Equivalent Beam Model Research Articles

Global jack-up rig behaviour next to a footprint

This paper reports the effect of the global behaviour of three-legged jack-up rigs due to the reinstallation of spudcan footings next to seabed footprints. Two reinstallation scenarios are discussed: (i) two legs first installed on flat ground, and then the third leg installed near a footprint (representing what is known as leg-by-leg preloading); and (ii) the three legs installed simultaneously (representing simultaneous preloading). The spudcan-soil interaction was simulated using a coupled Eulerian-Lagrangian (CEL) approach. A simplified global jack-up model was developed by considering an equivalent beam model for the hull and legs. The results of the jack-up installations are compared against the responses of the more common modelling of a spudcan with a fixed head condition. A detailed parametric study assessing the consequences of spudcan-footprint interactions, such as the risk of the jack-up and spudcan sliding towards the footprint centre, overturning of the jack-up rig and of structural failure of the jack-up leg due to excessive stresses, is also discussed. The ability of a recently developed novel spudcan with a flat base and 4 holes, coupled with the global jack-up model, to mitigate the consequences of spudcan-footprint interactions is highlighted.

A novel framework for deriving the unified SCF in multi-planar overlapped tubular joints

For the past few decades, a significant number of research efforts have been devoted to the studies of SCF values and parametric design formulae at certain positions in various uniplanar and multi-planar tubular joints. However, very few investigations on the multi-planar overlapped tubular joints have been reported. The main reason may lie in the complexity of combining effects between multi-planarity and overlapping. In this paper, a novel framework for deriving the unified SCFs is proposed by reducing joint modeling from multi-planar out-of-plane overlapping to equivalent uniplanar non-overlapping. By integrating the equivalent beam model with solid finite element modeling for the overlapped tubular KK-joint in offshore jack-ups, the procedures for computing the unified SCF values in the equivalent beam stick model are successfully developed. Verification of the proposed framework is obtained by comparing the unified SCFs based on basic load cases with those based on actual wave loading typically experienced by the jack-up.

Damage Identification of Beam with Breathing Crack under Fractal Dimension

Damage identification has been more urgent in engineering, especially beam structure which is often damaged by ambient excitation. It is based on time-frequency domain analysis of beam with breathing crack under fractal dimension in this paper. An equivalent cantilever beam model is constructed. The stiffness cosine model with time as parameter is used to simulate the opening and closing process of crack. The most widely used box dimension in fractal dimension is selected to calculate and analyze the displacement response of beam structure. The results show that the changes of box dimensional of beam structure displacement response can determine whether there is damage or not and identify the damage degree intuitively. It is more practical for damage identification in actual engineering.

Design and Dynamic Equivalent Modeling of Double-Layer Hoop Deployable Antenna

This study proposes deployable units driven by elastic hinges and a double-layer hoop deployable antenna composed of these units. A rational modeling method based on the energy equivalence principle is presented to develop an equivalent model of the double-layer hoop antenna in accordance with the structural characteristics of the antenna. The equivalent beam models of the rods with elastic hinges are proposed. The relationship of geometrical and material parameters is established considering the strain energy and the kinetic energy of the periodic unit, which are the same as those of the equivalent beam in the same displacement field. The equivalent model of the antenna is obtained by assembling several equivalent beam models in the circumferential direction. The precision of the equivalent model of the antenna is acceptable as found by comparing the modal analysis results obtained through equivalent model calculation, finite element simulation, and modal test.

Mechanical behavior of FRP confined steel tubular columns under impact

This paper presents experimental and analytical results of fiber reinforced polymer (FRP) confined steel tubular columns under transverse impact loads. Influences of applied impact energy, thickness of FRP jacket and impact position were discussed in detail, and then the impact responses of FRP confined steel tubes were compared with bare steel tubes. The test results revealed that the FRP jacket contributes to prevent outward buckling deformation of steel at the clamped end and inward buckling of steel at the impact position. For the given applied impact energy, specimens wrapped with one layer and three layers of FRP have the lower peak impact loads than those of the bare steel tubes, whereas specimens wrapped with five layers of FRP exhibit the higher peak impact loads. All the FRP confined steel tubular specimens displayed a longer duration time than the bare steel tubes under the same magnitude of impact energy, and the specimen wrapped with one layer of FRP had the longest duration time. In addition, increasing the applied impact energy leads to the increase of peak impact load and duration time, whereas increasing the distance of impact position from the clamped end results in the decrease of peak impact load and the increase of duration time. The dynamic analysis software Abaqus Explicit was used to simulate the mechanical behavior of FRP confined steel tubular columns, and the numerical results agreed well with the test data. Analytical solution for lateral displacement of an equivalent cantilever beam model subjected to impact load was derived out. Comparison of analytical and experimental results shows that the maximum displacement can be precisely predicted by the present theoretical model.

A Structural Calculation Model of Shield Tunnel Segment: Heterogeneous Equivalent Beam Model

A heterogeneous equivalent beam model (HEB model) of the shield tunnel segment structure is proposed based on a systematical analysis on the stress state of the cross section of segment joints. This model treats a noncontinuous segment structure as a continuous heterogeneous structure, on the basis of the principle of equivalent stress state on a section and equivalent conversion of the mechanical parameters. For a comprehensive demonstration of the proposed HEB model, an interpretative solution of equivalent mechanical parameters of the joint section is obtained through theoretical derivation, and a specific iterative computation flow is provided in accordance. Model validation and comparative analysis are also conducted for two industrial applications. It is found that the iterative process of calculation has good convergence, leading to reliable numerical results for all cases under consideration. Resulting simulations reveal that the proposed HEB model can reflect the effect of joints on overall rigidity of a segment structure. Compared with the computation results obtained using other models presented in the literature, there are smaller axial force deviation and larger bending moment deviation (up to 20% or higher), demonstrating that the model selection is important in design and computation of a segment structure of shield tunnels. The proposed model and analysis for model performance may provide useful reference for engineers in shield tunnel community.

Equivalent parameterized beam model for nailed connections in low-rise residential buildings

Abstract Increased frequency and intensity of coastal storms has renewed interest in the structural performance of coastal low-rise residential homes. Post hazard surveys indicate connections that form the load path from sheathing to framing to foundation play a pivotal role in the failure modes of these non-engineered structures. Nonlinear spring elements are a common means of modeling nailed connections for structural analysis based on experimentally observed behavior. Due to complex connection behavior, three independent springs are usually defined to consider 3D translational displacements. This common approach may introduce error in large displacement analyses due to independently defined directional spring properties. After a brief discussion of issues encountered with nonlinear spring element connection modeling schemes, an equivalent parameterized beam connection model is proposed to characterize softening-type connection behavior. Comparison analyses between the equivalent parameterized beam connector (EPBC) and equivalent nonlinear spring connector (ENSC) are carried out using 1D and 2D single element examples as well as 3D panel models. This new connection modeling scheme could greatly reduce meshing efforts in large models and provide more accurate solutions in critical areas of the structure such as corners and edges by coupling the axial and transverse connection responses.

An optimization study on load alleviation techniques in gliders using morphing camber

This study explores wing morphing for load alleviation as a means to reduce the required wing structural weight without compromising aircraft performance. A comparative study between the lift-to-drag ratio (L/D) performance of a fixed wing glider (FWG) and a cambered morphing wing glider (CMWG) is presented. Both aircraft are aero-structurally optimized for the best L/D for a given speed and payload mass. A combination of lifting-line theory and 2D viscous calculations is used for the aerodynamics and an equivalent beam model is employed for the structural analysis. Pull-up and -down maneuvers at 25 m/s and near stall angle of attack are assumed as critical load cases. Results of the FWG optimization are shown for several trimmed flight conditions with varying mass and velocity. Results are compared to the ones from the CMWG optimization and conclusions are drawn on the improvement in the L/D ratio throughout the flight envelope and on potential reductions in the wing structural mass due to the load alleviation strategy. The wing camber adaptation provides significant performance gains in a large range of flight speeds with negligible penalties in the low speeds range. However, maneuverability is penalized.

Free vibration analysis of cantilever open-hole composite plates

The free vibration behavior of quasi-isotropic carbon fiber laminated composite plates containing circular holes with free-clamped boundary conditions are numerically, analytically, and experimentally investigated. Finite element models based on classical plate theory (Kirchhoff) and the shear deformable theory (Mindlin) within the framework of equivalent single-layer and layer-wise concepts as well as the three-dimensional theory of elasticity are developed. These models are created using the finite element software, Abaqus, to determine the natural frequencies and the corresponding mode shapes. In addition, an analytical model based on Kirchhoff plate theory is developed. Using this approach, an equivalent bending-torsion beam model for cantilever laminated plates is extracted taking into account the reduction in local stiffness and mass induced by the center hole. Experimental vibration analyses are carried out using an optically-based vibration measurement tool to extract the frequency response functions and to measure the natural frequencies. Numerical and analytical natural frequency values are then compared with those obtained through experimental vibrational tests, and the accuracy of each finite element (FE) and analytical model type is assessed. It is shown that the natural frequencies obtained using the analytical and FE models are within 8% of the experimentally determined values.

Electromechanical bending behavior study of soft photocurable ionogel actuator using a new finite element method

The photocurable ionogel actuator (PIA) is one of the most promising driving mechanisms for the future due to its extraordinary features such as its light weight, flexibility, low-energy consumption and ability to work in open air. However, before the benefits of PIA can be effectively exploited for applications, a mathematical model is required to enhance the understanding of the parameters influencing the actuator electromechanical bending behavior. In this work, a model based on the finite element method (FEM) for the electromechanical bending behavior of PIA is established. It is assumed that the PIA consists of one ionogel layer and two activated carbon electrode layers. With reference to its operational principles, an analogy is drawn between thermal strain and induced strain in the PIA due to the volume change of the activated carbon electrode layer, which is a coupled structural/thermal model and can be solved by FEM. The distribution of net charge in the activated carbon electrode layer is mimicked using temperature distribution, and the electromechanical coupling coefficient is mimicked using the thermal expansion coefficient. Compared with the traditional equivalent bimorph beam model, the proposed model can predict the distribution of the induced strain more exactly. On the basis of the model, experiments are carried out to investigate the impact of selected parameters on the tip displacement, electromechanical coupling coefficient and induced strain of the PIA. The voltage of the input signal, and three geometrical parameters, length, width, and thickness, of the PIA are selected in this work. The experimental and simulation results indicate that the voltage, length, and thickness show significant influence on the electromechanical bending behavior of the PIA, but the width does not. As a whole, these results can be beneficial for providing enhanced degrees of understanding, predictability and control of PIA performance.

등가 보 모델링 방법을 이용한 차량 배기계의 벨로우즈 동특성 예측

배기계는 엔진 및 현가계와 함께 차량의 주요 가진원 중의 하나이다. 배기계는 엔진과 직접적으로 연결된 시스템으로서 차체와의 연결 마운트를 통하여 엔진 구동 시의 진동을 차체로 전달한다. 따라서 배기계로부터 전달되는 진동을 저감하기 위해서는 배기계 진동특성을 예측해야 하고, 배기계의 주요부품인 벨로우즈의 정확한 특성을 묘사해야 한다. 그러나 벨로우즈는 복잡한 형상으로 인하여 특성을 예측하는 데에 어려움이 있었다. 설계 단계에서 벨로우즈에 대한 등가 변환 이론이 적용되었지만, 구간에 따라 주름의 크기가 달라지는 차량용 벨로우즈에 적용하기에는 부족함이 있다. 본 연구에서는 유한요소 해석기법을 이용하여 차량용 벨로우즈의 모델링 기법을 제시하고, 그 정확성을 실험결과와 비교하여 입증하였다.

SSPS Dynamic Modeling and the Flexible Vibration Suppression

Space solar power satellite (SSPS) as a very large flexible spacecraft structure with complex configuration, large size and number of units bring the difficulties to dynamics modeling and analysis. Considering SSPS structure characteristics, equivalent strain and kinetic energy theory is adopted to establish the equivalent beam model of SSPS truss structure. The assumed mode method is adopted to describe the flexible body. The modal truncation method implements the dynamics system order reduction. Mixed coordinates method is adopted to establish the rigid-flexible coupled dynamic model. The established dynamic model can reflect dynamic characteristics of SSPS, achieve control requirements for SSPS and decrease the workload of simulation calculation. The independent modal space control (IMSC) method is proposed to active control research view of the large displacement, nonlinearity, low and dense mode frequency, light damping of flexible structures. Simulation results on flexible solar array show the effectiveness of the control method.

Comparison between Numerical Results of 1D Beam and 2D Plane Stress Finite Element Analyses Considering Aspect Ratio of Cantilever Beams

There exist different kinds of aircrafts, such as conventional airplane, rotorcraft, fighter, and unmanned aerial vehicle. Their shape and feature are dependent upon their own assigned mission. One of the fundamental analyses performed during the aircraft design is the structural analysis. It becomes more complicated and requires severe computations because of the recent complex trends in aircraft structure. In order for efficiency in the structural analysis, a simplified approach, such as equivalent beam or plate model, is preferred. However, it is not clear which analysis will be appropriate to analyze the realistic configuration, such as an aircraft wing, i.e., between an equivalent beam and plate analysis. It is necessary to assess the limitation for both the one-dimensional beam analysis and the two-dimensional plate theory. Thus, in this paper, the static structural analysis results obtained by EDISON solvers were compared with the three-dimensional results obtained from MSC NASTRAN. Before that, EDISON program was verified by comparing the results with those from MSC NASTRAN program and other analytic solutions.

Simplified Analytical Methods to Analyze Lock Gates Submitted to Ship Collisions and Earthquakes

Abstract This paper presents two simplified analytical methods to analyze lock gates submitted to two different accidental loads. The case of an impact involving a vessel is first investigated. In this situation, the resistance of the struck gate is evaluated by assuming a local and a global deforming mode. The super-element method is used in the first case, while an equivalent beam model is simultaneously introduced to capture the overall bending motion of the structure. The second accidental load considered in this paper is the seismic action, for which an analytical method is presented to evaluate the total hydrodynamic pressure applied on a lock gate during an earthquake, due account being taken of the fluid-structure interaction. For each of these two actions, numerical validations are presented and the analytical results are compared to finite-element solutions.

Equivalent nonlinear beam model for the 3-D analysis of shear-type buildings: Application to aeroelastic instability

Tower buildings can be very sensitive to dynamic actions and their dynamic analysis is usually carried out numerically through sophisticated finite element models. In this paper, an equivalent nonlinear one-dimensional shear–shear–torsional beam model immersed in a three-dimensional space is introduced to reproduce, in an approximate way, the dynamic behavior of tower buildings. It represents an extension of a linear beam model recently introduced by the authors, accounting for nonlinearities generated by the stretching of the columns. The constitutive law of the beam is identified from a discrete model of a 3D-frame, via a homogenization process, which accounts for the rotation of the floors around the tower axis. The macroscopic shear strain in the equivalent beam is produced by the bending of columns, accompanied by negligible rotation of the floors. A coupled nonlinear shear–torsional mechanical model is thus obtained. The coupling between shear and torsion is related to a non-symmetric layout of the columns, while mechanical nonlinearities are proportional to the slenderness of the columns. The model can be used for the analysis of the response of tower buildings to any kind of dynamic and static excitation. A first application is here presented to investigate the effect of mechanical and aerodynamic coupling on the critical galloping conditions and on the postcritical behavior of tower buildings, based on a quasi-steady model of aerodynamic forces.

Analysis of lateral vibrations of the axially loaded helical spring

It is shown in this paper that the proposed concept by Kruzelecki and Życzkowski (1990) of the equivalent rod can be applied in calculations of natural lateral vibrations of springs and that the obtained results will be nearer FEM results than the standard model based on the Timoshenko equivalent beam. The model, created on this base, allows one to calculate natural frequencies of the clamped-clamped spring. It is also shown that models based on the equivalent beam concept, which are easier to apply than the models treating the spring as the spatially curved rod, have only a slightly smaller accuracy. It is also indicated that in the most common practice making of manufacturing end coils of springs, the natural frequencies differ significantly from the frequencies calculated by means of all tested methods. The performed simulations show that differences between the first and the second as well as the third and the fourth natural frequency of the spring are small and, therefore, the axially symmetrical equivalent beam model can be used without a large error. The diagram allowing one to determine whether the desired frequencies are lower or higher than the cut-off frequency is developed for the presented model.

SU‐E‐T‐211: Comparison of Seven New TrueBeam Linacs with Enhanced Beam Data Conformance Using a Beam Comparison Software Tool

Purpose:To develop an independent software tool to assist in commissioning linacs with enhanced beam conformance, as well as perform ongoing QA for dosimetrically equivalent linacs.Methods:Linac manufacturers offer enhanced beam conformance as an option to allow for clinics to complete commissioning efficiently, as well as implement dosimetrically equivalent linacs. The specification for enhanced conformance includes PDD as well as profiles within 80% FWHM. Recently, we commissioned seven Varian TrueBeam linacs with enhanced beam conformance. We developed a software tool in Visual Basic to allow us to load the reference beam data and compare our beam data during commissioning to evaluate enhanced beam conformance. This tool also allowed us to upload our beam data used for commissioning our dosimetrically equivalent beam models to compare and tweak each of our linac beams to match our modelled data in Varian's Eclipse TPS. This tool will also be used during annual QA of the linacs to compare our beam data to our baseline data, as required by TG‐142.Results:Our software tool was used to check beam conformance for seven TrueBeam linacs that we commissioned in the past six months. Using our tool we found that the factory conformed linacs showed up to 3.82% difference in their beam profile data upon installation. Using our beam comparison tool, we were able to adjust the energy and profiles of our beams to accomplish a better than 1.00% point by point data conformance.Conclusion:The availability of quantitative comparison tools is essential to accept and commission linacs with enhanced beam conformance, as well as to beam match multiple linacs. We further intend to use the same tool to ensure our beam data conforms to the commissioning beam data during our annual QA in keeping with the requirements of TG‐142.

Coupling equivalent plate and beam models at conceptual design level

Purpose – The purpose of this paper is to present a formulation that couples equivalent plate and beam models for aircraft structures analysis, suitable in conceptual design in which fast model generation and efficient analysis capability are required. Design/methodology/approach – Assembling the complete model with common techniques such as Lagrange multipliers or penalty function method would require a solver capable of handling the combined set of linear equation. The alternative approach proposed here is based on a static reduction of the beam model at specified connection points and the subsequent “embedding” into the equivalent plate model using a coordinate transformation, translating physical dfs in Ritz coordinates, i.e. polynomial coefficients. Displacements and forces on beam elements are recovered with the inverse transformation once the solution is computed. Findings – An aeroelastic trim analysis on a Transonic CRuiser (TCR) civil aircraft conceptual model validates the hybrid model: as the ...

Programmatic Lattice Generation for Additive Manufacture

Advances in additive manufacturing hardware have enabled the creation of lattice structures for engineering purposes; however the use of standard CAD software for the design of lattice structures is grossly inefficient, time consuming, and can lead to processing issues. To assist designer engineers that intend to implement large lattice structures a highly customisable free open source method of generating periodic lattice structures directly to the generic STL format has been developed. Programmatic method also offers a significant advantage to designers seeking to optimise or conduct finite element simulations on lattice structures allowing a batch export of both STL parts and a geometrically equivalent FE beam models.

Comparison of different approaches to load calculation for the OWEC Quattropod jacket support structure

Accurate load simulations are necessary in order to design cost-efficient support structures for offshore wind turbines. Due to software limitations and confidentiality issues, support structures are often designed with sequential analyses, where simplified wind turbine and support structure models replace more detailed models. The differences with an integrated analysis are studied here for a commercial OWEC Quattropod. Integrated analysis seems to generally predict less damage than sequential analysis, decreasing by 30-70 percent in two power production cases with small waves.Additionally it was found that using a different realization of the wave forces for the retrieval run in sequential analysis leads to an increase of predicted damage, which can be explained as the effect of applying two independent wave force series at the same time.The midsection of the detailed support structure model used shell elements. Additional analyses for a model with an equivalent beam model of the midsection showed only small differences, mostly overpredicting damage by a few percent. Such models can therefore be used for relatively accurate analysis, if carefully calibrated.