second is a nonlinear, large deflection beam theory to calculate the forces on the suspended segment. The accuracy of the numerical calculations has been verified against the output of commercial software with good results. Furthermore, high-order shear effect, which has been largely ignored in other publications, is discussed. The results show that computational accuracy can be improved by 3.1% by taking this effect into account. Therefore, the mechanical model proposed in this article is quicker and more accurate for determining the forces encountered during J-lay operations.

Torsional Stiffness Effects on the Dynamic Stability of a Horizontal Axis Wind Turbine Blade

Aeroelastic instability problems have become an increasingly important issue due to the increased use of larger horizontal axis wind turbines. To maintain these large structures in a stable manner, the blade design process should include studies on the dynamic stability of the wind turbine blade. Therefore, fluid-structure interaction analyses of the large-scaled wind turbine blade were performed with a focus on dynamic stability in this study. A finite element method based on the large deflection beam theory is used for structural analysis considering the geometric nonlinearities. For the stability analysis, a proposed aerodynamic approach based on Greenberg’s extension of Theodorsen’s strip theory and blade element momentum method were employed in conjunction with a structural model. The present methods proved to be valid for estimations of the aerodynamic responses and blade behavior compared with numerical results obtained in the previous studies. Additionally, torsional stiffness effects on the dynamic stability of the wind turbine blade were investigated. It is demonstrated that the damping is considerably influenced by variations of the torsional stiffness. Also, in normal operating conditions, the destabilizing phenomena were observed to occur with low torsional stiffness.

A Model for Large Deflections of Nanobeams and Experimental Comparison

Bending tests are commonly used for characterization of materials at the nanoscale. Beams are also key elements of nanomechanical and nanoelectromechanical devices. This paper is motivated by recent experiments of large deflections of chromium cantilevers and modeling based on the classical large deflection beam theory to simulate experiments. A review of nanobeam experiments shows complex size dependency of elastic modulus that is influenced by beam thickness (or diameter) and end boundary conditions. A new large deflection beam model that accounts for surface energy effects is presented. It is shown that the model is capable of simulating experiments by using size-independent properties such as bulk elastic modulus and surface residual stress. The model is then used to explain the softening or stiffening behavior observed experimentally in nanocantilevers and relative size independence of clamped-clamped beams. Size dependence of elastic modulus (or stiffening/softening) is a modeling artifact introduced due to the use of classical elasticity theory for nanostructures and the current model shows that simulations based on classical beam theory require careful interpretation.

Aeroelastic Analysis of a Hingeless Rotor Using a Dynamic Wake Model

Aeroelastic Analysis of a Hingeless Rotor Using a Dynamic Wake Model

FLUID-STRUCTURE INTERACTION ANALYSIS OF HINGELESS ROTOR BLADES IN HOVER CONSIDERING WAKE EFFECTS

Aeroelastic analysis of hingeless rotor blades in hover was performed. Large deflection beam theory was applied to analyze blade motions with effects of geometric structural nonlinearity. Aerodynamic loads for aeroelastic analysis were calculated through a three-dimensional aerodynamic model which is based on the unsteady vortex lattice method. Wake geometry was described using a time-marching free-wake method. Lead-lag damping ratio and frequency were calculated to evaluate aeroelastic stability of hingeless rotor system. Numerical results of aeroelastic analysis for hingeless rotor blades were presented and compared with results based on experimental data and two-dimensional quasi-steady strip theory in which uniform inflow model was used. It was shown that wakes significantly affect the steady-state deflections and aeroelastic stability.

FLUID-STRUCTURE INTERACTION ANALYSIS OF A HIGH-ASPECT-RATIO WING CONSIDERING STRUCTURAL NONLINEARITY

In this research, fluid-structure interaction problem including geometric structural nonlinearity is studied for a high-aspect-ratio wing. When a high-aspect-ratio wing structure is interacted with external airload, geometric structural nonlinearity can be caused by large deflection of a wing. For the investigation of such a fluid-structure interaction problem, the transonic small disturbance theory for the aerodynamic analysis and the large deflection beam theory for the structural analysis are used, respectively. For the coupling between fluid and structure, the transformation of a displacement from the structural mesh to the aerodynamic grid is performed by a shape function which is used for the finite element and the inverse transformation of force by work equivalent load method. Static deformations in the vertical and twist deflections caused by gravity loading are compared with experimental results. Also, static aeroelastic analysis results are compared with experimental data. From the analysis results, effects of structural nonlinearity on static aeroelastic characteristics are investigated.

Nonlinear Structural Analysis of High-Aspect-Ratio Structures using Large Deflection Beam Theory

The nonlinear structural analyses of high-aspect-ratio structures were performed. For the high-aspect-ratio structures, it is important to understand geometric nonlinearity due to large deflections. To consider geometric nonlinearity, finite element analyses based on the large deflection beam theory were introduced. Comparing experimental data and the present nonlinear analysis results, the current results were proved to be very accurate for the static and dynamic behaviors for both isotropic and anisotropic beams.

Aeroelastic analysis of bearingless rotors with a composite flexbeam

An aeroelastic analysis of bearingless rotors is investigated using large deflection beam theory in hover and forward flight. The bearingless configuration consists of a single flexbeam with a wrap-around torque tube and pitch links located at the leading edge and trailing edge of the torque tube. The outboard main blade, flexbeam, and torque tube are all assumed as an elastic beam undergoing arbitrary large displacements and rotations, that are discretized into beam finite elements. In the bearingless rotors, a flexbeam has various sections made of laminate. The sectional elastic constants of a composite flexbeam, including the warping deformations, are determined from a refined cross-sectional finite element method. Numerical results of the static deflections and the aeroelastic modal damping are presented for various configurations of a composite flexbeam and are compared with previously published experimental results and theoretical values obtained from a modal analysis using a moderate deflection-type beam theory.

자유후류기법을 이용한 무힌지 로터 시스템의 정지비행시 정적 공탄성 해석

본 연구에서는 자유후류기법을 이용하여 복합재 무힌지 로터 블레이드에 대한 정적 공탄성 해석을 수행하였다. 1차원 보의 거동을 해석하기 위하여 대변형 보 이론이 적용되었다. 또한, 복합재 블레이드의 단면 해석을 위하여 이방성 보 이론이 적용되었다. 공탄성 해석에 필요한 공력 하중들은 와류격자법(VLM)에 기초한 3차원 공기력 모델을 통하여 계산되었다. 이때, 정지비행시의 후류는 순차적 시간 적분 자유후류법을 통하여 묘사되었다. 복합재 무힌지 로터 블레이드의 정적 변형에 대한 해석 결과를 2차원 준정상 공기력과 경험후류기법을 통한 해석 결과들과 비교하여 살펴보았다. 결과적으로, 정지비행시 후류 효과에 의해 정적 변형의 결과가 달라짐을 확인하였다. The static aeroelastic analysis of composite hingeless rotor blades in hover was performed using free-wake method. Large deflection beam theory was applied to analyze blade motions as a one-dimension beam. Anisotropic beam theory was applied to perform a cross-sectional analysis for composite rotor blades. Aerodynamic loads were calculated through a three-dimensional aerodynamic model which is based on the unsteady vortex lattice method. The wake geometry in hover was described using a time-marching free-wake method. Numerical results of the steady-state deflections for the composite hingeless rotor blades were presented and compared with those results based on two-dimensional quasi-steady strip theory and prescribed wake method. It was shown that wakes affect the steady-state deflections.

무 베어링 로터 시스템의 정지 및 전진 비행시 공력탄성학적 해석

In this study, the aeroelastic response and stability of bearingless rotors are investigated using a large deflection beam theory. The outboard main blade, flexbeam, and torque tube are all assumed to be an elastic beam undergoing arbitrary large displacements and rotations. The finite element equations of motion obtained from Hamilton`s principle. Two-dimensional quasi-steady strip theory is used to evaluate aerodynamic forces. In hover, the modal approach method based on coupled rotating natural modes is used for the stability analysis. In forward flight, the nonlinear periodic blade steady response is obtained by integrating the full finite element equation in time through a coupled trim procedure with a vehicle trim. The results of the full finite element analysis using the large deflection beam theory are compared with those of a previously published modal analysis using the moderate deflection-type beam theory.