Beam Finite Element Model Research Articles

Stability analysis of stiffness reduction models on rotary- and non-rotary straightened W-shapes

This paper presents a parametric study of stiffness reduction models on rotary- and non-rotary straightened hot-rolled steel W-shapes to examine if the models for non-rotary straightened sections are appropriate for stability analysis of rotary-straightened members. Four stiffness reduction models were investigated, which include (1) a conventional model adopted by AISC 360, which is known as the CRC model, (2) a model fitting the column strength curves provided in Eurocode 3, and models fitting cross-section distributed plasticity curves incorporating (3) the ECCS residual stress pattern and (4) a residual stress pattern of rotary-straightened sections. Beam finite element models were created and second-order inelastic analyses were conducted. A range of different cross-section geometries typically used for beam–columns was investigated, which includes various aspect ratios and flange-to-web area ratios. Columns and beam–columns were investigated with uniaxial bending about the major and minor axes with several axial utilization ratios. The effects of the stiffness reduction models on the stability limit state are discussed. The results of the parametric study are presented along with comparisons of the stiffness reduction values for hot-rolled steel members, which provide further understanding of the stiffness reduction model’s influence on the stability analysis of rotary straightened hot-rolled steel members.

Finite Element Modeling of RC Beams Repaired and Strengthened Using Jackets of Cementitious Materials and subjected to Elevated Temperatures

Finite Element Modeling of RC Beams Repaired and Strengthened Using Jackets of Cementitious Materials and subjected to Elevated Temperatures

Mechanism of interconnected synchronized switch damping for vibration control of blades

The Synchronized Switch Damping (SSD) is regarded as a promising alternative to mitigate the vibration of thin-walled structures in aero-engines, especially for blades or bladed disks. The common manner is to shunt the switch circuit independently to a single piezoelectric structure. This paper is aimed at exploring a novel way of using the SSD, i.e., the SSD is interconnected between two piezoelectric structures or substructures. The damping mechanism, performance, and effective range of the interconnected SSD are studied numerically and experimentally. First, based on a dual cantilever beam finite element model, the time domain and frequency domain modeling and solving methods of the interconnected SSD are deduced and validated. Then, the influence of the amplitude and phase relationship on the damping effect of the interconnected SSD is numerically studied and compared with the shunted SSD. A self-sensing SSD control board is developed, and experimental studies are carried out. The results show that the interconnected SSD establishes an additional energy channel between the corresponding piezoelectric structures. When the amplitudes of the two cantilever beams are different, the interconnected SSD balances the vibration level of each beam. When the amplitudes of the two cantilever beams are the same, if the appropriate interconnection manner is selected according to the phase, the resonance peak can be reduced by more than 30%. When the vibration is in-phase/out-of-phase, the damping generated by the interconnected SSD in a cross/parallel manner is even more significant than the shunted SSD. Furthermore, this novel connection scheme reduces the number of SSD circuits in half. Finally, for engineering applications, we implement the proposed damping technology to the finite element model of a typical dummy bladed disk. A piezoelectric damping ratio of 13.7% is achieved when the amount of piezo material is only 10% of blade mass. Compared with traditional friction dampers, the major advancements of the interconnected SSD are: (A) it can reduce the vibration level of blades without friction interface; (B) the space constraint is overcome, i.e., the vibration energy is not necessarily dissipated independently in one sector or through physically adjacent blades, and instead, the dissipation and transfer of vibrational energy can be realized between any blade pair. If a specific gating circuit is adopted to adjust the interconnection manner of the SSD, vibration mitigation under variable working conditions with different engine orders will be expected; (C) designers do not need to worry about the annoying nonlinearities related to working conditions anymore.

스톡브릿지 댐퍼를 포함한 송전선의 초기 처짐을 고려한 유한요소 보 모델 기반 동적 거동 해석

본 연구에서는 스톡브릿지 댐퍼를 포함하며 초기 변형을 가지는 송전선에 대한 동적 거동 해석에 관한 연구를 수행하였다. 송전선은 가늘고 긴 형상으로 인해서 케이블 요소로 모델링하는 것이 일반적이나, 송전선에 스톡브릿지 댐퍼를 부착할 경우 감쇠력이 집중하중으로 작용하기 때문에 굽힘 저항을 고려해야 한다. 또한, 송전선은 중력에 의한 초기 처짐과 이를 지탱하기 위한 초기 장력에 의해서 인장-처짐을 연계한 변형률 가정 및 초기 변위 조건 부과가 필수적이다. 본 연구에서는 초기 변형을 고려한 송전선의 보 유한요소 정식화를 새롭게 제시하였으며, 제안 모델을 이용하여 와류 흘림 하중을 받는 송전선과 스톡브릿지 댐퍼를 포함한 송전선의 동적 거동 해석을 수행하였다. 기존의 해석적 방법 및 상용소프트웨어를 이용한 동적해석 결과 비교를 통해서 제안 모델의 정확성을 검증하였다.

A Beam Finite Element Model Considering the Slip, Shear Lag, and Time-Dependent Effects of Steel–Concrete Composite Box Beams

A beam finite element model considering the slip, shear lag, and time-dependent effects of steel–concrete composite box beams have been proposed in this study. The element is employed to a one-dimensional analytical method that is solved involving an expression of spatial and time-dependent variables. A step-by-step method that does not involve storing the stress and strain histories, which is more accurate than the single-step algebraic method, is employed to solve the time variables. A recursive method was elaborated to determine spatial and time-dependent variables through the above method. The validity of the proposed method in instantaneous analysis is attested by the numerical data of the elaborate finite element model established in a commercial software, ANSYS, and that of the time-dependent analysis is verified by the existing test results on the long-term performance of composite beams. The proposed beam finite element model is applied to predict the time-related behavior of simply supported composite beams after validation. The results show that concrete shrinkage and creep significantly influence the structural responses of the composite box beams. From the initial load on the 28th day to that in the 3rd year, the vertical deflection at the cross-section of the mid-span increased by 47.01%. The interface slip at the end increased by −10.99%. The warping intensity function of the concrete slab and the steel beam at the end caused by shear lag increased by 111.64% and 7.01%, respectively. The maximum compressive stress on the concrete slab and the maximum tensile stress at the steel bottom flange increased by −6.75% and 4.56%, respectively.

РАБОТА СТАЛЬНЫХ ДВУТАВРОВЫХ БАЛОК С ТОНКОЙ НАКЛОННО-ГОФРИРОВАННОЙ СТЕНКОЙ

The efficiency of the use of cross-corrugated beams can be increased by tilting the corrugations on the supporting sections of their walls. The paper presents the results of a study of the stress-strain state of steel I-beams with a thin inclined-corrugated wall, depending on the angle of inclination of the generatrix of the corrugations to the plane of the cross-section of the beam. The finite element models of beams with different inclination angles of the generating corrugations (corrugation profile triangular continuous open) are presented, as well as the results and a brief analysis of numerical experiments carried out using the software package LIRA-SAPR. In the course of the experiment, for each model, the forms of wall buckling with safety factors, deformed schemes and distribution isofields of normal, tangential and principal stresses in beam elements were obtained. The presented results indicate an additional increase in the stability of the wall with downward corrugations, a change in the forces in the chords of the beams, and a slight increase in their deformability.

Nonlinear Finite Element Analysis of Corroded Reinforced Concrete Beams

Corrosion in reinforcing bars is a major cause of concern for sustainability of Reinforced Concrete (RC) structures exposed to extreme environmental conditions. Various RC structures, such as bridges and buildings are adversely affected due to the rebar corrosion, reducing its global load carrying capacity and ductility. In order to ensure an earthquake resistant design of any structure, the ductility of structural members is of chief concern. However, corrosion of reinforcing steel in RC members reduces its seismic performance. Thus, for safety and economic viability of any RC structure, an effective maintenance and repair work strategy is necessary. Based on the strong column - weak beam design concept of RC frames, the beams are the first structural members to absorb damage due to earthquake. Thus, to carry out maintenance and repair work, structural health assessment of RC beams considering the effect of reinforcement corrosion is of utmost importance. The present study aims at establishing a relation between the amount of corrosion induced and its effect on the ductility of an RC beam. A 3D Finite Element (FE) model of an RC beam including the effects of corrosion for nonlinear performance assessment has been modelled in ABAQUS. The FE model is validated with past experimental study including the effects of corrosion. Modelling of uniform corrosion in reinforcement bars involves defining the loss of bond between rebars and concrete, inducing spalling stresses on concrete and reduction in the cross-section area of the rebars. Bond-slip model between surface of concrete and reinforcement has been incorporated through cohesive surface. Spalling stress for uniform corrosion is applied in form of outward uniform pressure on the reinforcement and concrete interface. The cracking of cover concrete due to corrosion along with the flexural cracking in concrete due to incremental loading are implemented together in the present study. A comprehensive FE model is developed in order to obtain correct assessment of corroded beams. As observed from the FE model, the failure mechanism of the considered corroded RC beam is observed to be mostly shear failure as the corrosion level increases. Concrete crushing at the center of the RC beam is identified at the failure point of the beam due to corrosion induced damage. Evolution of displacement ductility index with respect to corrosion is determined for an RC beam based on the numerical study. It has been observed that the displacement ductility index of the beam is reduced significantly after considering a corrosion level of about 12%. Hence, the present study is an effort to establish a relation between structural performance of RC beams and level of reinforcement corrosion, which will be useful in proactive maintenance and repair work for corroded RC beams.

A wavelet-based dynamic mode decomposition for modeling mechanical systems from partial observations

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function but should generally approximate the input–output behavior of the underlying dynamics. A novel methodology for modeling those classes of dynamical systems is proposed in the present work, using wavelets in conjunction with the input–output dynamic mode decomposition (ioDMD). The wavelet-based dynamic mode decomposition (WDMD) builds on the ioDMD framework without the restrictive assumption of full state measurements. Our non-intrusive approach constructs numerical models directly from trajectories of the full model’s inputs and outputs, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model or observing the original dynamical systems’ response to inputs in an experimental framework. Hence, the present methodology is applicable for dynamical systems whose internal state vector measurements are not available. Instead, data from only a few output locations are only accessible, as often the case in practice. The present methodology’s applicability is explained by modeling the input–output response of an Euler–Bernoulli finite element beam model. The WDMD provides a linear state-space representation of the dynamical system using the response measurements and the corresponding input forcing functions. The developed state-space model can then be used to simulate the beam’s response towards different types of forcing functions. The method is further validated on a real (experimental) data set using modal analysis on a simple free–free beam, demonstrating the efficacy of the proposed methodology as an appropriate candidate for modeling practical dynamical systems despite having no access to internal state measurements and treating the full model as a black-box.

Finite Element Modelling of Corrosion-Damaged RC Beams Strengthened Using the UHPC Layers.

This paper describes a study on finite element modeling (FEM) carried out on the ABAQUS platform for the prediction of flexural strength of corrosion-damaged reinforced concrete (RC) beams strengthened using layers of ultra-high-performance concrete (UHPC). Considering different combinations of the degree of reinforcement corrosion and thickness and configuration of UHPC layers, a total of twenty-two corroded, un-strengthened, and strengthened RC beam specimens were tested to record their flexural behavior. Following the flexural testing, the FEM was carried out considering the degradation in the diameter and the yielding strength of the corroded reinforcing bars. The cohesive surface bonding approach was used to simulate the interfacial bond stress slip between the corroded bars and surrounding concrete. The results of the FEM were validated using the experimental test results of the respective beam specimens. The FEM results (including crack pattern, flexural strength, stiffness, and linear and nonlinear behavior of the strengthened RC beams) were found to be in close agreement with the corresponding experimental test results. This indicates that the proposed FEMs can capture the flexural behavior of the corroded RC beams strengthened using layers of UHPC with high accuracy. Furthermore, a parametric study was carried out using the validated FEMs to investigate the effects of varying the compressive strength and thickness of UHPC layers on the flexural strength of the corroded strengthened RC beams.

Time-domain Analytical Method for Aeroelastic Analysis of High Aspect Ratio Wing Using Unsteady Indicial Aerodynamics

This paper deals with the development of a novel time-domain analytical method to perform an aeroelastic stability analysis of a high aspect ratio wing. The aerodynamic model in this paper is built upon the frequency domain of Theodorsen aerodynamics. An inverse Fourier transform technique is applied to convert the Theodorsen frequency domain transfer function to the Wagner time-domain response function. Later, lift and moment expressions, containing aerodynamic lag states are obtained using the indicial function approach which performs the convolution of the unit step response Wagner lift function with arbitrary input and its time derivative using the principle of superposition. Additional equations containing the derivative of aerodynamic lag states are coupled with previously obtained lift and moment expressions to fully get the complete unsteady aerodynamic model in the time-domain. This time-domain unsteady aerodynamic model is then coupled with a combined bending torsion beam finite element model, using the state space approach. A complex eigenvalue analysis of this state space system is performed, using MATLAB, to determine both the static and dynamic aeroelastic stability boundary. Finally, in this paper, aeroelastic stability analysis of the high aspect ratio wing is performed using the current method and results are validated with MSC Nastran aeroelastic analysis and those available in the literature.

Nonlinear analysis of flexural performance of reactive powder concrete beams reinforced with hybrid GFRP and steel bars

In this paper, flexural performance of reactive powder concrete (RPC) beams reinforced with hybrid glass fiber reinforced polymer (GFRP) and steel bars was investigated by finite element (FE) analysis, and predicted formulae of flexural capacity was proposed. First, based on the corresponding tests, the FE models of reinforced RPC beams were built, and the applicability of FE method with RPC material was verified. After that, the FE models of RPC beams reinforced with hybrid GFRP and steel bars was designed, and the flexural performance of such beams was investigated. The influence of GFRP bar ratio, steel bar ratio, and resultant force of hybrid reinforcements on the vertical load – deflection curves were observed. Finally, the formulae of the flexural capacity of the normal section of RPC beams reinforced with hybrid GFRP and steel bars was derived. By comparing the results of proposed formulae and FE analysis, it was found that they were in good agreement. Therefore, the proposed formulae can be used to predict the flexural capacity of such RPC beams with hybrid reinforcements.

On the Modelling of “Fork” Supports Using geometrically Exact Thin‐walled Beam Finite Elements

AbstractThis paper discusses issues related to the modelling of so‐called “fork” supports using geometrically exact 3D thin‐walled beam finite elements whose rotations are parametrized using the rotation vector. This study is motivated by the fact that isolated members with “fork” supports are commonly employed in numerical and experimental studies, for the development of design rules for steel members. These supports are defined in the small displacement range, restraining the cross‐section in‐plane displacements and the torsional rotation of the beam (along the beam initial axis). This definition is usually extended to the large displacement case for beam finite element models, whereas in experimental tests and shell finite element models, a two‐axis gimbal‐type support is used instead. This paper thus aims at (i) showing how the two‐axis gimbal support may be modelled using beam elements which are based on a rotation vector parametrization of finite rotations and (ii) highlighting the differences between the two support types. Numerical examples are presented to illustrate the differences, which are quite significant for moderate‐to‐large displacements, but do not seem to affect the collapse load of standard steel members.

Refined Beam Theory for Geometrically Nonlinear Pre-Twisted Structures

This paper proposes a novel fully nonlinear refined beam element for pre-twisted structures undergoing large deformation and finite untwisting. The present model is constructed in the twisted basis to account for the effects of geometrical nonlinearity and initial twist. Cross-sectional deformation is allowed by introducing Lagrange polynomials in the framework of a Carrera unified formulation. The principle of virtual work is applied to obtain the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. In the nonlinear governing formulation, expressions are given for secant and tangent matrices with linear, nonlinear, and geometrically stiffening contributions. The developed beam model could detect the coupled axial, torsional, and flexure deformations, as well as the local deformations around the point of application of the force. The maximum difference between the present deformation results and those of shell/solid finite element simulations is 6%. Compared to traditional beam theories and finite element models, the proposed method significantly reduces the computational complexity and cost by implementing constant beam elements in the twisted basis.

Axial Compression and Buckling Analysis of Columnar Structures with Tetra-Anti-Chiral Configuration

Abstract The present work is focused on the investigation of tetra-anti-chiral structures by means of numerical and analytical methods. Specimens were evaluated under compressive load using analytical and numerical methods. The paper summarizes a theoretical solution for the estimate of Poisson’s ratio and the plateau force. The models can handle structures with various configurations, such as the radius of the connection node, lengths, and thickness of the ligaments. A section dedicated to the evaluation of the buckling load is included to extend the investigation of the behavior under compressive loads. The theoretical model is based on Euler’s formula, and a series of amendments are performed to adapt the formula to the analysis of chiral structures. Throughout the paper, theoretical results are compared with results from the simulations to validate the principles stated. Two sets of numerical models were developed: a fully 3D model using hexahedral finite elements and a 2.5D model using a beam finite element model. An overall comparison of results is presented, showing a good agreement between datasets. The present work might set the background for future activities, allowing for a selection of individual investigation methods.

Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part II: Bifurcation and quasi-periodic response

In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by periodic orbits of the full system was reduced to locating the solution branches of equilibria of the corresponding reduced-order model. Here, we use bifurcations of the equilibria of the reduced-order model to predict bifurcations of the periodic response of the full system. Specifically, we identify Hopf bifurcations of equilibria and limit cycles in reduced models on SSMs to predict the existence of two-dimensional and three-dimensional quasi-periodic attractors and repellers in periodically forced mechanical systems of arbitrary dimension. We illustrate the accuracy and efficiency of these computations on finite-element models of beams and plates.

The Uncertainty Propagation for Carbon Atomic Interactions in Graphene under Resonant Vibration Based on Stochastic Finite Element Model.

Graphene is one of the most promising two-dimensional nanomaterials with broad applications in many fields. However, the variations and fluctuations in the material and geometrical properties are challenging issues that require more concern. In order to quantify uncertainty and analyze the impacts of uncertainty, a stochastic finite element model (SFEM) is proposed to propagate uncertainty for carbon atomic interactions under resonant vibration. Compared with the conventional truss or beam finite element models, both carbon atoms and carbon covalent bonds are considered by introducing plane elements. In addition, the determined values of the material and geometrical parameters are expanded into the related interval ranges with uniform probability density distributions. Based on the SFEM, the uncertainty propagation is performed by the Monte Carlo stochastic sampling process, and the resonant frequencies of graphene are provided by finite element computation. Furthermore, the correlation coefficients of characteristic parameters are computed based on the database of SFEM. The vibration modes of graphene with the extreme geometrical values are also provided and analyzed. According to the computed results, the minimum and maximum values of the first resonant frequency are 0.2131 and 16.894 THz, respectively, and the variance is 2.5899 THz. The proposed SFEM is an effective method to propagate uncertainty and analyze the impacts of uncertainty in the carbon atomic interactions of graphene. The work in this paper provides an important supplement to the atomic interaction modeling in nanomaterials.

Coupled Actuator Line and Finite Element Analysis Tool

Fluid-dynamic loading of many solid bodies can be simulated using geometry resolving computational fluid dynamics methods, where the body's shape is resolved in the mesh. In some cases though slender bodies, like ropes or cables, spars, turbine blades, foils and lattice structures would require prohibitively high cell counts, since the geometrical features to be resolve are much smaller than the overall domain. Such bodies are usually made up of generic cross sections like round, square or standardised technical profiles like the famous NACA digit series for which good parametrisations of reaction forces to incoming flow exist. Actuator line methods apply inflow dependent reaction forces to the fluid domain, thus allowing the computationally efficient simulation of slender bodies and have been used extensively, for example in wind and tidal turbine simulations. Beam elements representing slender bodies are standard building blocks in structural finite element models. Combining actuator line theory with a finite element beam model allows the efficient simulation of flexible structures under fluid loads, like turbine blades or nettings used in fish farms. This paper presents an implementation of such a coupled model in OpenFOAM based on the existing turbineFoam actuator line model. The underlying numerical method is detailed and first test cases are provided.

Elastic compressive buckling resistance for back-to-back double angle assemblies

The present study investigates the elastic buckling resistance of compression members consisting of non-slender hot-rolled double angles connected back-to-back with discrete interconnectors. Towards this goal, the study (a) formulates a thin-walled beam finite element buckling solution that treats both angles as independent members away from the intermediate connector locations while constraining the displacements for both angles at interconnector locations, and (b) develops an extension of the Vlasov thin-walled beam theory, originally intended for monolithic members, to determine the effective torsional/warping sectional properties for back-to-back double angle members. The validity of the thin-walled beam finite element model is then verified against experimental results and shell finite element models and its predictions are shown to asymptotically converge to the Vlasov theory extension developed in the present study as the number of interconnectors is increased. A systematic parametric study consisting of 1250 finite element runs is then conducted and the database of results generated is used to propose a simple equation to predict the elastic compressive buckling resistance of double angle compression members.

Topological homogenization of metamaterial variability

With the proliferation of additive manufacturing and 3D printing technologies, a broader palette of material properties can be elicited from cellular solids, also known as metamaterials, architected foams, programmable materials, or lattice structures. Metamaterials are designed and optimized under the assumption of perfect geometry and a homogeneous underlying base material. Yet in practice real lattices contain thousands or even millions of complex features, each with imperfections in shape and material constituency. While the role of these defects on the mean properties of metamaterials has been well studied, little attention has been paid to the stochastic properties of metamaterials, a crucial next step for high reliability aerospace or biomedical applications. In this work we show that it is precisely the large quantity of features that serves to homogenize the heterogeneities of the individual features, thereby reducing the variability of the collective structure and achieving effective properties that can be even more consistent than the monolithic base material. In this first statistical study of additive lattice variability, a total of 239 strut-based lattices were mechanically tested for two pedagogical lattice topologies (body centered cubic and face centered cubic) at three different relative densities. The variability in yield strength and modulus was observed to exponentially decrease with feature count (to the power −0.5), a scaling trend that we show can be predicted using an analytic model or a finite element beam model. The latter provides an efficient pathway to extend the current concepts to arbitrary/complex geometries and loading scenarios. These results not only illustrate the homogenizing benefit of lattices, but also provide governing design principles that can be used to mitigate manufacturing inconsistencies via topological design.

Parametric study on internal resonances for a simplified nonlinear blade model

This article proposes to determine and identify the physical contributions that drive the internal resonance between the bending and torsion modes of a blade. The blade is modeled as a nonlinear beam including warping, twist and pre-bending, and a discretization scheme based on a Rayleigh–Ritz approximation is performed. The modal properties of the model are compared and validated using beam theory and finite element modeling. Several configurations of the model allowing the occurrence of an internal resonance between the first torsional and the second bending modes are considered. The frequency responses near the second bending mode are obtained through the Harmonic Balance Method coupled with a branch switching algorithm to locate and track bifurcated branches related to internal resonances. Attention is paid to the identification of the geometrical nonlinear terms that enable the appearance of an internal resonance. With the help of a multiple scale analysis, it is shown that it is essentially driven by a small set of coupling parameters involving bending and torsion displacements of the commensurate modes. It is also observed in a rotating situation thanks to the hardening of the bending mode.