Conventional Beam Model Research Articles

Dynamic vehicle–track interaction and structural loading in a crossing panel – calibration and assessment of a model with a 3D representation of the crossing rail

A three-dimensional (3D) finite element model of a railway crossing panel for use in multibody simulation (MBS) of dynamic vehicle–track interaction is presented. It is a two-layer track model with stock rails and sleepers represented by beam elements and a crossing rail represented by 3D solid elements. The track model uses linear bushings for the rail fastenings and bi-linear bushings for the ballast to allow for potentially voided sleepers. Based on the output from the MBS, the structural loading of the crossing in terms of strains, stresses and sleeper-ballast contact pressures is extracted in a post-processing step. The model is calibrated and validated to measurement data from a comprehensively instrumented switch & crossing (S&C) demonstrator installed in the Austrian railway network as a part of the European research programme Shift2Rail. The applied procedure for the calibration and critical assessment of the crossing model is described in detail. It is based on a model parameterisation with eight parameters relating to the rail fastening and foundation stiffnesses and to a distribution of the ballast voids. The calibration method uses Latin hypercube samples to explore the parameter space in a sensitivity analysis before a parameter optimisation is performed using a gradient-based method on a response surface built from a polyharmonic spline. In a comparative study it is shown that the 3D model and a more conventional beam model of the crossing rail show similar calibration results and good agreement with the measured data. The 3D model allows for the extraction of stress concentrations in the crossing rail but has an increased computational time of about 30% compared to the beam model.

Multidamage Detection of Breathing Cracks in Plate‐Like Bridges: Experimental and Numerical Study

Bridges may develop breathing cracks under excessive overloading vehicles, while conventional beam models are ineffective in analyzing the effect of spatial distribution of these cracks. This study proposes a data‐driven detection model with the consideration of spatial distribution of breathing cracks that can detect the multiple damage locations and degrees of breathing cracks in plate‐like bridges. Firstly, a 2D vehicle–bridge interaction model containing breathing cracks is established, and the damage indicator, contact point displacement variation (CPDV), is calculated using vehicle acceleration data. Next, a dataset with CPDV as the input feature is generated using the finite element method to train the CatBoost‐based damage prediction model, which considers the random distribution of single and multiple cracks, as well as the influence of different vehicle speeds. Finally, by calculating the CPDV related to the actual bridge and feeding it into the trained model, the location and degree of the damage can be predicted. The numerical simulation results demonstrate that this approach can accurately detect complex crack information under various vehicle speeds and exhibits robustness against road roughness. A laboratory experiment further confirms the effectiveness, applicability, and feasibility of this method to multiple damage locations and degree of breathing cracks.

Beam based rotordynamics modelling for preloaded Hirth, Curvic and butt couplings

Gas turbine and other machinery rotating assemblies are frequently manufactured as multiple components for cost and component alignment reasons. Butt joint, Hirth, and Curvic coupling are widely used for this purpose. Localized joint flexibility in these preloaded couplings introduce non-beamlike behavior which affects rotordynamic critical speeds, imbalance response and stability, rendering a conventional beam model inadequate. 3D solid finite element models of the couplings with Greenwood Williamson (GW) asperity interface features provide accurate representations of the couplings, however computational costs are impractical for use in an industrial design setting, which are limited to beam element models. A novel modeling approach for the coupling is developed that derives equivalent beam element Young's modulus and shear form factor properties, that replicate the bending behavior of the high fidelity 3D solid models, including GW based interface asperity stiffness. The equivalent beam models for butt, Hirth and Curvic couplings are validated using measured natural frequencies as a benchmark, for a range of through-bolt preloads. The equivalent beam model and the 3D solid model in this correlation incorporate GW contact models derived with experimentally measured surface roughness parameters. An Ecoupling sensitivity study for GW surface roughness parameters was conducted and showed a significant level of sensitivity. The effect of the coupling on an industrial class rotor's critical speed is included to illustrate usage of the approach.

Multiaxial Fatigue Analysis of Jacket-Type Offshore Wind Turbine Based on Multi-Scale Finite Element Model.

The fatigue damage of a local joint is the key factor accounting for the structural failure of a jacket-type offshore wind turbine. Meanwhile, the structure experiences a complex multiaxial stress state under wind and wave random loading. This paper aims to develop a multi-scale modeling method for a jacket-type offshore wind turbine, in which local joints of the jacket are modeled in a detail by using solid elements, and other components are modeled via the common beam element. Considering the multiaxial stress state of the local joint, multi-axial fatigue damage analysis based on the multiaxial S-N curve is performed using equivalent Mises and Lemaitre methods. The uniaxial fatigue damage data of the jacket model calculated using the multi-scale finite element model are compared with those of the conventional beam model. The results show that the tubular joint of jacket leg and brace connections can be modeled using the multi-scale method, since the uniaxial fatigue damage degree can reach a 15% difference. The comparison of uniaxial and multiaxial fatigue results obtained using the multi-scale finite element model shows that the difference can be about 15% larger. It is suggested that the multi-scale finite element model should be used for better accuracy in the multiaxial fatigue analysis of the jacket-type offshore wind turbine under wind and wave random loading.

Análise e dimensionamento de vigas de seção “L” de concreto pré-moldado utilizando o Método das Bielas

Dentre os elementos presentes nas estruturas de concreto pré-moldado estão as vigas de seção “L”, largamente utilizadas no perímetro (bordas e fachadas) das edificações. A geometria tridimensional e as cargas externas aplicadas excentricamente na aba lateral fazem com que este tipo de viga esteja submetido simultaneamente a tensões normais e tensões de cisalhamento, gerando assim um complexo estado tensional. O fato das ligações com os apoios também estarem submetidas a torção torna o projeto estrutural das vigas de seção “L” um dos mais complexos entre os elementos da indústria de concreto pré-moldado por particularidades que não ocorrem nos modelos de vigas convencionais. Nesse contexto, o presente artigo tem como objetivo apresentar a análise e dimensionamento de vigas de seção “L” utilizando o Método das Bielas. Para tanto, foi desenvolvido um estudo de caso com auxílio do software CAST contemplando todas as etapas de dimensionamento e respeitando os parâmetros recomendados pela ABNT NBR 6118:2014. Por fim a metodologia apresentada foi validada através de diferentes métodos analíticos alternativos presentes na literatura internacional, demonstrando que o Método das Bielas é uma ferramenta bastante atrativa para o dimensionamento de vigas de seção “L” de concreto pré-moldado.

О расчетах прочности и жесткости килеватых днищевых перекрытий и выборе доковых стоек поперечных переборок корабля

This paper explains how to calculate the correction factor for keel inertia moment due to the dead rise of grillage and how to consider bulkhead plating in calculation of dock strut response to keel cribbing. The solutions described in this study are different from the commonly used ones. New formulas have been obtained for taking into account inertia moment of grillages with dead rise, as well as for calculation of Euler stresses in dock struts, and their design algorithm has also been updated. The results offer more accurate calculations of grillages with dead rises and more accurate design of transverse bulkheads in terms of conventional beam models and methods of structural mechanics.

16.05: Evaluation of simplified models for short span bridges: Based on a measured train crossing and included substructure

ABSTRACTIn recent times numerous studies concerning bridges under dynamic loading through train crossing were made. It was found out that there are significant deviations of the measured field results and the results determined by simulations using conventional beam models for bridges with short spans (up to 10m). It was shown that a simply supported beam is not a sufficient model for these structures, since the influence of the subsoil and the substructure cannot be neglected for short bridges.The main goal of this article is to achieve a better accordance between the measured and the calculated results. Therefore, the model of the simply supported beam is expanded at both supports by: vertical springs and additional nodal masses. Also, different models for the load are examined. To evaluate the quality of this models, an acceleration measurement of a 4m span bridge during a train crossing is used.It is shown that the measured accelerations can be predicted with acceptable accuracy with an extended beam model by including the load distribution through the rails and the ballast layer (by the method suggested in Eurocode 1).

New Insights on the Deflection and Internal Forces of a Bending Nanobeam**Supported by the National Natural Science Foundation of China under Grant Nos 11672334, 11672335 and 11611530541, and the Fundamental Research Funds for the Central Universities under Grant No 15CX08004A.

Nanowires, nanofibers and nanotubes have been widely used as the building blocks in micro/nano-electromechanical systems, energy harvesting or storage devices, and small-scaled measurement equipment. We report that the surface effects of these nanobeams have a great impact on their deflection and internal forces. A simply supported nanobeam is taken as an example. For the displacement and shear force of the nanobeam, its dangerous sections are different from those predicted by the conventional beam theory, but for the bending moment, the dangerous section is the same. Moreover, the values of these three quantities for the nanobeam are all distinct from those calculated from the conventional beam model. These analyses shed new light on the stiffness and strength check of nanobeams, which are beneficial to engineer new-types of nano-materials and nano-devices.

Distortional Analysis of Beams of Arbitrary Cross Section Using BEM

This paper presents a general formulation for the distortional analysis of beams of arbitrary cross section under arbitrary external loading and general boundary conditions. The nonuniform distortional/warping distributions along the beam length are taken into account by employing independent parameters multiplying suitable deformation modes accounting for in-plane and out-of-plane cross-sectional deformation (distortional/warping functions). The paper proposes a novel procedure for cross-sectional analysis which results in the solution of separate boundary value problems for each resisting mechanism (flexure, torsion) on the cross-sectional domain instead of relying on eigenvalue analysis procedures encountered in the literature. These distortional and warping functions are computed employing a boundary element method (BEM) procedure. Subsequently, sixteen boundary value problems are formulated with respect to displacement and rotation components as well as to independent distortional/warping parameters along the beam length and solved using the analog equation method (AEM), a BEM-based technique. After the establishment of kinematical components, stress components on any arbitrary point of each cross section of the beam can be evaluated, yielding a prediction in good agreement with three-dimensional finite-element method (FEM) solutions, in contrast to conventional beam models.

Slenderness effects in the free vibration of laminated magnetoelectroelastic beams

A semi-analytical discrete-layer approach is used to evaluate slenderness effects in the free vibration of laminated magnetoelectroelastic beams under various boundary conditions. Piecewise continuous approximations are used through the thickness direction of the beam and either continuous polynomial or trigonometric functions are used in the axial direction. Conventional beam models, including those of Euler–Bernoulli and Timoshenko, can be recovered to predict frequency estimates and are compared with results of the present model. Numerical examples are used to show the effects of beam slenderness on frequency and modal order for beams under simply-supported, fixed–fixed, and cantilever conditions. The results of these analyses clearly illustrate the thickness effects for axial, torsional, and bending modes and also provide some results useful for comparison for theses laminated beams.

Influence of initial geometric imperfections in the lateral buckling problem of thin walled pultruded GFRP I-profiles

This paper aims at investigating the influence of some typical manufacturing geometric imperfections on the pre-buckling behavior of transversally loaded GFRP I-beam. One dimensional mechanical approach is proposed by modelling each panel of the cross section as a Timoshenko rectangular beam. In addition to the usual displacement and rotational degrees of freedom used in conventional beam models, few extra degrees of freedom are introduced in order to account for sectional distortions.The model is based on the common assumptions of linear elasticity with small strains and moderate rotations.Two kinds of manufacturing imperfection are taken into account: minor axis out-of-straightness and web/flange planes non-orthogonality the latter representing a particular feature of the present model.Numerical analyses, developed via finite elements, show that such kind of imperfections can significantly influence the pre-buckling behavior making deformability requirements a fundamental design rule.

Analysis of Piezoelectric Energy Harvesters of a Moderate Aspect Ratio With a Distributed Tip Mass

Various mathematical beam models have been proposed for the efficient analysis of a piezoelectric energy harvester (PEH) and carrying out parameter study but there appears no beam model suitable for a PEH of a moderate width-to-length aspect ratio with a distributed tip mass, and so, moderate width-to-length aspect ratios and distribution effects of a tip mass over a finite length will be mainly focused on in the present beam analysis. To deal with a wide range of aspect ratios, the material coefficients appearing in the constitutive equations of a PEH beam will be interpolated by those of the limiting plane-strain and plane-stress conditions. The key idea in the interpolation is to derive the interpolation parameter analytically by using the fundamental frequency of a cantilevered beam of moderate aspect ratios. To deal with the distribution effects of a tip mass over a finite length, the use of a set of polynomial deflection shape functions is proposed in the assumed mode approach. The equations to predict the electrical outputs based on the proposed enhanced beam model are explicitly expressed in template forms, so one can calculate the outputs easily from the forms. The validity and accuracy were checked for unimorph and bimorph PEHs by comparing the results from the developed beam model, the conventional beam model, and a three-dimensional finite element model. The comparisons showed substantial improvements by the developed model in predicting the electrical outputs.

Structural Mechanics of Railguns in the Case of Discrete Supports

In this paper, numerical calculations concerning the dynamic behavior of a railgun are presented. At the first stage, the structural problem can be decoupled from electromagnetic phenomena as well as from the local projectile behavior. The magnetic pressure repelling the rails from each other and expanding with the speed of the projectile serves as a boundary condition for purely mechanical calculations. The particularity of the investigation is represented by the type of railgun housing. For some years, the ISL has been using laboratory housings of an open design allowing, for instance, to take flash radiographs during launch. The repelling forces are mainly taken by discrete supports in the form of steel bolts. These bolts are connected to bars made of glass fiber-reinforced plastics, while the rails are mounted on these bars. A 2-D finite-element model of a complex housing was developed in this paper. Bars, including rails, are described by plane-stress elements, while bolts, playing the role of discrete elastic supports, are presented by truss elements. The model is implemented using the ANSYS code. Deformation properties of the rail section and elastic supports are examined by considering a static solution, assuming constant loading. Differences between 2-D and conventional beam models being of importance for this kind of problem are briefly discussed. Transient analysis was performed for a set of constant loading velocities (600-1600 m/s) and for the experimentally derived transient-loading profile. The latter was obtained in the railgun experiments performed using the ISL-railgun EMA3 with a caliber of 15times30 mm2 and typical muzzle velocities up to 1600 m/s as well as peak currents of about 600 kA.

TH‐C‐M100E‐07: A CT Based Total Body Irradiation Technique Using Intensity Modulated Beams

Purpose: To report experience with a novel total body irradiation (TBI) technique. 3D planning techniques are used to deliver a uniform dose to a patient using a conventional linear accelerator in a standard bunker. Manually segmented intensity modulated fields are employed to provide dose compensation for contour variation, tissue heterogeneity, inverse square law effects and junction dose stability. Methods and Materials: The technique uses a conventional Elekta Synergy linear accelerator together with a custom designed floor couch. The couch, positioned 102.5 cm below the machine isocentre, provides treatment distances near 180 cm SSD. The couch is oriented in the gantry rotation plane, with couch motion along the cranial‐caudal axis enabling a match of beam divergence through patient translations and gantry rotations. Treatment is delivered by a set of 2 to 3 divergence matched abutting fields, with field modulation feathering junctions through 4 cm on the patient. Treatment plans are created using conventional beam models in Pinnacle 7.6C and whole body CT scan data. Independent plans for supine and prone orientations are constructed to deliver a uniform dose at mid‐separation throughout the patient and create a composite uniform dose. Segmentation is used to adjust the dose at mid‐plane, correcting for effects of patient thickness, inverse square law, and lung density. Results: A total of 11 patients have been treated with this new technique. Dosimetry measurements in phantom at extended distance and in‐vivo measurements have demonstrated an accurate dose delivery. Composite AP‐PA dose assessments based on contributions to uniquely identified anatomical points have shown that a dose within 10% of the prescribed dose is achieved throughout the treatment volume. Conclusions: A new TBI technique has been implemented which employs modern imaging and delivery methods to achieve a uniform patient dose. The technique utilizes standard equipment, and does not require specialized bunker design.

A non-discretized global method for free vibration of generally laminated fibre-reinforced pre-twisted cantilever plates

The paper presents a computational method for characterizing the resonant frequency properties of cantilever pre-twisted plates composed of fibre-reinforced laminated composites. It aims to simulate a laminated turbomachinery blade or a fan blade with a relatively small aspect ratio for which the conventional beam model fails to provide accurate solutions. The strain and kinetic energy components are expressed in area integration equations with respect to the plate mid-surface. An energy functional is defined and a governing eigenvalue equation is derived. There is no domain mesh generation in the numerical analysis thus reducing accuracy loss due to discretization. New numerical solutions are presented and the effects of angle of pre-twist, aspect ratio, and symmetric and antisymmetric lamination for two different composite laminates are analyzed in detail. The limit of linear twisting curvature omitted in previous analysis is strictly adopted here and the consequences of exceeding the limit are discussed.

Linear and geometrically non-linear analysis of composite beams under transverse loading

The flexural analysis of fiber-reinforced composite beams based on a higher-order shear deformation theory is studied. The geometric non-linearity is incorporated in the formulation by considering the von Karman strains. The finite element method is used to solve the non-linear governing equations by direct iteration. Unlike conventional beam models, the present beam model accounts for y direction strains. It is observed that the solution obtained from the two approaches differ slightly in the case of cross-ply laminates, but there exists a considerable difference in the case of angle-ply laminates. The influence of boundary conditions, beam geometries, and ply orientations on the deflections and stresses of laminated beams is shown both in tabular and graphical form.