3D Shell Model Research Articles

Accuracy of an efficient framework for structural analysis of wind turbine blades

AbstractThis paper presents a novel framework for the structural design and analysis of wind turbine blades and establishes its accuracy. The framework is based on a beam model composed of two parts—a 2D finite element‐based cross‐section analysis tool and a 3D beam finite element model. The cross‐section analysis tool is able to capture the effects stemming from material anisotropy and inhomogeneity for sections of arbitrary geometry. The proposed framework is very efficient and therefore ideally suited for integration within wind turbine aeroelastic design and analysis tools. A number of benchmark examples are presented comparing the results from the proposed beam model to 3D shell and solid finite element models. The examples considered include a square prismatic beam, an entire wind turbine rotor blade and a detailed wind turbine blade cross section. Phenomena at both the blade length scale—deformation and eigenfrequencies—and cross section scale—3D material strain and stress fields—are analyzed. Furthermore, the effect of the different assumptions regarding the boundary conditions is discussed in detail. The benchmark examples show excellent agreement suggesting that the proposed framework is a highly efficient alternative to 3D finite element models for structural analysis of wind turbine blades. Copyright © 2015 John Wiley & Sons, Ltd.

Free vibration analysis of FGM shell structures with a discrete double directors shell element

Free vibration response of functionally graded material (FGM) shell structures is studied by using an efficient 3d-shell model based on a discrete double directors shell element. With this element, the vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. The mechanical properties of the shell structure are assumed to vary continuously in the thickness direction according to the general four-parameter power-law distribution in terms of the volume fractions of the constituents. The fundamental equations for the FGM shell structures are derived using principle of virtual work. Performance and accuracy of the present discrete double directors shell model (DDDSM) are confirmed by comparing the present solutions obtained from finite element analyses with the existing results in the literature.

Analysis of loads on the shearing edge during electrohydraulic trimming of AHSS steel in comparison with conventional trimming

In order to achieve further weight reduction in automotive components, the technology of manufacturing of automotive panels from advanced high strength steels is being developed. Electrohydraulic trimming technology eliminates the necessity of accurate alignment of the shearing edges in trimming operation. Analysis of loads on the tool during high-rate EH trimming process has been performed. In order to investigate the effect of the process on the shearing edge performance, a dedicated finite element analysis procedure combining 3D shell and 2D solid models was developed. EH trimming experiments were carried out to validate the simulation model where elastic plastic deformation of the shearing edge was taken into account. The effects of the die geometry and number of trimming cycles on the tool contact loads and tool's plastic deformation were analyzed. This analysis was based on numerical simulation of deformation and fracture of the blank being trimmed in contact with the deformable shearing edge. Numerical analysis of the shearing edge deformation was performed in elasto-plastic formulation for the D2 tool steel inserts used in the experimental study and also in elastic formulation to define the maximum stresses which tool material needs to withstand to avoid its plastic deformation.The results of the analytical study indicate that the maximum contact pressure is applied to the trimming tool at the lower endpoint of the shearing edge, but the point of maximum plastic deformation in the tool is found on the vertical wall of the shearing edge where it contacts the area of the blank where separation takes place. The shearing edge of the EH trimming die experiences less contact pressure and less plastic deformation with increase of the radius of the shearing edge. The shearing edge of the EH trim die has a tendency to dull after a number of trimming cycles. In addition, when compared with conventional trim die, the shearing edge of the EH trimming tool experiences slightly higher (10–15%) contact loads than in conventional trimming. However, plastic deformations occurring in the conventional trim die for shearing of identical material are larger. Analysis of loads on the EH trimming tool was repeated for purely elastic tool material to formulate the requirements to the material of the shearing edge.

Discrete double directors shell element for the functionally graded material shell structures analysis

In this paper, the accuracy and the efficiency of the 3d-shell model based on a double directors shell element for the functionally graded material (FGM) shell structures analysis is studied. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. Thus, the third-order shear deformation plate theory (TSDT) is a particular case of the discrete double directors shell model (DDDSM) used in the present work. The DDDSM is introduced to remove the shear correction factors, when using the first-order shear deformation theory (FSDT), and improve an excellent performance when compared with other works. This model can be used for static, free vibration and buckling analyses of FGM. The convergence of the proposed model is compared to other well-known formulations found in the literature.

A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes

The free vibration analysis of Single-Walled Carbon NanoTubes (SWCNTs) is proposed in the present paper. A continuum approach (based on an exact elastic three-dimensional shell model) is used for natural frequency investigation of simply supported SWCNTs. In order to apply this continuum model, carbon nanotubes are defined as isotropic cylinders with an equivalent thickness and Young modulus. Preliminary remarks are proposed concerning the possible use of a continuum approach and the most convenient definitions of the equivalent thickness and Young modulus. Subsequently, the 3D shell method is compared with different beam analyses to show the limitations of 1D beam models. Finally, zigzag, armchair and general chirality SWCNTs (with various lengths and geometries) are analyzed via the 3D shell model to calculate their vibration modes.

Spatial Distribution of Perfusion Abnormality in Acute MCA Occlusion is Associated with Likelihood of Later Recanalization

The aim of this study is to investigate whether different spatial perfusion-deficit patterns, which indicate differing compensatory mechanisms, can be recognized and used to predict recanalization success of intravenous fibrinolytic therapy in acute stroke patients. Twenty-seven acute stroke data sets acquired within 6 hours from symptom onset including diffusion- (DWI) and perfusion-weighted magnetic resonance (MR) imaging (PWI) were analyzed and dichotomized regarding recanalization outcome using time-of-flight follow-up data sets. The DWI data sets were used for calculation of apparent diffusion coefficient (ADC) maps and subsequent infarct core segmentation. A patient-individual three-dimensional (3D) shell model was generated based on the segmentation and used for spatial analysis of the ADC as well as cerebral blood volume (CBV), cerebral blood flow, time to peak (TTP), and mean transit time (MTT) parameters derived from PWI. Skewness, kurtosis, area under the curve, and slope were calculated for each parameter curve and used for classification (recanalized/nonrecanalized) using a LogitBoost Alternating Decision Tree (LAD Tree). The LAD tree optimization revealed that only ADC skewness, CBV kurtosis, and MTT kurtosis are required for best possible prediction of recanalization success with a precision of 85%. Our results suggest that the propensity for macrovascular recanalization after intravenous fibrinolytic therapy depends not only on clot properties but also on distal microvascular bed perfusion. The 3D approach for characterization of perfusion parameters seems promising for further research.

Strong Convergence Results for the Asymptotic Behavior of the 3D-Shell Model

We revisit the asymptotic convergence properties—with respect to the thickness parameter—of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong convergence results for the 3D-shell model in the two main types of asymptotic regimes, namely, bending- and membrane-dominated behavior. This is an important achievement, as it completely substantiates the asymptotic consistency of the 3D-shell model with 3D linearized isotropic elasticity.

An Improved Plasticity-Based Distortion Analysis Method for Large Welded Structures

The plasticity-based distortion prediction method was improved to address the computationally intensive nature of welding simulations. Plastic strains, which are typically first computed using either two-dimensional (2D) or three-dimensional (3D) thermo-elastic-plastic analysis (EPA) on finite element models of simple weld geometry, are mapped to the full structure finite element model to predict distortion by conducting a linear elastic analysis. To optimize welding sequence to control distortion, a new theory was developed to consider the effect of weld interactions on plastic strains. This improved method was validated with experimental work on a Tee joint and tested on two large-scale welded structures—a light fabrication and a heavy fabrication—by comparing against full-blown distortion predictions using thermo-EPA. 3D solid and shell models were used for the heavy and light fabrications, respectively, to compute plastic strains due to each weld. Quantitative comparisons between this method and thermo-EPA indicate that this method can predict distortions fairly accurately—even for different welding sequences—and is roughly 1-2 orders of magnitude faster. It was concluded from these findings that, with further technical development, this method can be an ideal solver for optimizing welding sequences.

Numerical validation of a finite element thin‐walled beam model of a composite wind turbine blade

ABSTRACTThis paper presents a numerical validation of a thin‐walled beam (TWB) finite element (FE) model of a realistic wind turbine rotor blade. Based on the theory originally developed by Librescu et al. and later extended to suit FE modelling by Phuong, Lee and others, this computationally efficient yet accurate numerical model is capable of capturing most of the features found in large blades including thin‐walled hollow cross section with variable thickness along the section's contour, inner reinforcements, arbitrary material layup and non‐linear anisotropic fibre‐reinforced composites; the present application is, for the time being, restricted to linearity. This one‐dimensional (1D) FE model allows retaining information of different regions of the blade's shell and therefore approximates the behaviour of more complex three‐dimensional (3D) shell or solid FE models more accurately than typical 1D FE beam models. A 9.2 m rotor blade, previously reported in specialized literature, was chosen as a case study to validate the static and dynamic behaviour predicted by a TWB model against an industry‐standard 3D shell model built in a commercial software tool. Given the geometric and material complexities involved, an excellent agreement was found for static deformation curves, as well as a good prediction of the lowest frequency modes in terms of resonance frequencies, mode shapes and frequency response functions; the highest (sixth) frequency mode shows only a fair agreement as expected for an FE model. It is concluded that despite its simplicity, a TWB FE model is sufficiently accurate to serve as a design tool for the recursive analyses required during design and optimization stages of wind turbines using only readily available computational tools. Copyright © 2011 John Wiley & Sons, Ltd.

Refined finite element modelling for the vibration analysis of large rotating machines: Application to the gas turbine modular helium reactor power conversion unit

This paper is aimed at presenting refined finite element modelling used for dynamic analysis of large rotating machines. The first part shows an equivalence between several levels of modelling: firstly, models made of beam elements and rigid disc with gyroscopic coupling representing the position of the rotating shaft in an inertial frame; secondly full three-dimensional (3D) or 3D shell models of the rotor and the blades represented in the rotating frame and finally two-dimensional (2D) Fourier model for both rotor and stator. Simple cases are studied to better understand the results given by analysis performed using a rotating frame and the equivalence with the standard calculations with beam elements. Complete analysis of rotating machines can be performed with models in the frames best adapted for each part of the structure. The effects of several defects are analysed and compared with this approach. In the last part of the paper, the modelling approach is applied to the analysis of the large rotating shaft part of the power conversion unit of the GT-MHR nuclear reactor.

A variational approach for coupling kinematically incompatible structural models

In this work an extended variational framework aimed at properly addressing the coupling of kinematically incompatible structural models is presented. The main goal is to variationally state the theoretical bases to deal with the coupling of structural models with different dimensionality. In this approach, the coupling conditions are naturally derived from the governing variational principle formulated at the continuous level. Furthermore, by means of a real parameter γ we manage to build different continuous mechanical models that have different mechanical and mathematical features. In particular, the coupling of 3D solid models and 2D shell models, under Naghdi hypothesis, is treated by introducing the corresponding kinematical assumptions into the proposed extended variational principle. Also, the coupling between 3D solid and 1D beam models, under Bernoulli hypothesis, is presented. Moreover, for the continuous 3D–2D coupled problem a numerical approximation is addressed via the finite element method and some numerical results are given, comparing the responses of the system when the discrete model varies by changing the value of the parameter γ . Finally, a discussion comprising the main conclusions of the work is given.

Energy Absorption Efficiency and Mode Bifurcation of Thin-Walled Circular Tubes under Dynamic Axial Crushing

With a view to examine the axial crushing behavior of thin-walled tubes, which form the parts of transports such as aircrafts and automobiles, under dynamic compressive loads, a series of numerical simulations for thin-walled circular tubes of various dimensions was carried out by using the explicit FEM code LS-DYNA. The energy absorption efficiency and the bifurcation conditions of the collapse modes of these tubes subjected to dynamic axial compression were primarily investigated. In order to confirm the validity of the simulations, first, some calculated results such as the load - displacement relation, the collapse behavior, the absorbed energy per unit volume, and so forth by using the axisymmetric FE model were compared with those obtained by way of experiment under the corresponding condition. Here, the absorbed energy per unit volume was formulated on the basis of Alexander's theory and the Johnson-Cook model, and the results obtained by this formulation were compared with the corresponding results obtained by the simulations and experiments for many tubes of various dimensions. Next, the effects of the initial imperfection and the inertial force on the bifurcation of the axial-collapse mode were examined by using the 3D-shell model. It was clarified that the mode of the dynamic progressive buckling was affected by the natural vibration mode.

Asymptotic Considerations Shedding Light on Incompressible Shell Models

The incompressible singularity found in 3D elasticity when Poisson’s ratio approaches 1/2 is not present in classical shell models, nor in the limit models obtained from 3D elasticity when performing an asymptotic analysis with respect to the thickness parameter. However, some specific shell models – such as the 3D-shell model – do retain the incompressible singularity. These observations raise the issue of how adequately shell models can represent incompressible conditions, which this paper aims at investigating. We first perform a combined asymptotic analysis of 3D elasticity with respect to both the thickness parameter and Poisson’s ratio and we obtain a commuting property, which is very valuable as a justification of the concept of an “incompressible shell”, and substantiates the use of classical shell models with incompressible materials. We then show that the 3D-shell model does not enjoy a similar commuting property; nevertheless we propose a simple modification of this model for which commuting is obtained, hence consistency with incompressibility is recovered. We also illustrate our discussions with some numerical results.

The plastic collapse and energy absorption capacity of egg-box panels

The plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression has been measured and modelled. It is observed that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism. Drop weight tests have been performed at speeds of up to 6 m s −1 , and an elevation in strength with impact velocity is noted. A 3D finite element shell model is needed in order to reproduce the observed behaviours. Additional calculations using an axisymmetric finite element model give the correct collapse modes but are less accurate than the more sophisticated 3D model. The finite element simulations suggest that the observed velocity dependence of strength is primarily due to strain-rate sensitivity of the aluminium sheet, with material inertia playing a negligible role. Finally, it is shown that the energy absorption capacity of the egg-box material is comparable to that of metallic foams.

Fracture mechanics based fatigue analysis of steel bridge decks by two-level cracked models

An alternative fatigue assessment is introduced for orthotropic highway bridge decks, based on fracture mechanics. Crack growth simulation is carried out by the numerical integration of the Paris formula, using K factors obtained from two-level cracked models of the bridge deck. Prior to the simulation, unit wheels are applied to the 3D-shell model of the deck, and the translations of characteristic points are transferred to the 2D plane strain or plane stress finite element sub-models of fatigue-sensitive areas. The K factor is computed by numerical extrapolation, introducing cracks in the sub-models. Fixed values of input parameters (initial- and critical crack length, crack growth rate data, and the error of K factor computation) are used for single simulations as well as parametric studies for sensitivity analysis. Reliability assessment is performed by repeated crack growth analysis, using histograms to generate input parameters by Monte-Carlo simulation at the start of each “virtual experiment”.