Beam Finite Element Research Articles

Global Sensitivity Analysis and Surrogate Models for Evaluation of Limit States in Steel Truss Structures

This article presents the global sensitivity analysis of the serviceability limit state of a steel truss using Monte Carlo simulations. The focus is on the probabilistic assessment of deflection, with failure probability defined as the likelihood of exceeding the deflection limit. Deflection is computed using the beam finite element method. A surrogate model is introduced to reduce computational costs. By integrating the surrogate and original models, significant CPU cost reductions are achieved. Furthermore, classical Sobol sensitivity analysis is used to examine the model outputs and analyze the significance of member loading and stiffness on the deflection. This study advances the use of surrogate models in global sensitivity analysis, enhancing computational efficiency and the understanding of interactions between input variables in the reliability assessment of steel truss structures.

A generalized Timoshenko beam with embedded rotation discontinuity coupled with a 3D macroelement to assess the vulnerability of reinforced concrete frame structures

A generalized finite element beam with an embedded rotation discontinuity coupled with a 3D macroelement is proposed to assess, till complete failure (no stress transfer), the vulnerability of symmetrically reinforced concrete frame structures subjected to static (monotonic, cyclic) or dynamic loading. The beam follows the Timoshenko beam theory and its sectional behavior is described in terms of generalized forces and generalized strains. The beam response up to the peak is described by a macroelement, based on plasticity theory, that adopts a 3D failure criterion expressed in terms of axial force, shear force and bending moment. The Embedded Finite Element Method is then adopted to reproduce bending dominated failure, with a global cohesive model that links the cohesive moment to a rotational jump. The formulation allows for remedy of localization phenomena and significant reduction of the necessary computational time. The performance of the proposed simplified strategy is illustrated by comparison with experimental results.

A modified quasi-3D theory and mixed beam element method for static behaviour analysis of functionally graded beams

This paper develops a modified quasi-3D theory and the mixed beam element model for static analysis of functionally graded beams. The modified quasi-3D theory encompasses two innovations. Firstly, the accurate distribution of transverse shear stress is derived from the differential equilibrium equation that describes the relationship between stresses, rather than the traditional one derived from geometric relations and constitutive equations. Secondly, the effect of distributed loads associated with transverse stretching deformation, a factor typically overlooked in the existing quasi-3D theory-based beam models, is involved. In the development of beam finite element model, the mixed variational principle is firstly utilized to formulate the model of a quasi-3D theory-based beam element, where generalized displacements and internal forces are treated as two types of independent field quantities. Two numerical examples are conducted to investigate the validity and accuracy of the proposed theory and beam element. Numerical results indicate that the proposed mixed beam element can accurately predict the stress distributions over the cross-section and produce accurate displacement solutions. Meanwhile, it is noted that the effect of distributed loads related to the transverse stretching deformation should be correctly considered in the analysis of functionally graded beams based on quasi-3D theory.

Few-mode optical fiber-based flexible pressure feedback tentacle doped with fluorescence temperature pointer

Abstract In this paper, a flexible fiber pressure feedback whisker is proposed, which consists of a water droplet shaped polydimethylsiloxane (PDMS) elastomer with an embedded balloon shaped few mode fiber. The mechanical sensing performance of the device was analyzed and optimized using a combination of finite element method and beam propagation method (BPM). The built-in cladding corroded few-mode fiber increases pressure sensitivity by more than four times. The collection efficiency of fluorescence signal is improved by cladding corrosion. The PDMS elastomer was doped with upconversion nanoparticles NaYF4:Yb, Er@NaYF4 in order to achieve temperature measurement by fluorescence intensity ratio technology. The combination of fluorescence signal and interference spectrum can not only achieve real-time and accurate pressure detection at different temperatures, but also incorporate fluorescent materials into flexible bionic skin for temperature self-compensation, which has potential application value for the development of bionic fiber micro-nano sensing and control devices.

Free Vibration Analysis of Curvilinearly Tapered Axially Functionally Graded Material Beams

The study focuses on the free vibration analysis of beams made of axially functionally graded materials (AFGM) with curvilinear variable cross-sections along their length. The beams encompass various shapes, including concave and convex conic sections, with axial material properties varying according to polynomial and exponential laws. The equations of motion are derived using Hamilton’s principle within the framework of Timoshenko beam theory. These governing equations, subjected to various boundary conditions, are solved using the differential transform method (DTM). The proposed solution technique is validated by comparing computed natural frequencies with the existing literature and results obtained using three-dimensional finite element analysis in ABAQUS. The incorporation of material gradients into the beam finite element models was achieved using the user-defined material subroutine (UMAT). Additionally, a comprehensive study is conducted to examine the influence of various factors on the natural frequencies of functionally graded beams. These factors include parameters of material laws, types of variable beam shapes, slenderness ratio, and specific boundary conditions. This study provides a thorough understanding of the modal dynamics of the considered beams, offering valuable insights into the behavior of FGM structures.

Mesh objective characteristic element length for higher-order finite beam elements

The use of fracture energy regularization techniques can effectively mitigate the mesh dependency of numerical solutions caused by the strain softening behavior of quasi-brittle materials. However, the successful regularization depends on the correct estimation of the crack bandwidth in Finite Element solutions. This paper aims to present an enhanced crack band formulation to overcome the strain localization instability especially for the higher-order elements developed in the framework of Carrera Unified Formulation (CUF). Besides, a modified Mazars damage method incorporating fracture energy regularization is employed to describe the nonlinear damage behavior of the concrete. To evaluate the efficiency of the proposed crack band formulation, three experimental concrete benchmarks are selected for the numerical damage analysis. By comparing numerical and experimental results, the proposed method can guarantee mesh objectivity despite varying finite element numbers and orders, indicating perseved fracture energy consumption within proposed higher-order beam models.

Active vibration control of a large space telescope based on H∞ control with unilateral and constrained input

The development of the telescope with large aperture is driven by the increasing demand for higher imaging resolution and imaging area. The large membrane diffraction space telescope is particularly attractive due to their lightweight nature, ease of folding and unfolding, and high precision imaging capabilities. However, the flexible and large structure of these telescope makes them prone to long-time, low-frequency vibrations in space. These vibrations can degrade the imaging quality and potentially cause damage to the instrument in the space telescope. Therefore, it is crucial to develop effective active vibration control methods to suppress these structural vibrations. This paper proposes a control method that utilizes cables as actuators. Since cables can only withstand tension and have limited output tension, this constraint is taken into account during the control design process. Firstly, a dynamics model of the membrane diffraction space telescope with hinge flexibility is developed by the beam theory and finite element method. Next, an active controller is designed by combining H∞ control theory and Linear Matrix Inequalities (LMI). Additionally, the optimal positions of cable actuators are determined using the Gram controllability criterion and a particle swarm algorithm. Finally, the effectiveness of the control method is verified through numerical simulations. The simulation results demonstrate that the hinge flexibility significantly influences the structural vibration behavior of the telescope. Furthermore, the proposed control method demonstrates the ability to effectively suppress the vibrations of the telescope while also exhibiting robustness to changes in natural frequencies of the structure.

Optimizing Coupled Fluid-Structure Simulations for Nuclear-Relevant Geometries

Abstract The numerical simulation of fluid-structure interactions (FSI) has gained interest to study flow-induced vibrations. Nevertheless, the high computational resources required by such simulations can represent a significant limitation for their application to industrial configurations. Therefore, simplified modeling approaches, when physically applicable, can represent an interesting compromise. This can be the case of slender structures (tubes, rods) often encountered in nuclear power plants. In this paper, an Euler–Bernoulli beam finite element model is implemented inside the computational fluid dynamics (CFD) code code_Saturne. With the goal of finding CFD methods less expensive than large eddy simulations (LES), unsteady Reynolds Navier–Stokes (URANS) and hybrid URANS/LES approaches are considered. The resulting fluid-structure model is able to calculate the vibration response of cantilever beams under a fluid flow, avoiding the necessity of CFD-finite element method (FEM) code coupling. The first part of the paper describes the model and its implementation: it allows to perform 2-way explicit fluid-structure coupling, using the Arbitrary Lagrangian-Eulerian approach to account for the structure deformations. Validation test cases are presented in the second part: first, the model is validated in terms of frequency, added mass, and damping for a cylinder vibrating in static air and water; then, the model is validated toward the vortex-induced resonance and lock-in mechanisms for a cylinder subjected to water cross-flow. The model is then applied to a real experimental configuration of two in-line cylinders in water cross-flow: the calculated vibrations are found to be in good agreement with the experimental measurements.

On the Shear Force Redistribution in Composite Steel and Concrete Beams with Web Openings

As far as research into the field of composite steel and concrete beams with web openings has shown, the initiation of a complex stress state due to the introduction of web openings is, unfortunately, inevitable. As a logical consequence, estimation of the resistance becomes complex as well. Aiming to provide a more convenient approach, especially for evaluation of the bending resistance to the Vierendeel effect with the presence of high shear forces, a marked simplification with respect to quantification of the shear force redistribution between T-sections is presented. This novel approach stands on strong fundamentals of experimental evidence and parametric finite element (FE) investigation. Concretely, within the experimental part of this investigation, the load response of four composite beam samples was recorded and profoundly analyzed. Subsequently, a detailed FE analysis in the software ANSYS 2024 R1 (ANSYS Inc., Canonsburg, PA, USA), exploiting its parametric design language (APDL), was conducted. Finally, concise data compilation and their comprehensible interpretation were enabled by employing the software MATLAB 2024a (The MathWorks, Inc., Natick, MA, USA). In view of this treatment, a cornerstone for successive assessment of the obtained data was laid. Attempting to identify the key factors influencing the shear force proportion between the tees, integration of the shear stresses along the vertical sections with regular spacing along the FE beam models was conducted. By virtue of this concept, not only the magnitudes of the shear forces for the tees were obtained but also the leading importance of the opening depth was demonstrated. Furthermore, a complete picture of the shear force behavior along the composite perforated beams was derived. On this basis, a novel method representing a simpler and more accurate form of estimation of the shear force proportion for T-sections was proposed.

Reduced-order modelling of floating offshore wind turbine: Aero-hydro-elastic stability analysis

A reduced-order aero-hydro-elastic analysis tool for performing the stability analysis on floating offshore wind turbines is presented. In this work, a high-order non-linear aero-elastic model initially developed for onshore wind turbines is extended by utilizing a super-element body, which models the floating platform, the mooring system and the hydrodynamic contributions. The turbine structure is modelled by a Finite beam Element Method, and the aerodynamic loads are modelled by the Blade Element Momentum method coupled with a Beddoes-Leishman type dynamic stall model in a state-space formulation. The linearization is performed around steady state equilibrium at any given mean wind speeds, rotor speeds and collective blade pitch angles utilizing Coleman transformation to remove the periodic terms. The order reduction is based on two projections to reduce the number of structural states and aerodynamic states separately using the structural modal project matrix and the aerodynamic shape functions. Concurrently, we investigate the effect of unsteady aerodynamic states on the stability analysis of a floating wind turbine. The results show the low-order aero-hydro-elastic model expands the scope of numerical tools available for conducting structural modal analysis and aero-hydro-elastic stability analysis on floating wind turbines.

High-performance beam finite element for predictive response in monitoring existing bridges

High-performance beam finite element for predictive response in monitoring existing bridges

Contact formulations for analysis of micropolar media with finite continuum beam elements

Microscale beam-like structures are standard components of micromechanical systems in many devices. However, the small dimensionality affects their deformation characteristics and leads to misinterpretations of the results. Presenting such size dependency is possible with advanced continuum descriptions via introducing additional variables compared to the classical one. Hence, the problems where contact occurs require the readjustment of boundary conditions considering these extra parameters. That burdens the already challenging task of contact problem calculations and restricts most demonstration examples to two-dimensional problems and geometrical linearity. The resolution of the imposed restrictions within finite element modeling further emphasizes the usage of advanced media in design and facilitates its application to various problems, which is the aim of this paper. The delivery of that task is as follows. Firstly, we present the kinematics and material descriptions for the micropolar media. The authors propose to use a newly developed continuum-based micropolar beam formulation to avoid an overwhelming computational burden and, at the same time, deal with nonlinear stress–strain relations. Secondly, the work develops a contact approach within the micropolar theory from two-dimensional to three-dimensional elasticity, although the contact is considered frictionless. Finally, it compares two existing contact formulations, including the developed one, for the contact beam problems, using the examples of two collinear sliding beams’ bending.

Large displacement model for the nonlinear behaviour of the face plate component

This paper deals with the face plate component in steel joints and addresses the full characterization of the nonlinear behaviour of the face plate component. An equivalent beam strip model is proposed that tackles the connection of a beam to the column web of open I-sections in a minor axis joint or the face of tubular columns, covering endplate or fin plate joint typologies. Closed-form analytical solutions are obtained for the elastic large displacement and the elastic-plastic large displacement behaviour of the equivalent beam strip. Criteria for the establishment of the design resistance using the continuous strength method are also proposed. It was concluded that the model is easy to apply, was validated against a large parametric study using finite element beam models, leads to accurate solutions and demonstrates the need to consider membrane effects in design.

Stochastic robustness analysis of wing-aileron flutter suppression systems

In this work a stochastic robustness analysis approach is used to compare the performances of two non-linear flutter suppression systems designed for stabilization of a wing-aileron lifting structure. A reduced order modelling approach based on an alternative aeroelastic beam finite element is presented and used for the flutter suppression systems design, which are driven by a simple adaptive controller and a sliding mode controller, respectively. A heuristic algorithm is used to determine the simple adaptive controller invariant parameters at the design point while a simple parametric study is performed to tune the sliding mode controller. The performances of each closed loop system are evaluated taking into account mass, stiffnesses, and aerodynamics uncertainties of the aeroelastic plant also considering the presence of discrete gust disturbances.

Correction: Comparison of classical beam theory and finite element modelling of timber from fibre orientation data according to knot position and loading type

Correction: Comparison of classical beam theory and finite element modelling of timber from fibre orientation data according to knot position and loading type

Fluid-Structure Interactions Response of a Composite Hydrofoil Modelled With 1D Beam Finite Elements

_ In this paper, the hydroelastic response of a NACA0015 composite hydrofoil is studied experimentally and numerically. The foil is made of composite materials with fibers not aligned with the span of the foil, which results in the occurence of a bend-twist coupling in the material. Computations are performed using a partitioned approach. The flow problem is solved using a boundary element method. The structural response of the foil is modelled with two different finite element models. In the first one, the foil is modelled with 2D shell and 3D solid finite elements and in the second model, the foil is modelled with 1D beam finite elements. The experiments are conducted in an open circulation water channel. Hydrodynamic forces and structural displacements are measured for several angles of attack, free stream velocities and submergence depth. This paper shows that the mechanical behaviour of a composite hydrofoil submitted to hydrodynamic loads can be modelled with 1D beam finite elements. This model gives results very similar to a finite element analysis realized with 2D shell and 3D solid finite elements, which are commonly used to model composite structures. The present work also shows that the experimental results can be well predicted by numerical simulations, but it requires a precise modeling of the bend-twist coupling in the materials constituting the foil. Keywords Hydrofoil; Equivalent Beam; Fluid-Structure Interactions; Composite; Bend-Twist Coupling

Experimental and Numerical Analyses of Timber–Steel Footbridges

In addition to traditional building materials, such as steel and concrete, wood has been gaining increasing prominence in recent years. In the past, the use of wood was limited due to its susceptibility to damage by fungi, insects, and temperature. These shortcomings were gradually eliminated as the quality of wood processing increased and thanks to modern high-quality insulating and protective materials. The return to the utilisation of this natural building material was also supported by the development of new wood-based materials, such as glued laminated wood, and new types of mechanical fasteners, as well as by the introduction of new design methods provided in the Eurocodes. Within this context, this paper focuses on using wood in transport infrastructure, especially as the basic material for footbridges and small road bridges. Combined timber–steel bridges emerge as a very effective type of superstructure in contemporary road bridges and footbridges, especially in areas with natural exposure. Usually, wood is used for the main bridge girders, while steel is preferred for bridge deck elements—stringers and cross-girders. The results of this parametric study offer optimal structural solutions for footbridges with spans of 12.0–24.0 m, reflecting satisfactory static and dynamic footbridge behaviour. Particular attention is paid to a problematic structural detail—the connection between the steel cross-girder and the timber main girder. Firstly, this connection’s characteristics were measured experimentally using nine laboratory samples made of two glued laminated timber blocks, simulating main girders connected with a hot-rolled steel cross-girder. The connection was prepared in three variants, with different heights of the end plates and different numbers of bolts. Subsequently, these characteristics were computed using two numerical FEM models. The first model was created using SCIA Engineer software with a combination of shell and beam finite elements. The second, more sophisticated model was created in the ANSYS software environment using 3D finite elements, allowing us to better take into account the plasticity and orthotropic properties of wood and the points of contact between the individual members. Finally, the experimental results produced by sample testing in the laboratory were compared to the outputs of FEM numerical studies.

Digital Twin Implementation for Three-Dimensional Rotordynamic Response via Physics-Informed LSTM Neural Networks

Abstract The rotating assemblies of critical machinery are complex dynamical systems and rotordynamic model response prediction inaccuracy risks machinery failure leading to high production losses. Jeffcott, Euler beam, and high-fidelity 3D solid finite element models are frequently utilized for rotordynamic analyses. Even though the 3D rotor has the higher accuracy, beam models are still widely used in industrial applications. To improve prediction accuracy of the lower-fidelity Jeffcott and beam models, a rotordynamics physics-informed neural network (R-PINN) is proposed. This models physics-informed long short-term memory (LSTM) neural networks that utilize partial or limited measured data, by incorporating physical laws. This approach enables the creation of a Digital Twin, which can produce additional data and help remove noise and outliers. In the current study, two R-PINNs are introduced to validate the superior capability of the model for both low- and high-fidelity physics. Random noise of 10% is introduced into the measured data produced by the Digital Twin to replicate real-world noisy measurements. The result shows that both low- and high-fidelity physics R-PINNs can achieve high accuracy even with high noise data, thereby increasing the robustness of the model. The results clearly demonstrate the ability of the proposed R-PINN algorithm to enhance an Euler beam model's predicted response to the level of accuracy of a 3D solid element model's predicted response, the latter acting as a surrogate for test measurements in an actual application.

Accurate free and forced vibration behavior prediction of functionally graded sandwich beams with variable cross-section: A finite element assessment

The current investigation proposes an enhanced finite element beam model to assess the dynamic behavior of functionally graded sandwich beams with variable cross-sections. By integrating the shear effect, this beam model integrates both C0 and C1 continuities to generate elementary matrices using an efficient three-unknown shear deformation beam theory. The model focuses on advanced sandwich beams with functionally graded material face-sheets and metallic cores, exploring various geometric arrangements. The originality of this study addresses variable cross-sections in sandwich beams, evaluating the influence of material composition and geometric configurations on free and forced vibration responses, including different boundary conditions. The methodology uses the eigenvalue method for examining free vibration and applies Newmark’s algorithm for solving forced vibration problems. The current model expands the scope of analysis compared to previous models that primarily focus on uniform cross-sections and conventional material distributions. The developed model incorporates non-uniform geometrics, material gradient parameters, and advanced finite element analysis to enhance precision and efficacy through detailed parametric investigations and comparisons with existing literature. This contribution significantly improves the mechanical modeling of composite sandwich structures, particularly those incorporating functionally graded materials and complex geometrical aspects.

A Nonlinear Beam Finite Element with Bending–Torsion Coupling Formulation for Dynamic Analysis with Geometric Nonlinearities

Vibration analysis of wing-box structures is a crucial aspect of the aeronautic design to avoid aeroelastic effects during normal flight operations. The deformation of a wing structure can induce nonlinear couplings, causing a different dynamic behavior from the linear counterpart, and nonlinear effects should be considered for more realistic simulations. Moreover, composite materials and aeroelastic tailoring require new simulation tools to include bending–torsion coupling effects. In this research, a beam finite element with bending–torsion coupling formulation is used to investigate the effects of the deflection of beam structures with different aspect ratios. The nonlinear effects are included in the finite element formulation. The geometrical effect is considered, applying a deformation dependent transformation matrix. Stiffness effects are introduced in the stiffness matrix with Hamilton’s Principle and a perturbation approach. The results obtained with the beam finite element model are compared with numerical and experimental evidence.