Beam Elements Research Articles

Fourth-Order Accurate Strain-Parameterized Shape Representation of Beam Elements for Modeling Continuum Robots and Robotic Manipulation of Slender Objects

Abstract Soft rods and tubular elements are the main building blocks of continuum robots. Kinetostatic models along with a geometrically exact description of the kinematics on SE(3) are now an established foundation for simulation and control. A key aspect is the reconstruction of the actual shape of a soft slender element. This involves numerically solving nonlinear differential equations on SE(3), which is problematic, in particular for real-time applications. To circumvent this, shape functions are used to approximate the deformation. A widely used approach is based on the constant curvature assumption. This has limited accuracy, however. In this article, an interpolation is presented that leads to a fourth-order accurate approximation of the deformation of a Cosserat beam. This serves as a strain-parameterized shape function. Either the strain at the two ends of the beam or the strain and its derivative at one end are specified. The presented interpolation is relevant also for shape control when handling flexible slender objects with robotic manipulators.

Analyzing the Impact of Multiple Foundation Stiffness Correlation on the Natural Frequency of Offshore wind turbines

The analysis of wind turbine behavior should avoid unplanned resonance, as it can increase fatigue damage. It is essential to rigorously evaluate the natural frequency of wind turbines in the initial design stage. This estimation can be done through two steps, the first one is the computing of the fixed base natural frequency of the wind turbine. The second is the estimation of the foundation stiffness effect. This paper examines the error margin of four correlations of foundation stiffness namely Randolph, Davies and Budhu, DNV, and Higgins in the estimation of the natural frequency of wind turbines. The fixed base natural frequency was estimated in this paper using a special-purpose finite element computer program called TurbiSoft through beam and volume elements. A reference 5.0 MW offshore wind turbine and 9 other turbines from different wind farms have been analyzed. For the fixed base natural frequency, obtained results demonstrate the reliability of the finite element program TurbiSoft through an error margin between 1-4% for the reference 5.0 MW offshore wind turbine. For the natural frequency of the whole system, the estimated error marking was between 9-20% which is an important value.This significant error is attributed to the low accuracy of these four correlation formulas for predicting the foundation flexibility contribution. The results from the four correlation formulas used are quite similar, with a difference in the error margin of less than 1%. However, the largest error margins are observed with the Higgins formula, which has been originally developed for short monopiles, even though the analyzed monopiles can be considered short, with monopile slenderness ratios less than 8.

The Behaviour of Elbow Elements at Pure Bending Applications Compared to Beam and Shell Element models

Abstract This paper studies the response of ELBOW31 and ELBOW31B element types under pure bending conditions, using shell and beam element models for benchmarking. Various model lengths are evaluated, showing that a model length of six pipe diameters exhibits a hardening effect when total strain exceeds 3.5%, though a strain up to 1% is deemed sufficient for pipeline design. The study examines the effects of ovality modes and boundary conditions such as NOWARP and NOOVAL on the bending response. ELBOW31 with one or two ovality modes yields accurate results, while additional ovality modes or zero ovality mode can lead to overprediction of the elastic bending moment capacity. The introduction of the NOWARP condition enhances the accuracy of the ELBOW31 model, while the NOOVAL condition alone produces unrealistic results. The simplified ELBOW31B model shows good agreement with the ELBOW31-NOWARP model but similarly overpredicts when zero ovality mode is used. The study also finds that Poisson?s ratio and model length have no significant impact on the bending response when no restrictions are applied. Additional analyses, as presented in Appendices A and B, highlight the importance of D/t ratios in pipeline performance. A D/t ratio of 20 offers a stiffer response with reduced ovalization, while a D/t ratio of 50 results in greater flexibility and increased ovalization. These findings provide valuable insights for the selection of element types, boundary conditions, and D/t ratios in robust pipeline design.

Third-order geometric stiffness formulation for improved mesh convergence of thin and wide spatial beams in the generalized strain beam formulation

AbstractThis paper presents the stiffness formulation of a beam element with the relevant third-order nonlinear geometric effects for relatively wide and thin rectangular beams, in particular when loaded in the plane and simultaneously deformed out of the plane. The element is initially straight in its undeformed configuration. The formulation is based on Timoshenko beam theory with nonuniform torsion and Wagner effects. The derivation is carried out by means of the Hellinger–Reissner variational principle with custom interpolation functions. The element is incorporated into the generalized strain beam formulation for multibody systems. Numerical simulations of precision flexure mechanisms show that the use of a single third-order element per flexible member can already yield adequate performance, at a significant reduction of the necessary degrees of freedom and the computation time, compared with using multiple second-order elements in the generalized strain beam formulation.

An improved coupled beam method for predicting longitudinal bending behaviour in luxury cruise ships

ABSTRACT This paper describes an improved coupled beam method, designated as MBS-CB, that estimates elastic response in the longitudinal bending of a cruise ship. Initially, the ship structure is discretised into beams, and the coupling relationships between adjacent beams are analysed. Secondly, connector elements with equal stiffness constraints are refined to simulate the coupling behaviour between adjacent beam elements. Meshed beam sections are introduced to simplify the beams involved in total longitudinal bending. A spatial beam system model of the ship structure is established to predict the interaction between adjacent beams and to characterise the longitudinal bending behaviour of the ship. Ultimately, the accuracy of the method is validated through instance analysis. Furthermore, the method is employed to investigate the longitudinal bending characteristics of a large passenger ship, and the participation of different superstructures in the ship's longitudinal bending is obtained through moment distribution coefficients and length proportions.

Instability of porous FGM rectangular hollow section (RHS) beam element in a thermal environment.

Instability of porous FGM rectangular hollow section (RHS) beam element in a thermal environment.

Effectiveness of shear key on torsional resistance of precast beam: An experimental and numerical investigations

The present study evaluates the behaviour of wet precast beam-to-beam connection under pure torsion through experimental and numerical studies. A wet connection is provided at the central region of the precast beam. Two precast beam elements are connected by welding the overlapped portion of reinforcement bars projecting from each beam element. Furthermore, inward and outward shear keys are provided within the connection region to examine the efficacy of shear keys on the torsional resistance of the precast beam. Also, the behaviour of precast beams with and without shear keys is compared with monolithic beams. Experiments are conducted using a loading frame, designed and fabricated to create a pure torsion effect on the beam specimen under the application of monotonic vertical load. The response of test specimens is evaluated through various parameters such as torque and corresponding twist at different phases of loading, torsional ductility index, crack formation and failure propagation. Experimental studies show that shear keys provided within the connection region effectively contribute to force transfer and enhance torsional resistance of the precast beam by 16 %−24 % as compared to monolithic beam and precast beam without the shear key. A numerical analysis of the precast beam is carried out, and the behaviour of test specimens obtained from experimental studies is compared. The damage pattern and torque-twist behaviour obtained from numerical studies adequately simulate the response of test specimens observed during the experimental study.

Rapid dynamic load estimation procedure for lifting propellers in forward flight

AbstractLifting propellers operate at oblique inflow and thus encounter severe dynamic loads during forward flight, impacting structural integrity, fatigue, and vibration. Numerical optimization approaches consider aerodynamic, structural mechanical, and aeroacoustic aspects within preliminary design. To also account for dynamic loads during forward flight, a novel procedure allows their rapid estimation. Based on steady-state simulations combining strip theory and finite beam elements, aerodynamic excitation, damping, and stiffness are defined in the frequency domain. Loads are derived through a linear inflow model and quasi-steady aerodynamics. Damping and stiffness loads are linearized and transferred into matrix form to calculate the frequency response. The computationally expensive need for simulations in the time domain is thus avoided. Applicability extends to both fixed and variable pitch lifting propellers utilized in large multicopters for cargo or passenger transportation. Comparisons to time-marching simulations show good agreement with deviations of approximately 10 %. The analytical derivation yields physical insights to understand and reduce dynamic loads and their magnification due to resonance.

Lateral Response Analysis of a Large‐Diameter Pile Under Combined Horizontal Dynamic and Axial Static Loads in Nonhomogeneous Soil

ABSTRACTThe large diameter piles are widely used in structures such as offshore wind turbines due to their superior lateral load‐bearing capacity. To explore the lateral response of a large‐diameter pile under combined horizontal dynamic and axial static loads in nonhomogeneous soil, a simplified analytical model of the pile–soil interaction is developed. This model represents the pile as a Timoshenko beam resting on the Pasternak foundation, incorporating the double‐shear effect by considering both pile and soil shear. The governing matrix equations for the pile elements are derived from the principle of virtual work. Further, the pile's lateral deformations and internal forces are obtained using the modified finite beam element method (FBEM) and then validated through existing analytical solutions. Finally, the contribution of various properties of pile, soil, and applied load to the pile's lateral vibration response are performed. It is found that both pile and soil shear effects significantly impact the lateral dynamic response of a large‐diameter pile. Additionally, in nonhomogeneous soil, decreasing surface soil strength and dimensionless frequency lead to increased lateral displacements and bending moments of the pile, which are significantly affected by the P‐Δ effect under increasing axial load.

Research on a macro joint model for progressive collapse analysis of L-CFST column frames

In this study, a macro joint model was developed to evaluate the progressive collapse resistance of L-shaped column composed of concrete-filled steel tubes (L-CFST column) frames, accounting for joint performance. The methods used to calculate the spring stiffness in each part of the macro joint model were derived using the component method and deformation coordination principle. Additionally, an L-CFST frame model consisting of fibre beam elements and macro joint models was created. For frame models with different parameters, the dynamic response of column removal was analysed. These parameters included the loading conditions, the connection types, the location of the failed columns, the height and number of floors, and the span-depth ratio of the steel beams. The results indicated that the macro joint model had high accuracy in predicting progressive collapse resistance. The L-CFST column frames with novel side-plate reinforced connections fully exploited the catenary mechanism and Vierendeel action. All the variables affected the vertical displacement at the position of the failed columns, with the span-depth ratio having the most significant impact.

Modeling and analysis of creep at elevated temperature analysis on thin-walled profile structures

Abstract High-strength steel plays a crucial role in aerospace because of its excellent performance. The high temperatures experienced during a spacecraft’s re-entry to Earth may result in creep in the steel, potentially leading to structural failure, so the finite element software is utilized in this paper to establish a calculation model and analyze the impact of temperature and fire duration on the creep strain of high-strength I-section steel beams under elevated temperatures. Among them, the high-temperature parameter significantly affects the creep strain variation of the mid-span element of the high-strength I-section steel beam. When the temperature parameter is increased by 100%, the maximum creep strain variation of the mid-span component of the beam will increase by about 24%. Under the exact increase, the maximum creep strain variation of the high-temperature duration parameter will only increase by about 3.78%; thus, when conducting a high-strength steel structure, fire resistance analysis should mainly consider the influence of temperature on its creep at elevated temperature strain.

Development and commissioning of ion-optical elements for ion and antiproton beams with energies up to 5 keV

In nuclear and atomic physics experiments, charged ion beams often need to be guided from the ion production to the experimental site. In the PUMA experiment, an ion source beamline was developed, which can be operated with up to 5 keV beam energy at a base pressure of 10-9 mbar or better. In this technical report, a low-energy pulsed drift tube for beam energy modification, a hybrid einzel lens assembly for beam focusing and steering and an iris shutter assembly for separating beamline sections with different vacuum requirements are described with their design principles and performances.

A Vertical Polarized Endfire Phased Array Antenna With Wide-Angle Scanning Using Heterogeneous Beam Elements

A Vertical Polarized Endfire Phased Array Antenna With Wide-Angle Scanning Using Heterogeneous Beam Elements

Advanced finite element modeling methods for tensile and bending analysis of arresting gear cables

This study addresses the gap in understanding the dynamic bending behavior of multi-layer twisted steel cable, pivotal in various industrial applications such as naval aircraft arresting systems. Utilizing advanced finite element modeling, the research explores the mechanical responses of these cables under macroscopic bending scenarios. By integrating beam elements and connectors within the finite element framework, the study simulates complex inter-strand interactions under various loading conditions. Results indicate that this method significantly enhances the prediction accuracy of the cables’ mechanical properties, thus offering substantial improvements in design and performance analysis of arresting gear systems. This study’s value lies in its potential to refine mechanical modeling of complex cable systems, thereby optimizing operational efficiency and safety in engineering applications.

Toward Limited Durability of Load-Bearing Beams of Metal Bridge Spans

The paper considers the limited durability as a structural property which continuously maintains operability during certain time under random loading of beam elements and proposes the definition for durability as the main criterion of failure and destruction of beam elements or beam as a whole.Methodology: Structural analysis; cumulative model of quasi-monotonic damage accumulation and failure of beam elements.Purpose: To develop methods to determine the durability based on damages representing a random, non-stationary loading process.Research findings: The damage accumulation is calculated for beams. The process is considered as quasi-monotonic. Stress-strain curves are obtained, including changes in probabilistic characteristics of not only structural materials, but also loading modes from the damage growth. The durability limitations of span girders are estimated both by nominal stresses and total damage in the more dangerous section.

Simulation and experimental analysis of traveling wave resonance of flexible spiral bevel gear system

Considering the traveling wave resonance (TWR) phenomenon of the spiral bevel gear system in the aero engine accessory casing, the flexible spiral bevel gear model is established by three-dimensional (3D) shell element and beam element. The dynamic model of flexible bevel gear system considering the change of meshing teeth pairs in the operating process is established by component mode synthesis (CMS) method and rotational modal projection method. The proposed model is verified by finite element (FE) solid model and experiment test results. On this basis, the TWR phenomenon of the bevel gear system is studied in combination with dynamic response and vibration stress experimental test. The results show that the bevel gear system has 3 nodal diameter resonance speeds within the actual operating speed range, which are one 1st nodal diameter resonance of pinion and two 1st nodal diameter resonance of gear. When the bevel gear system operates at TWR state, the amplitude corresponding to fm ± m·fr (fm is meshing frequency, m is nodal diameter number, fr is shaft rotational frequency) is larger than that corresponding to fm in the Fast Fourier transform (FFT) spectrum of the of the gear foundation vibration stress, and the vibration stress cloud map of the gear foundation shows the corresponding nodal diameter vibration shape. The research results provide a theoretical basis for feature recognition and influence law evaluation of TWR of bevel gear system.

Study on the Effect of Cracks in Diaphragm Couplings on the Dynamic Characteristics of Shaft System

Diaphragm couplings are prone to developing diaphragm cracks under prolonged high-speed operating conditions, which can lead to degradation in the performance of the transmission system and affect the dynamics of the shafting system. To investigate the effects of diaphragm cracks on the dynamics of couplings and the shafting system, a finite element model of a diaphragm coupling with a crack failure is established using ANSYS finite element software to analyze the time-varying characteristics of the diaphragm coupling’s angular and radial stiffness. A shaft dynamics model of the diaphragm coupling with a crack is developed using Timoshenko beam elements to analyze the impact of different crack lengths and locations on the dynamics of the shafting system. The validity of the dynamic model for a diaphragm coupling with a crack is verified through a constant speed experiment conducted on a rotor test bench. The results indicate that diaphragm crack failure causes a change in the periodicity of the time-varying stiffness of the diaphragm coupling, leading to a distinct 2× component appearing in the frequency domain of the transmission shaft system.

Research on the energy absorption performance of lattice filling structures based on homogenization analysis technique

The lattice structure has great application prospects in the field of energy absorption, but the high cost of numerical analysis makes it difficult to carry out related structural designs. Therefore, this article studies the feasibility of the homogenization analysis technique for the analysis of energy absorption processes in lattice-filled structures. In the study, compression experiments and numerical simulations were conducted for four different types of unit cells (including periodic truss-lattice cells and triply periodic minimal surface (TPMS cells). In the experiments, two compression samples with different numbers of periods were designed for the same unit cell structure. The research shows that the homogenized numerical model takes a lot less time to run than the classical beam and shell element models. The results of the simulation are also in line with the data from the experiments. On the other hand, the material curve constructed based on a small number of unit cell samples has excellent analytical accuracy. This means that relevant research can obtain the material experimental data required for homogenized analysis using lattice samples with low manufacturing costs. Understanding these phenomena can provide a basis for the design of energy absorption structures.

Dynamic Analysis Techniques for Road Bridges Under Large Traffic Flows

This work focuses on the dynamic analysis of road bridges under large microsimulated traffic flows, contributing an efficient dynamic analysis framework for future fatigue, comfort or driving safety studies in which realistic interactions between vehicles are considered. Different strategies to define the loading vector in the governing dynamic equations are presented for bridges discretized with beam and shell elements. The proposed interpolation techniques for beam-like models include a recursive binary search and a novel vectorized strategy based on shape functions expanded to the entire length of the deck. These are applied to a short simply supported bridge and a very long cable-stayed bridge under traffic flows generated with a cellular automata microsimulation model. The strategies presented here reduce the computational time required in conventional load interpolation algorithms, particularly in long bridges subject to dense traffic flows. Finally, the binary search algorithm is applied to the study of bridge decks discretized with shell elements under microsimulated traffic, demonstrating that high vehicle densities increase the contribution of the transverse vibration of the slab and the potential discomfort of pedestrians.

Three-dimensional numerical analysis of the effect of foundation stiffness on soil-structure interaction

Stiffness-related geometric characteristics are closely linked to the performance of structural systems. The influence of foundation stiffness on the soil-structure interaction (SSI) mechanism was investigated by numerical modeling of different building foundations. Numerical tools (PLAXIS 3D and TQS/CAD) were used for decoupling analyses of the interaction between the structural components. Results obtained from instruments installed in a building case study were used to refine the numerical calculations. Linear elastic constitutive models and beam elements were useful in reducing computational processes and ensuring study feasibility. The simulation results provided a satisfactory representation of field observations. Interaction between piles and the environment governs the relationship between foundation stiffness and uniform settlement. Rigid pile groups are achieved with greater pile length, diameter and spacing. This study highlights the different effects of pile geometric parameters on loading and unloading rates in pillars, demonstrating that the SSI mechanism is more sensitive to less rigid foundations, particularly those with greater pile embedment. It was concluded that numerical simulations to predict settlement as realistically as possible require understanding and selecting the most appropriate model and type of calculation.