Beam Finite Element Model Research Articles

Efficient coupled polynomial interpolation scheme for out-of-plane free vibration analysis of curved beams

The performance of two curved beam finite element models based on coupled polynomial displacement fields is investigated for out-of-plane vibration of arches. These two-noded beam models employ curvilinear strain definitions and have three degrees of freedom per node namely, out-of-plane translation (v), out-of-plane bending rotation (θz) and torsion rotation (θs). The coupled polynomial interpolation fields are derived independently for Timoshenko and Euler–Bernoulli beam elements using the force-moment equilibrium equations. Numerical performance of these elements for constrained and unconstrained arches is compared with the conventional curved beam models which are based on independent polynomial fields. The formulation is shown to be free from any spurious constraints in the limit of ‘flexureless torsion’ and ‘torsionless flexure’ and hence devoid of flexure and torsion locking. The resulting stiffness and consistent mass matrices generated from the coupled displacement models show excellent convergence of natural frequencies in locking regimes. The accuracy of the shear flexibility added to the elements is also demonstrated. The coupled polynomial models are shown to perform consistently over a wide range of flexure-to-shear (EI/GA) and flexure-to-torsion (EI/GJ) stiffness ratios and are inherently devoid of flexure, torsion and shear locking phenomena.

Structural modeling and validation of an active twist model rotor blade

DLR has been researching on active twist rotor blade control for at least 15 years now. This research work included the design and manufacturing of model rotor blades within the blade skin integrated actuators. As a main subject, numerical benefit studies with respect to rotor noise, vibration, and performance were carried out with DLR’s rotor simulation code S4. Since this simulation code is based on a modal synthesis, it uses the natural blade frequencies and mode shapes to model the blade dynamics. Both, natural blade frequencies and mode shapes, are computed in advance employing a finite element beam model of the blade. Each beam element possesses certain structural properties that are derived from an ANSYS model for certain cross sections of the blade. Since model rotor blades are built for wind tunnel testing, they are highly instrumented with sensors and therefore vary in their structural properties along span. Modifications in the structural properties due to the instrumentation are not included in the ANSYS model. However, to account for these variations, two experimental methods have been developed. They allow the determination of the real values for the most important structural blade properties such that the structural blade model is improved. The paper describes the experimental methods, as well as the development of an advanced structural blade model for rotor simulation purposes. It shows a validation of the structural blade model based on the measured non-rotating and rotating frequencies.

Structural modeling of cold-formed steel portal frames

The paper describes the modeling of pitched roof cold-formed steel portal frames with slender cross-sections. Two types of finite element models are introduced: a shell finite element model and a modified beam finite element model. The shell element model involves explicit modeling of each structural member and accounts for the semi-rigid behavior of apex and eave joints by incorporating spring-like elements. The beam element model utilizes a reduced tangent rigidity method to account for cross-sectional instability. Both models are compared with results of experimentally tested portal frames, and good agreement is demonstrated.

Accuracy of an efficient framework for structural analysis of wind turbine blades

AbstractThis paper presents a novel framework for the structural design and analysis of wind turbine blades and establishes its accuracy. The framework is based on a beam model composed of two parts—a 2D finite element‐based cross‐section analysis tool and a 3D beam finite element model. The cross‐section analysis tool is able to capture the effects stemming from material anisotropy and inhomogeneity for sections of arbitrary geometry. The proposed framework is very efficient and therefore ideally suited for integration within wind turbine aeroelastic design and analysis tools. A number of benchmark examples are presented comparing the results from the proposed beam model to 3D shell and solid finite element models. The examples considered include a square prismatic beam, an entire wind turbine rotor blade and a detailed wind turbine blade cross section. Phenomena at both the blade length scale—deformation and eigenfrequencies—and cross section scale—3D material strain and stress fields—are analyzed. Furthermore, the effect of the different assumptions regarding the boundary conditions is discussed in detail. The benchmark examples show excellent agreement suggesting that the proposed framework is a highly efficient alternative to 3D finite element models for structural analysis of wind turbine blades. Copyright © 2015 John Wiley & Sons, Ltd.

Evaluation of the accuracy of classical beam FE models via locking-free hierarchically refined elements

It is well known that the classical 6-DOF (Degrees of Freedom) beam theories that are incorporated in commercial finite element (FE) tools are not able to foresee higher-order phenomena, such as elastic bending/shear coupling, restrained torsional warping and three-dimensional strain effects. In this work, the accuracy of one-dimensional (1D) finite elements based on the classical theories (Euler–Bernoulli and Timoshenko theories as well as a 6-DOF model including torsion) is evaluated for a number of problems of practical interest and modelling guidelines are given. The investigation is carried out by exploiting a novel hierarchical, locking-free, finite beam element based on the well-known Carrera Unified Formulation (CUF). Thanks to CUF, the FE arrays of the novel beam element are written in terms of fundamental nuclei, which are invariant with respect to the theory approximation order. Thus, results from classical as well as arbitrarily refined beam models can be formally obtained by the same CUF beam element. Linear Lagrange shape functions are used in this paper to interpolate the generalized unknowns and shear locking phenomena are avoided by adopting a MITC (Mixed Interpolation of Tensorial Components) scheme. Different sample problems are addressed, including rectangular and warping-free circular cross-sections as well as thin-walled beams. The results from classical theories and the 6-DOF model are compared to those from higher-order refined beam models, both in terms of displacement and stress fields for various loading conditions. The discussion focuses on the limitations of the commonly used 1D FEs and the need for refined kinematics beams for most of the problems of common interest. The research clearly depicts CUF as a valuable framework to assess FE formulations such as the 6-DOF model herein considered, which is one of the most known and used finite element for the analysis of structures.

A smart composite-piezoelectric one-dimensional finite element model for vibration damping analysis

A one-dimensional finite element method for generally layered smart beams is presented in this paper. The model implements the first-order shear deformation beam theory and is based on the preliminary analytical condensation of the electric state to the mechanical state. This allows us to establish an effective mechanical beam kinematically equivalent to the original smart beam including the effects of electro-elastic couplings. The contributions of the external electric loads are included in both the equivalent stiffness properties and the equivalent mechanical boundary conditions. Hermite shape functions, which depend on parameters representative of the staking sequence through the equivalent electro-elastic stiffness coefficients, are used to formulate the finite element method. The state space representation is then invoked for the assembled smart beam finite element model to favor its implementation in a block diagram environment for multi-domain simulation. Validation results and solutions for passive and active vibrations damping system are presented last.

TBM 세그먼트 조립 특성에 따른 부재력 변화 연구

본 연구는 수치해석을 통하여 TBM 세그먼트의 분할 수와 인접한 링의 이격각도가 라이닝의 부재력에 어떤 영향을 미치는 살펴보았다. 수치해석은 Midas civil 2012+ 프로그램을 사용하였고, 모델링은 2링빔 스프링 모델을 이용하였다. TBM 세그먼드 부재력은 다양한 요소에 의해 결정된다. 본 논문에서는 세그먼트 분할 수와 분포를 제외한 다른 요소인 이음부 스프링 계수, 지반반력계수를 통제하고 특정한 분할 수와 분할 특성을 통해 case를 선정함으로써 분할 수와 분포와 같은 분할 특성이 부재력에 미치는 영향을 분석하였다. 이로써 TBM 세그먼트 시공 설계시 구조적으로 유리하거나 불리한 이음부 특성을 확인할 수 있다. This paper presents a numerical study on the effect of segment assembly characteristics on the TBM segmental lining member section forces. Analyses have been carried out through the two-ring beam finite element model by Midas civil 2012+. TBM segment lining member forces are determined by various joint characteristics. In this study, the segmental member forces were investigated with various joint number and orientation at fixed values of joint stiffness, ground spring parameters. The numerical results were used to identify trends of the member forces in the tunnel lining with the segment assembly characteristics.

Modeling and simulation of partially delaminated composite beams

A finite-element model for beams with partially delaminated layers is used to investigate their behavior. In this formulation account is taken of lateral strains and the first-order shear deformation theory is used. Both displacement continuity and force equilibrium conditions are imposed between the regions with and without delamination. Numerical results of the present model are presented and its performance is evaluated for static and dynamic problems.

A large torsion beam finite element model for tapered thin-walled open cross sections beams

A 3D finite element beam element model is investigated for the behavior, the buckling and the post-buckling analyses of thin-walled tapered beams with open cross sections. For the purpose, a non-linear model is performed in large torsion context according to a new kinematics that accounts for large torsion, flexural–torsional coupling and the presence of tapering terms in bending and torsion. The equilibrium equations are carried out and new tapering stress resultants are then present. This model is extended to finite element formulation in the same circumstances. 3D beams elements with two nodes and seven degrees of freedom per node are adopted. Due to large torsion assumption and flexural–torsional coupling, new matrices are established in both the geometric and the initial stress parts of the tangent stiffness matrix. The Arclength method is adopted as solution strategy of the non-linear equations. Many applications are presented that deal with the behavior, the buckling and the post-buckling equilibrium. Comparisons are made with some available solutions and with shell elements of a commercial code. The bifurcation points are in accordance with non-linear stability solutions. Moreover, the present element is also compared to similar tapered beam finite element without the new tapering terms. The proposed beam element is efficient and accurate in both linear and non-linear behavior analyses. It follows a non negligible gain in computation time especially when the post-buckling behavior is performed.

Sensitivities of biomechanical assessment methods for fracture healing of long bones

There is a controversy as to whether the biomechanical methods are feasible to assess fracture healing of long bones. This paper investigated the sensitivities of two biomechanical methods, torsion and bending, for assessing fracture healing of long bones; both a simplified beam model and finite element model of an artificial femur were employed. The results demonstrated that, in the initial healing stage, the whole-bone stiffness of the fractured bone is extremely sensitive to the variation of the callus stiffness at the fracture site; when the shear (or Young's) modulus of the callus reaches 15% that of the intact bone, the whole-bone stiffness rises up to 90% that of the intact bone. After that, the whole-bone torsional (or bending) stiffness increases slowly; it becomes less sensitive to the variation of the callus stiffness. These results imply that the whole-bone stiffness is of limited reliability to assess the healing quality particular at late stages of the healing process. The simplified model in this paper provided a theoretical framework to explain why the whole-bone stiffness is insensitive to the healing process of fractured long bones in the late stage of healing. The conclusions obtained from the simplified model were verified with the finite element simulations of the artificial femur.

Evaluating the fidelity and robustness of calibrated numerical model predictions

Purpose – Numerical models are being increasingly relied upon to evaluate wind turbine performance by simulating phenomena that are infeasible to measure experimentally. These numerical models, however, require a large number of input parameters that often need to be calibrated against available experiments. Owing to the unavoidable scarcity of experiments and inherent uncertainties in measurements, this calibration process may yield non-unique solutions, i.e. multiple sets of parameters may reproduce the available experiments with similar fidelity. The purpose of this paper is to study the trade-off between fidelity to measurements and the robustness of this fidelity to uncertainty in calibrated input parameters. Design/methodology/approach – Here, fidelity is defined as the ability of the model to reproduce measurements and robustness is defined as the allowable variation in the input parameters with which the model maintains a predefined level of threshold fidelity. These two vital attributes of model predictiveness are evaluated in the development of a simplified finite element beam model of the CX-100 wind turbine blade. Findings – Findings of this study show that calibrating the input parameters of a numerical model with the sole objective of improving fidelity to available measurements degrades the robustness of model predictions at both tested and untested settings. A more optimal model may be obtained by calibration methods considering both fidelity and robustness. Multi-criteria Decision Making further confirms the conclusion that the optimal model performance is achieved by maintaining a balance between fidelity and robustness during calibration. Originality/value – Current methods for model calibration focus solely on fidelity while the authors focus on the trade-off between fidelity and robustness.

Experimental validation of a drive-by stiffness identification method for bridge monitoring

An experimental investigation is carried out to verify the feasibility of using an instrumented vehicle to detect and monitor bridge dynamic parameters. The low-cost method consists of the use of a moving vehicle fitted with accelerometers on its axles. In the laboratory experiment, the vehicle–bridge interaction model consists of a scaled two-axle vehicle model crossing a simply supported steel beam. The bridge model also includes a scaled road surface profile. The effects of varying the vehicle model configuration and speed are investigated. A finite element beam model is calibrated using the experimental results, and a novel algorithm for the identification of global bridge stiffness is validated. Using measured vehicle accelerations as input to the algorithm, the beam stiffness is identified with a reasonable degree of accuracy.

Finite Element Analysis of Large Mining Height Hydraulic Support Top Beam

In this paper, Solid works software and finite element analysis software ANSYS workbench combined for ZY10000/26/55 type two columns shield large mining height hydraulic support top beam finite element modeling, through the mathematical model analysis to determine the mechanical load, and then using ANSYS software to analyze the stress and displacement law by three conditions: both ends of the beam in concentrated load, unilateral loads and torsional loads. In this way, we know the stress and displacement of hydraulic support beam after the distribution of load, for stress concentration, which make rationalization proposals on large mining height hydraulic support design, we recommend reinforcing ribs, increasing cover thickness or using higher strength material (Q460) and providing a reference in other measures to improve the strength and stiffness of the hydraulic support top beam.

Catenary riser sliding and rolling on seabed during induced lateral movement

Catenary risers have an interaction zone with the seabed, usually referenced as flowline. Movements in this region can be induced by sea currents and large offsets in floating unit, leading to touchdown position changes and affecting internal loads along riser length. In this work the contact flowline-seabed is modeled including sliding and rolling friction. Case studies involving large offsets in floating unit and lateral sea currents are solved to better understand the consequences of possible rolling and large sliding. The riser is modeled using a geometrically-exact finite element beam model. The contact is addressed with a new technique to include rotation movements from underlying beam models. This leads to global riser models including complex kinematics, being able to represent scenarios with alternating sliding/rolling and its consequences on internal loads of riser structure. A parametric study is performed to measure the influence of the friction coefficient in tension and torsion along typical flexible pipe and steel pipe catenary risers.

Buckling Analysis of Thin-Walled Steel Structural Systems Using Generalized Beam Theory (GBT)

This paper deals with the application of beam finite element models based on generalized beam theory (GBT) to analyze the buckling behavior of four thin-walled steel structural systems, namely (i) beams belonging to storage rack systems, (ii) pitched-roof industrial frames, (iii) portal frames built from cold-formed rectangular hollow section (RHS) profiles and (iv) roof-supporting trusses, exhibiting different support conditions and subjected to various loadings. In particular, taking advantage of the GBT unique and structurally clarifying modal features, it is possible to assess how different geometries and/or bracing arrangements affect (improve) the local, distortional and/or global buckling behavior of the above structural systems. The accuracy of the GBT-based buckling results is assessed through the comparison with values yielded by rigorous shell finite element analyzes carried out in the code ANSYS. In spite of the disparity between the numbers of degrees of freedom involved, which are orders of magnitude apart, there is a virtual coincidence between the critical loads and mode shapes provided by the GBT (beam) and ANSYS (shell) finite element analyzes.

FREE VIBRATION ANALYSIS OF PASSENGER BOAT

Vibration is the oscillatory motion of a structure which is influenced by various excitation forces on it. Vibration of a passenger boat may cause passenger discomfort, structural damage etc. If the frequency of excitation coincides with any of the system natural frequency, resonance occurs. So the estimation of vibration is important in any passenger vessel. In this paper, the natural frequency of a passenger boat SWTD 75 is determined using a finite element beam model. The comparison has been carried out with classical methods. Suitable boundary conditions have been selected for approximating wave and still water conditions. Free vibration analysis of boat has been carried out in various load conditions. This may be helpful to determine the condition in which system vibrates unsafely. ANSYS, finite element software is used for analysis.

A non-reflecting boundary for use in a finite element beam model of a railway track

Some beam-like structures such as a railway track are effectively infinite in nature. Analytical solutions exist for simple structures but numerical methods like the finite element (FE) method are often employed to study more complicated problems. However, when the FE method is used for structures of infinite extent it is essential to introduce artificial boundaries to limit the area of computation. Here, a non-reflecting boundary is developed using a damped tapered tip for application in a finite element model representing an infinite supported beam. The FE model of the tapered tip is validated against an analytical model based on Bessel functions. The reflection characteristics of the FE tapered tip are quantified using a wave/FE superposition method. It is shown that the damped tapered tip is much more effective than its constant counterpart and achieves reduction of the model size. The damped tapered tip is applied to a simple FE railway track model and good agreement is found when its point mobility is compared with an analytical infinite track model.

Review and comparison of finite element flexural–torsional models for non-linear behaviour of thin-walled beams

The authors have developed a beam finite element model in large torsion context for thin-walled beams with arbitrary cross sections [1]. In the model, the trigonometric functions of the twist angle θx (c=cos θx−1 and s=sin θx) were included as additional variables in the whole model without any assumption. In the present paper, three other 3D finite element beams are derived according to three approximations based on truncated Taylor expansions of the functions c and s (cubic, quadratic and linear). A finite element approach of these approximations is carried out. Finally, it is worth mentioning that the promising results obtained in [1,2] encourage the authors to extend the formulation of the model in order to include load eccentricity effects. Solution of the non-linear equations is made possible by Asymptotic Numerical Method (ANM) [3]. This method is used as an alternative to the classical incremental iterative methods. Many comparison examples are considered. They concern the non-linear behaviour of beams under twist moment and the post buckling behaviour of struts under axial loads or the beam lateral buckling under eccentric bending loads. The obtained results highlight the discrepancies between the various approximations often employed in thin-walled beams literature for the geometrically non-linear analysis of beams in flexural–torsional behaviour.

Vibration modal analysis of three-dimensional and four directional braided composites

The composite has found extensive applications because of its excellent mechanical properties, but most conditions for the composite serving are subjected to dynamical loads. The parameters relevant to the performance under dynamical loads are system dynamical parameters, for example natural frequency, mode shape. For this aim, the three-dimensional (3D) and four directional braided composite was exemplified to explore the effect rule of the microstructure properties on the dynamical parameters. These macroscopic parameters are employed in discrete beam models and finite element models of continuous body to determine the natural frequencies and shapes. The simulation results were compared with experimental vibration modal analysis. Our study shows that the natural frequencies and shapes computed from both the discrete beam models and finite element models fit the experimental results well. This validates both our research approach and our theory from the microstructure properties to systematical dynamical properties.

Dynamic analysis of bridge girders submitted to an eccentric moving load

The cross-section warping due to the passage of high-speed trains can be a relevant issue to consider in the dynamic analysis of bridges due to (i) the usual layout of railway systems, resulting in eccentric moving loads; and (ii) the use of cross-sections prone to warping deformations. A thin-walled beam formulation for the dynamic analysis of bridges including the cross section warping is presented in this paper. Towards a numerical implementation of the beam formulation, a finite element with seven degrees of freedom is proposed. In order to easily consider the compatibility between elements, and since the coupling between flexural and torsional effects occurs in non-symmetric cross-sections due to dynamic effects, a single axis is considered for the element. The coupled flexural-torsional free vibration of thin-walled beams is analysed through the presented beam model, comparing the results with analytical solutions presented in the literature. The dynamic analysis due to an eccentric moving load, which results in a coupled flexuraltorsional vibration, is considered in the literature by analytical solutions, being therefore of a limited applicability in practice engineering. In this paper, the dynamic response due to an eccentric moving load is obtained from the proposed finite element beam model that includes warping by a modal analysis.