Beam Finite Element Research Articles

Stiffness-driven design and optimization of a 3D-printed composite prosthetic foot: A beam finite Element-Based framework

Composite foot prostheses are traditionally produced via lamination, a process that grants high structural efficiency. However, it is an expensive and time-consuming process. Production rate and customizability are thus limited. Additive manufacturing of composites can be a potential solution to these limitations. This work presents a tool to design and optimize Continuous Fiber-Reinforced Additively Manufactured (CFRAM) prosthetic feet using beam Finite Element (FE) modeling. This optimization tool was developed for weight minimization and obtaining a CFRAM prosthesis design matching up to three static stiffness parameters. The design variables were defined through parametrizing the geometry of the prosthesis designed and using the composite structure parameters. Thanks to the versatility of the tool, solutions to multiple optimization and design cases were used to assess different design concepts, such as the shape of the prosthesis (C-shape or J-shape). Also, the tool successfully duplicated the stiffness characteristics of an assumed laminated prosthesis. Finally, the sources of inaccuracy associated with the beam FE modeling approach were identified through a comparison with plane stress FE analysis.

Simplified homogenization technique for nonlinear finite element analysis of in-plane loaded masonry walls

The present investigation focuses on the nonlinear modelling of masonry walls under in-plane loading. To conduct this macro-scale study, a homogenization technique is applied to derive the equivalent secant moduli according to damage and friction sliding at the micro scale level for both bed mortar joint and brick material constituents. In the homogenization process the representative unit cell of masonry panel with a regular arrangement is first defined. Then a simplified kinematical model is proposed to describe the behaviour of the homogenized unit-cell under combined axial and shear stresses. This is based on the cohesive model for pure mode I and II and by allowing for the Coulomb's friction law for bed joint and the scalar damage model is adopted for the brick material. In the first stage, the proposed homogenization technique is verified for various unit cell constituents at micro-scale level. In the second step, this homogenization procedure was incorporated into proposed in-house finite elements software. To achieve this end, a new beam finite element is formulated in the context of the fibre higher order shear deformation theory HSDT. Using the proposed finite elements model, a numerical investigation is conducted to check the validity of the proposed model against the available experimental and numerical investigations. This allowed for the study of the effect of the applied compressive load on the lateral ultimate load.

A Hybrid Discrete-Finite Element method for continuous and discontinuous beam-like members including nonlinear geometric and material effects

This paper introduces a novel formulation, called Hybrid Discrete-Finite Element (HybriDFEM) method, for modelling one-directional continuous and discontinuous planar beam-like members, including nonlinear geometric and material effects. In this method, the structure is modelled as a series of distinct rigid blocks, connected to each other through contact pairs distributed along the interfaces. Each of those contact pairs are composed of two nonlinear multidirectional springs in series, which can represent either the deformation of the blocks themselves, or the deformation of their interface. Unlike the Applied Element Method, in which contact pairs are composed of one single spring, the current approach allows capturing phenomena such as sectional deformations or relative deformations between two blocks composed of different materials. This method shares similarities with the Discrete Element Methods in its ability to model contact interfaces between rigid or deformable units, but does not require a numerical time-domain integration scheme. More importantly, its formulation resembles that of the classical Finite Elements Method, allowing one to easily couple the latter with HybriDFEM. Following the presentation of its formulation, the method is benchmarked against analytical solutions selected from the literature, ranging from the linear-elastic response of a cantilever beam to the buckling and rocking response of continuous flexible columns, and rigid block stackings. One final example showcases the coupling of a HybriDFEM element with a linear beam finite element.

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

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

Static bending analysis of a transversely cracked strip tapered footing on a two-parameter soil using a new beam finite element

In this paper, a new beam Euler–Bernoulli finite element for the transverse static bending analysis of cracked slender strip tapered footings on an elastic two-parameter soil is presented. Standard Hermitian cubic interpolation functions are selected to derive the closed-form expressions of complete stiffness matrix and the load vector. The efficiency of the proposed finite element is verified on an example with several width tapering variations of a simple cracked footing with the results of governing differential equation. Another novelty of this study is improved bending moment functions with included discontinuity conditions at the crack location. These functions now accurately describe the bending moments in the vicinity of the crack of the finite element.

Nonlocal nonlinear higher-order finite element model for static bending of curved nanobeams including graphene platelets reinforcement

The aim of this work is concerned with the nonlocal nonlinear bending characteristics of non-classical isotropic and composite curved beams based on graphene platelets reinforcement, viz., nano size/micro beams. The size-dependant effect prominent in micro/nanobeams is incorporated in the formulation based on the nonlocal theory using size-dependent continuum approach. The proposed structural model includes both moderately large displacement and rotations, respectively. The system governing equations are established in terms of displacement functions using the principle of virtual work statements. A three-noded shear deformable curved beam finite element using a higher-order sinusoidal function based beam theory is employed; the solutions are obtained by adopting direct iterative procedure. The efficacy of the model is tested against the analytical studies available for the nano-size beams. A detailed analysis is made to highlight the influence of various design variables like thickness ratio, curvature of beam, nonlocal parameter, and the support conditions on the nonlinear bending behavior of curved nano/micro-size beams.

Enhanced beam and plate finite elements with shear stress continuity for compressible sandwich structures

This paper concerns and presents new improved beam and plate finite elements for analysing sandwich structures from the structural and modal points of view. In this study, the material behaviour is supposed to be linear elastic and orthotropic, but the method could be extended for nonlinear problems as well. The current models are able to treat the compressibility of the soft core materials, besides the interlaminar continuity conditions and the zero shear stresses on the shear-free surfaces are granted by the Lagrange multiplier method. In order to provide stress continuity along the element boundaries, the Hermite interpolation is employed for the elementary formulations that yields subparametric finite elements. On the contrary, the semi-analytical solutions of these enhanced beam and plate models are also discussed here for particular boundary conditions. The verification of the new finite elements is carried out by two case studies. The test examples are modelled and solved in commercial finite element software (ANSYS) with general shell and solid elements, too. The results derived from different models are subjected to a comprehensive comparison. Also, the structural and modal analyses of the test examples are presented during the case studies. The structural analysis of an overconstrained sandwich panel is also discussed to point out the significance of the proper shear stress distributions. Finally, the advantages and disadvantages of the newly developed elements and semi-analytical solutions are revealed in detail.

Nonlinear Modeling and Vibration Response Analysis of a Dual-Rotor System with an Inter-Shaft Graphite Seal

The inter-shaft graphite seal is a common structure in the dual-rotor system, and may generate nonlinear lateral excitation when there is large relative angular motion at the seal position. This paper represents the first attempt to study the nonlinear behaviors of a dual-rotor system with inter-shaft graphite seal excitations. First, an excitation model of the inter-shaft graphite seal is proposed by the analytical method. This model is then introduced into the beam finite element model of a dual rotor system, and the dynamic equations of the whole system are finally obtained. The vibration responses under the effect of the inter-shaft seal are clarified by analyzing 3D waterfall plots, rotor orbits, and time and frequency domain waveforms. The results show that the inter-shaft seal can lead to vibration coupling between HP and LP rotors. The axial spring stiffness and contact end face friction coefficient of the graphite seal have a significant effect on rotor vibration. When those two parameters are small, only coupling vibration phenomena can be observed, i.e., the rotation frequency of one rotor can be observed in another rotor vibration. With the increase in axial spring stiffness or contact end face friction coefficient, multiple modes of LP and HP rotors are excited, which dominates the vibration behaviors of the dual rotor system.

Efficiency of timber-concrete composite floors with discrete perfobond connections: A numerical study

To evaluate the behaviour of a single timber-concrete composite (TCC) T-beam, a simplified 2D finite element (FE) model in Abaqus is developed and validated using experimental tests and the Gamma method given in Annex B of EN 1995–1-1. The shear connection used in the beam consist of perfobond connectors, which are adhesively bonded to the timber beam. In the developed model, beam and shell finite elements have been used to simulate/reproduce the timber beam and the concrete slab, respectively. These have then been connected using connector elements which incorporate the mechanical behaviour of the tested shear connections, obtained in a previous research. After the successful validation of the FE model, this is used to further analyse different parameters such as: i) different number of connections (varying from 8 to 20), ii) different types of loading (point load, distributed load and line load), iii) different concrete slab widths and iv) connection models with elastic perfectly plastic behaviour applied to TCC T-beam and a 5 m by 5 m floor system. The results of the conducted study provide an in-depth understanding of the effect and impact of the investigated parameters which can support a future optimisation of the structural solution. Moreover, the results show that the use of a simplified 2D model can support designers to overcome the limitations of analytical approaches, such as the Gamma method, to analyse large spacing and to take benefit of bidirectional effects (load sharing) if analysed as a whole instead of a single T-beam.

Chatter Stability Prediction for Deep-Cavity Turning of a Bent-Blade Cutter.

The bent-blade cutter is widely used in machining typical deep-cavity parts such as turbine discs and disc shafts, but few scholars have studied the dynamics of the turning process. The existing mechanism of regenerative chatter in the metal-cutting process does not consider the influence of bending and torsional vibration, the change of tool profile and the complex machining geometry, so it cannot be directly used to reveal the underlying cause of the chatter phenomena in the deep inner cavity part turning process. This paper attempts to investigate the dynamic problem of the bent-blade cutter turning process. The dynamic model of a bent-blade cutter is proposed by considering the regenerative chatter effect. Based on the extended Timoshenko beam element (E-TBM) theory and finite element method (FEM), the coupling between the bending vibrations and the torsional vibrations, as well as the dynamic cutting forces, are modeled along the turning path. The vibration characteristics of the bending-torsion combination of cutter board and cutter bar, together with the dynamical governing equation, were analyzed theoretically. The chatter stability of a bent-blade cutter with a bending and torsion combination effect is predicted in the turning process. A series of turning experiments are carried out to verify the accuracy and efficiency of the presented model. Furthermore, the influence of cutting parameters on the cutting process is analyzed, and the results can be used to optimize the cutting parameters for suppressing machining vibration and improving machining process stability.

Fully Reconfigurable Photonic Filter for Flexible Payloads

Reconfigurable photonic filters represent cutting-edge technology that enhances the capabilities of space payloads. These advanced devices harness the unique properties of light to deliver superior performance in signal processing, filtering, and frequency selection. They offer broad filtering capabilities, allowing for the selection of specific frequency ranges while significantly reducing Size, Weight, and Power (SWaP). In scenarios where satellite communication channels are crowded with various signals sharing the same bandwidth, reconfigurable photonic filters enable efficient spectrum management and interference mitigation, ensuring reliable signal transmission. Furthermore, reconfigurable photonic filters demonstrate their ability to adapt to the dynamic space environment, withstanding extreme temperatures, radiation exposure, and mechanical stress while maintaining stable and reliable performance. Leveraging the inherent speed of light, these filters enable high-speed signal processing operations, paving the way to various space payload applications, such as agile frequency channelization. This capability allows for the simultaneous processing and analysis of different frequency bands. In this theoretical study, we introduce a fully reconfigurable filter comprising two decoupled ring resonators, each with the same radius. Each resonator can be independently thermally tuned to achieve reconfigurability in both central frequency and bandwidth. The precise reconfiguration of both central frequency and bandwidth is achieved by using the thermo-optic effect along the whole ring resonator path. A stopband rejection of 45 dB, with a reconfigurable bandwidth and central frequency of 20 MHz and 180 MHz, respectively, has been numerically achieved, with a maximum electrical power of 11.50 mW and a reconfiguration time of 9.20 µs, by using the scattering matrix approach, where the elements have been calculated through Finite Element Method-based and Beam Propagation Method-based simulations. This performance makes the proposed device suitable as key building block of RF optical filters, useful in the next-generation telecommunication payload domain.

Advanced Fiber Beam Finite Element Model for Neural Network Training in Vibration-Based Bridge Monitoring

Recent advancements in civil infrastructure monitoring have witnessed the increasingly high-performance sensor technologies and data-driven algorithms, opening up new possibilities for assessing structural conditions. In recent years, there has been a growing interest in leveraging the potential of Artificial Intelligence for civil infrastructure monitoring. One promising approach is the use of computational models to train and test data-driven algorithms aiming to tackle damage detection problems. To enhance the effectiveness of such procedures based on simulated data, this study proposes a high-performance beam finite element model for training a neural network model able to predict the dynamic response of the structure and for generating various damage scenarios. Compared to 2D and 3D finite element models, the advanced fiber beam model offers superior computational efficiency while accurately capturing the nonlinear behavior of structural elements. Specifically, a force-based beam finite element based on a damage-plasticity model is implemented to describe damage and degradation of materials in reinforced concrete girders. Through the simulation of the dynamic structural response under withe noise excitation, a neural network model representing the structure in the undamaged conditions is obtained. The prediction error of such network model is investigated as a suitable measure for the definition of a damage indicator able to detect the presence of damage (concrete cracks and reinforcement yielding). The integration of an advanced fiber beam model, accurate constitutive law and neural network models shows promising potential in the monitoring of existing bridges.

Оценка прочности каркаса кабины машиниста грузового локомотива при аварийных столкновениях

The article is based on an analysis of consequences after emergency collisions of freight locomotives at railway crossings. It assesses the strength of the driver’s cabin frame the design of which uses standard rolled and bent-welded profiles made of low-alloy steel. During the research calculations were performed using the finite element (FE) method in two software systems - foreign system ANSYS WORKBENCH 2023R1 and domestic system LIRA 10.12. Two FE models were developed using beam and shell finite elements which made it possible to evaluate the strength of the stress-strain state of the driver cabin frame. Based on the calculation results conclusions were drawn about the applicability of each of the models and possible directions for further research in the field of modeling emergency collisions of freight locomotives were proposed.

Finite Element Beam Propagation Method Based on Coordinate Transformation for Optimal Design of Optical Waveguide Devices

Finite Element Beam Propagation Method Based on Coordinate Transformation for Optimal Design of Optical Waveguide Devices

Vibration of solid and thin-walled slender structures made of soft materials by high-order beam finite elements

In this work, high-order beam (1D) finite element models for the modal analysis of structures made of compressible and nearly-incompressible hyperelastic soft materials are presented in the well-established framework of Carrera Unified Formulation (CUF). In this investigation, the modal behavior of soft structures subjected to progressively increasing loads can be correctly predicted by higher-order structural theories, and the influence of pre-stress conditions applied on the modal response of structures is investigated. The mathematical formulation of hyperelastic isotropic materials is presented in terms of invariants of the right Cauchy–Green strain tensor, obtaining the most general expression of the Piola–Kirchoff 2 stress tensor and tangent elasticity tensor, both independent of the model adopted for the material strain energy function. Governing equations in matrix forms for the static nonlinear analysis and subsequent vibration problem around non-trivial equilibrium states are derived through the Principle of Virtual Displacements (PVD) under a total Lagrangian formulation, defining the fundamental nuclei of stiffness matrices and internal and external forces vector, all independent of expansion theories and kinematic models adopted in the mathematical modeling of finite elements. Actual numerical results are obtained by an iterative Newton–Raphson linearized scheme coupled with line-search algorithms, and they are compared with results obtained by the commercial code ABAQUS. Our proposed models are tested with large strain problems involving hyperelastic slender and thin-walled structures, for which mode aberration such as crossing or bearing are observed.

Mould free laminated composites using eccentric fibre prestressing

Mould free fibre reinforced composites are an emerging manufacturing process that allows for complex shapes to be produced, independently from complex moulding. Previous examples demonstrated reconfiguration through thermal stresses induced by an asymmetrical stacking sequence within a laminate. However, asymmetry within the laminate can adversely influence the stiffness and geometric coupling which results in heavier structures. This paper presents eccentric prestressing as a novel method to produce more structurally efficient mould free laminated composites. Euler-Bernoulli beam theory and finite element methods were employed to predict the strain and deformation of laminated composites with selective fibre prestress. The internal and external strains were measured with chirped fibre bragg grating sensors, and surface mounted strain gauges respectively to validate the numerical and analytical predictions where a difference of 3.13% was reported. Finally, a comparative study was conducted to show the benefits of eccentric prestress over asymmetric 4D printed laminates.

DESIGN OF VISCO-ELASTIC SUPPORTS FOR TIMOSHENKO CANTILEVER BEAMS

The appropriate design of supports, upon which beams are usually placed as structural components in many engineering scenarios, has substantial significance in terms of both structural efficacy and cost factors. When beams experience various dynamic vibration effects, it is crucial to contemplate appropriate support systems that will effectively adapt to these vibrations. The present work investigates the most suitable support configuration for a cantilever beam, including viscoelastic supports across different vibration modes. Within this particular framework, a cantilever beam is simulated using beam finite elements. The beam is positioned on viscoelastic supports, which are represented by simple springs and damping elements. These supports are then included in the overall structural model. The equation of motion for the beam is first formulated in the temporal domain and then converted to the frequency domain via the use of the Fourier Transform. The basic equations used in the frequency domain are utilized to establish the dynamic characteristics of the beam by means of transfer functions. The determination of the ideal stiffness and damping coefficients of the viscoelastic components is achieved by minimizing the absolute acceleration at the free end of the beam. In order to minimize the objective function associated with acceleration, the nonlinear equations derived from Lagrange multipliers are solved using a gradient-based technique. The governing equations of the approach need partial derivatives with respect to design variables. Consequently, analytical derivative equations are formulated for both the stiffness and damping parameters. The present work introduces a concurrent optimization approach for both stiffness and damping. Passive constraints are established inside the optimization problem to impose restrictions on the lower and higher boundaries of the stiffness and damping coefficients. On the other hand, active constraints are used to ascertain the specific values of the overall stiffness and damping coefficients. The efficacy of the established approach in estimating the ideal spring and damping coefficients of viscoelastic supports and its ability to provide optimal support solutions for various vibration modes have been shown via comparative experiments with prior research.

Rigid body qualified curved beam approach for lateral torsional buckling of arches

The curved beam finite element approach based on the potential energy formulation is widely recognized as a versatile tool for lateral torsional buckling analysis of arches. However, there exist a variety of potentials, which were developed with distinct assumptions. The diversity of energy-based curved beam theories introduces confusions in practical applications. This paper aims to examine various potential energy formulations as to whether or not they obey the rigid body rule which is a prerequisite for valid second-order analysis. The induced moments at the ends of curved beam element that have been neglected from and/or the distributed moments that should be removed from available potentials are identified to help them become rigid body qualified. Based on the revised potential functional, a curved beam finite element formulation has been developed to effectively predict yet with less effort the out-of-plane critical load for circular and parabolic arches subject to various loading and constraint conditions. The results of numerical examples demonstrate that a potential energy formulation eligible for describing the out-of-plane behavior of curved beam is required to be rigid body qualified by fulfilling two aspects: (i) the neglected end moments that are imperative for satisfying the rigid body rule must be considered unless the virtual work done by them vanishes, and (ii) undesirable distributed moments that may be induced when undergoing the rigid body motion should be removed by considering all essential potential components.

The coupled band gap of the double beam with attached periodic spring-mass structure

This study presents a novel investigation into the phenomenon of coupled band gaps within double beam structures and achieves the construction of beam configurations featuring inherent coupled band gaps. Initially, the identification of coupled band gaps in double beam structures is discussed, and it is engineered within the low-frequency range by adjusting the thickness ratio of the two beams. Subsequently, double beam models are constructed using various methods. A comparative analysis between the Spectral Element Method and the Plane Wave Expand method validates the existence of coupled band gaps. Furthermore, through systematic exploration using the Plane Wave Expand method, we investigate the effect of different parameters on coupled band gaps. The attenuation properties within the identified coupled band gap are experimentally validated using double beam Finite Element models and a dedicated experiment for forced vibration testing. Consequently, controlled variations in thickness ratio confirm well-defined coupled band gaps exist in conventionally thick beam structures. Within this specific frequency range (254–279 Hz) for the double beam with thicknesses 0.01 m and 0.002 m, respectively, average attenuation rates of −3.79 dB and −11.16 dB are recorded correspondingly. It significantly contributes to applying theories on coupled band gaps to large-scale architectural frameworks.

GMNIA with beam elements and strain limits based fire design approach for steel beams and beam–columns

The use of advanced analysis techniques harnessing the capabilities of the currently available computational resources can lead to considerably more accurate fire design of steel structures relative to the currently adopted simple fire design methods in practice. In this paper, a structural steel fire design method by Geometrically and Materially Nonlinear Analysis with Imperfections (GMNIA) and using strain limits is put forward for the fire design of steel beams and beam–columns. In the proposed fire design method, the GMNIA of a steel member or structure is performed using computationally efficient beam finite elements and strain limits are adopted to account for the detrimental effects of local buckling on the ultimate capacities. To verify the accuracy of the proposed method, extensive numerical parametric studies are conducted through shell finite element modelling. The results indicate that the proposed approach provides accurate and safe ultimate resistance and limit temperature estimations for steel beams and beam–columns in fire, with a considerably higher level of accuracy and reliability relative to the provisions of the European structural steel fire design standard EN 1993-1-2.