Nonlinear Beam Element Research Articles

Influence of temperature on the vibration properties of tensegrity structures

Vibration health monitoring methods use the sensitivity of the natural frequencies to structural damage. Natural frequencies are sensitive to damage, but are also affected by environmental conditions like temperature changes. It is important to be able to distinguish between the effects of these different factors when using the vibration properties as a monitoring tool. This paper discusses the impact of damage and environment temperature changes on the natural frequencies of tensegrity (“tensile-integrity”) structures, in particular noting that component bending is a prominent vibration mode, which motivates a use of non-linear beam elements with axial-bending coupling. The model considers not only thermal expansion effects, but also the change of the elastic modulus with temperature. Changes in natural frequencies produced by environment temperature changes are shown to be similar to the ones produced by damage. The geometry of tensegrity structures, the support conditions and the materials are found to be important factors. The sensitivity of the natural frequency to temperature changes is found to be dependent on pre-stress level.

Application Of The Distributed Plasticity Concept In Quick Nonlinear Analysis Of Reinforced Concrete Shear Walls

Abstract The paper presents a simplified calculation method to predict, as accurate as possible, the most important characteristics of the behaviour of the slender reinforced concrete shear walls in the inelastic range: failure mode, strength capacity, flexural and shear deformations, sectional and element ductility. The formulation is based on nonlinear beam element with taking into account the influence of shear, both on strength and stiffness of the wall. The principal parameters incorporated in the calculation model are: the rectangular shape of the cross section, the aspect ratio of the wall, the most accurate constitutive relationships for the compressed concrete and for the reinforcement steel, both in compression and in tension (including the strengthening of the steel after yielding), the variation of the Poisson ratio of the concrete, the amount and distribution of the vertical reinforcement. The model uses the concept of distributed (smeared) plasticity along the element and so the flexural deformations are computed by integrating the actual curvatures on the height of the wall. The shear deformations are also calculated, in agreement with the results of some recent experimental researches. The calculation method was then applied to two experimental wall specimens and their force – horizontal top displacement curves were plotted.

Nonlinear modeling of compliant mechanisms incorporating circular flexure hinges with finite beam elements

Modeling of compliant mechanisms incorporating flexure hinges is mainly focused on linear methods. However, geometrically nonlinear effects cannot be ignored generally. This work shows that nonlinear behavior plays an important role in the deformation and stress analysis, which consequently impacts the design of compliant mechanisms. In this study a nonlinear higher order finite beam element based modeling approach is presented strongly reducing the computation time of nonlinear models. Planar deformation and mechanical stress of a single circular flexure hinge under a wide range of loads is modeled and computed with the proposed approach. A comparison with a 3D-nonlinear finite element model shows very good agreement and validates the beam model. It is shown that the linear and nonlinear deformation behavior of a single flexure hinge deviate marginally so that linear modeling approaches are sufficient. Furthermore a planar displacement amplification mechanism incorporating circular flexure hinges is studied by means of the same method highlighting the distinct deviation of the behavior of the geometrically nonlinear model from its linear prediction. In conclusion the nonlinear behavior at the system level can not longer be neglected. Finally, a study shows that different designs of the displacement amplification mechanism are achieved when linear or nonlinear modeling approaches are applied.

Dynamic Plastic Deformation of Deepwater Steel Catenary Risers Under Extreme Cyclic Compressive Loading

Steel catenary risers (SCRs) on a large-heave-motion vessel are susceptible to compression in the riser touchdown zone (TDZ). Dynamic compression can lead to overstress under extreme or abnormal weather conditions. The response of an SCR under compression is highly nonlinear and sensitive to various factors. However, the current available industry design codes and practices do not provide a clear guidance to address the acceptability of compression, overstress, and the resulting plastic strains. In addition, the current analysis method used in industry common practice cannot capture accurately the nonlinear behavior of an SCR involving accumulated plastic deformation, hysteresis effects, and local buckling. In this paper, a finite-element-analysis modeling method that uses combined beam and solid elements is presented. This method enables simulation of large plastic deformation, pipe ovality, and local pipe buckling in the TDZ of a deeppwater SCR. The model is developed with Abaqus (Dassault Systèmes 2009). The SCR nonlinear response is examined through dynamic analysis of a deepwater SCR that is hung from a semisubmersible. The key analysis results are compared with a nonlinear beam-element model. Moreover, dynamic-ratcheting analysis under multiple plastic-strain cycles by use of the proposed solid-riser model is conducted to understand the plastic-strain accumulation and to check the acceptability of the survival response of a deepwater SCR under a series of sever hurricanes in its service life. This paper presents the methodology for evaluating the compression and plastic deformation that could be experienced by deepwater SCRs, including the modeling approach, analysis results, possible failure modes, and conclusions. The impact of the study findings on the robustness and suitability of SCRs for deepwater application is discussed.

ENGLISH

A research was carried out to assess the effect of concrete creep on long-term performance of skewed Integral Abutment Bridge. Time-history transient analysis was conducted using Finite Element method for 75-year period. Parametric study was conducted in LUSAS to assess the effect of bridge total length (60m,90m,150m), skew angles (0 0 ,10 0 ,20 0 ,30 0 ,40 0 ), backfill soil stiffness (dense sand, loose sand) on the behaviour of the bridge measured by girder and abutment displacement, moment and shears. Three dimensional nonlinear thick beam element with CEP-FIP 1990 creep material properties was used to model bridge girders. Other structural members were modelled using three dimensional thick beam element. Bridge total span and skew angle were found to have predominant effect on behaviour of skewed IABs than backfill soil stiffness. Loose sandy backfill soil results in higher values of deformations in comparison to dense sandy soils. Most of the deformations are regular from zero to 20 0 skew, variations in deformation mostly occurred after 20 0 skew.

An experimental and numerical study of a semi-rigid bolted-plate connections (BPC)

The aim of this paper is to evaluate the bending stiffness of a new bolted-plate joint for single-layer or double-layer reticulated shells. In order to investigate the performance of the joint, experimental tests and numerical simulations were undertaken. ANSYS was used for the numerical study, with contact elements (target 170 and contact 174) and solid elements (solid 187), used to establish bending stiffness curves for the bolted-plate joints. The good agreement between numerical simulation and experiment indicated that the simulation is an accurate and effective way of evaluating the mechanical properties of the bolted-plate joint system. In addition, using nonlinear beam elements (beam 189 element) with end spring elements (combin39), the single-layer reticulated cylindrical shell with bolted-plate joints was analyzed for different rise to width ratios. The analyses determined the load-bearing capacity of the shell. It is concluded that the bolted-plate joint system is a good choice for space structures with small or medium spans.

Improved nonlinear displacement-based beam element on a two-parameter foundation

This paper presents a nonlinear beam element on a two-parameter foundation. A set of governing differential equations of the problem (strong form) is first derived. The displacement-based beam-foundation element with improved displacement shape functions (weak form) is then formulated based on virtual displacement principle. The improved functions are analytically derived based on homogeneous solution to the governing differential equilibrium equation of the problem and are employed to enhance the model accuracy. Tonti’s diagrams are used to conveniently represent the equations that govern both the strong and weak forms of the problem. An averaging technique previously proposed by the authors is employed to determine system parameters needed in evaluating the displacement shape functions. Finally, two numerical simulations are used to verify the accuracy and the efficiency of the proposed beam model. The first simulation is used to perform convergence studies of the proposed model and to show its accuracy in representing both global and local responses. The second simulation is used to address effects of the two-parameter foundation model on system responses when compared to the Winkler foundation model.

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. the influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

On successive differentiations of the rotation tensor: An application to nonlinear beam elements

On successive differentiations of the rotation tensor: An application to nonlinear beam elements

Experimental and numerical characterization of the structural dynamics of flapping beams

The nonlinear structural dynamics of a slender beam in flapping motion is examined both experimentally and computationally. In the experiments the periodic flapping motion is imposed on the clamped edge of the cantilever beam using a 4-bar crank-and-rocker mechanism. Aluminum beams with nominal dimensions of 150mm×25mm×0.4mm are tested in air over a range of flapping frequencies up to 1.3 times the linear first modal frequency at two different flapping amplitudes, 15° and 30°. The response of the beam is characterized experimentally through bending strain and tip displacement data obtained from foil strain gage and high-speed camera, respectively. It was determined that for the particular combination of beam specimen (dimensions, material properties) and forcing parameters investigated, all experimental responses were periodic. The frequency response curves based upon the experimental bending strain data reveal a secondary superharmonic peak in addition to the primary resonance peak. As the flapping frequency is increased, the response of the beam is observed to change from symmetric (with respect to equilibrium position) periodic vibrations with a period equal to the flapping period to asymmetric periodic vibrations with higher harmonic content featuring local oscillations in the time histories. Experimental tip displacement results show that the beam spends more time during stroke reversals when the flapping frequency is near primary and secondary resonance regions. In addition to experiment, numerical simulations are performed using two-node, isoparametric degenerate-continuum based geometrically nonlinear beam elements. The HHT-α version of the Newmark finite difference scheme is used to discretize the problem in time and a linear viscous damping model is assumed. Overall the numerical simulations agree well with the experiments and capture most of the nonlinear dynamical features of the beam response. It is, however, found that in resonance regions the simulation overpredicts response magnitudes, possibly due to the use of the linear damping model and linear elastic constitutive model. Additional numerical simulations of the beam tip response reveal dynamics which include periodic, asymmetric periodic, quasi-periodic and aperiodic motions.

A nonlinear two-node superelement for use in flexible multibody systems

A nonlinear two-node superelement is proposed for the modeling of flexible complex-shaped links for use in multibody simulations. Assuming that the elastic deformations with respect to a corotational reference frame remain small, substructuring methods may be used to obtain reduced mass and stiffness matrices from a linear finite element model. These matrices are used in the derivation of potential and kinetic energy expressions of the nonlinear two-node superelement. By evaluating Lagrange’s equations, expressions for the internal and external forces acting on the superelement can be obtained. The inertia forces of the superelement are derived in terms of absolute nodal velocities and accelerations, which greatly simplifies the dynamic formulation. Three examples are included. The first two examples are used to validate the method by comparing the results with those obtained from nonlinear beam element solutions. We consider a benchmark simulation of the spin-up motion of a flexible beam with uniform cross-section and a similar simulation in which the beam is simultaneously excited in the out-of-plane direction. Results from both examples show good agreement with simulation results obtained using nonlinear finite beam elements. In a third example, the method is applied to an unbalanced rotating shaft, illustrating the potential of the proposed methodology for a more complex geometry.

Open-loop frequency response analysis of a wind turbine using a high-order linear aeroelastic model

Wind turbine controllers are commonly designed on the basis of low-order linear models to capture the aeroelastic wind turbine response due to control actions and disturbances. This paper characterizes the aeroelastic wind turbine dynamics that influence the open-loop frequency response from generator torque and collective pitch control actions of a modern non-floating wind turbine based on a high-order linear model. The model is a linearization of a geometrically non-linear finite beam element model coupled with an unsteady blade element momentum model of aerodynamic forces including effects of shed vorticity and dynamic stall. The main findings are that the lowest collective flap modes have limited influence on the response from generator torque to generator speed, due to large aerodynamic damping. The transfer function from collective pitch to generator speed is affected by two non-minimum phase zeros below the frequency of the first drivetrain mode. To correctly predict the non-minimum phase zeros, it is essential to include lateral tower and blade flap degrees of freedom. Copyright © 2013 John Wiley & Sons, Ltd.

An accurate nonlinear 3d Timoshenko beam element based on Hu-Washizu functional

An accurate 3d mixed beam element that is efficient especially in nonlinear analysis is presented in this paper. The mathematical theory is based on Hu-Washizu principle that uses three-fields in the variational form. The composition of the variational form ensures independent selection of displacement, stress and strain fields. Timoshenko beam theory is extended to three dimensions for deriving strains from displacement field. Numerical integration of stress–strain relations along control sections is carried out for numerical analysis. The finite element approximation for the beam uses shape functions for section forces that satisfy equilibrium and discontinuous section deformations along the control sections of the beam. This form of the element permits coupling of the stress resultants and eliminates necessity of displacement components along the beam element except at the nodes. Consequently the element is free from shear-locking. Numerical examples on uniform and tapered structural members with solid and hollow circular sections demonstrate the nonlinear interaction between axial, shear force, bending moments and torsion, where the results compare well with closed form solutions and available data in literature. Furthermore, the proposed element has superior performance in both linear and nonlinear analysis compared to a locking-free higher order displacement based 3d Timoshenko beam element.

Three-Dimensional Cyclic Beam-Truss Model for Nonplanar Reinforced Concrete Walls

AbstractA three-dimensional nonlinear cyclic model for nonplanar reinforced concrete walls is presented. Nonlinear Euler-Bernoulli fiber-section beam elements are used to represent steel and concrete in the vertical direction, and nonlinear trusses are used to represent the steel and concrete in the horizontal direction and the concrete in the diagonal directions. The model represents the effects of flexure-shear interaction by computing the stress and strains in the horizontal and vertical directions and by considering biaxial effects on the behavior of concrete diagonals and accounts for mesh-size effects. The model is validated by comparing the experimentally measured and numerically computed response of three reinforced concrete T-shape, C-shape, and I-shape section wall specimens, respectively, with the response of the latter two characterized by crushing of the concrete in the diagonal direction. The overall force-deformation and local strain responses are presented. Finally, the computed response u...

Geometrically exact physics-based modeling and computer animation of highly flexible 1D mechanical systems

This paper presents a geometrically exact beam theory and a corresponding displacement-based finite-element model for modeling, analysis and natural-looking animation of highly flexible beam components of multibody systems undergoing huge static/dynamic rigid-elastic deformations. The beam theory fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, concepts of local displacements and orthogonal virtual rotations, and three Euler angles to exactly describe the coordinate transformation between the undeformed and deformed configurations. To demonstrate the accuracy and capability of this nonlinear beam element, nonlinear static and dynamic analysis of two highly flexible beams are performed, including the twisting a circular ring into three small rings and the spinup of a flexible helicopter rotor blade (Graphical abstract). These numerical results reveal that the proposed nonlinear beam element is accurate and versatile for modeling, analysis and 3D rendering and animation of multibody systems with highly flexible beam components.

Mechanical properties of double-layered graphene sheets

In this paper, the molecular structural mechanics method is employed to calculate the mechanical properties of a double-layered carbon graphene sheet more accurately. For this purpose, covalent bonds are modeled using nonlinear beam elements and van der Waals interactions are replaced by nonlinear truss elements. Morse potential and Lennard–Jones potential equations are used to simulate the covalent bonds and van der Waals interactions, respectively. For each atom, van der Waals forces are considered with respect to all the other atoms located in its cut-off radius. In addition to in-plane mechanical properties of single and double-layered graphene sheets some out-of-plane properties like the thickness-wise stiffness and shear modulus are studied. The results indicate that Young’s modulus of a double-layered carbon graphene sheet decreases linearly with strain while Poisson’s ratio is independent from it. Also it is noted that the thickness-wise stiffness significantly increases while the distance between the two layers declines however the shear modulus is independent from shear strain.

Nonlinear Winkler-based beam element with improved displacement shape functions

This paper presents a Winkler-based beam element capable of representing the nonlinear interaction mechanics between the beam and the foundation. The element is derived based on a displacement-based formulation using improved displacement shape functions. The improved displacement shape functions are analytically derived based on the homogeneous solution to the governing differential equilibrium equation of the problem, thus enhancing the model accuracy. An iterative technique is used to determine the length-scale parameter needed in evaluating the displacement shape functions. Two numerical examples are used to verify the accuracy and the efficiency of the proposed Winkler-based beam model.

3305 構造の機能つながりを考慮した初期設計解析手法の開発

In order to correspond flexibly to specification changes and light weighting and downsizing of the vehicle body, it is required to clarify and optimize the interface characteristics of the boundary portion and the functions of the module and components involved in the overall performance, in the early design stage. To solve the problems described above, we add the self-contact function within parts and the contact function with parts outside to the three-dimensional nonlinear finite element program consisting of non-linear spring elements and beam elements which has been developed intended for use in conceptual design stage, and carry out the verification analysis.

A Simple Co-Rotational Finite Planar Beam Element of Geometrical and Material Nonlinearity

A simple geometrical and material nonlinear co-rotational planar beam element of field consistency is proposed. Herein the element which produces a local stiffness matrix of 3 by 3 other than 6 by 6 is developed. Material nonlinearity is taken into account on the base of yield function of element internal forces. By applying static equilibrium relationship of classic beam theory for the transferring of local element nodal force to global element nodal force, a new transformation matrix different from the nodal displacement transformation matrix is established. Although this results in an asymmetric global tangential stiffness matrix, the new transformation is simpler, and gives rise to field consistency and makes it possible to compute very large beam deflection without remeshing of the deformed structure. Computations of numerical example indicates that formulations for the nonlinear beam element are of validation and high efficiency

Numerical simulation of shear-strengthened RC beams

A nonlinear and time-dependent fibre beam element model able to simulate the response of existing reinforced concrete (RC) frame structures subjected to repair and strengthening interventions is presented in this paper. The relevant attributes of the proposed formulation are: (i) its capability for considering shear effects in both service and ultimate levels and (ii) the step-by-step nonlinear sequential type of analysis, which allows capturing the strengthening effects, accounting for the state of the structure prior to the intervention. The 2D fibre beam element developed is based on the Timoshenko theory and a hybrid (kinematic/force) formulation is used to simulate the response of RC sections under combined normal and shear stresses. Biaxial constitutive equations assuming smeared rotating cracks are used to describe the behaviour of cracked concrete. The proposed model is validated with experimental results of a shear damaged and subsequently strengthened RC beam, available in the literature. An alternative shear strengthening solution with the use of prestressed stirrups is also presented. The importance of considering shear-bending interaction and previous damage in the numerical assessment of strengthened RC beams is highlighted.