Sectional Forces Research Articles

Numerical comparative study of five currently used implants for high tibial osteotomy: realistic loading including muscle forces versus simplified experimental loading

BackgroundMany different fixation devices are used to maintain the correction angle after medial open wedge high tibial osteotomy (MOWHTO). Each device must provide at least sufficient mechanical stability to avoid loss of correction and unwanted fracture of the contralateral cortex until the bone heals. In the present study, the mechanical stability of following different implants was compared: the TomoFix small stature (sm), the TomoFix standard (std), the Contour Lock, the iBalance and the second generation PEEKPower. Simplified loading, usually consisting of a vertical load applied to the tibia plateau, is used for experimental testing of fixation devices and also in numerical studies. Therefore, this study additionally compared this simplified experimental loading with a more realistic loading that includes the muscle forces.MethodTwo types of finite element models, according to the considered loading, were created. The first type numerically simulated the static tests of MOWHTO implants performed in a previous experimental biomechanical study, by applying a vertical compressive load perpendicularly to the plateau of the osteotomized tibia. The second type included muscle forces in finite element models of the lower limb with osteotomized tibiae and simulated the stance phase of normal gait. Section forces in the models were determined and compared. Stresses in the implants and contralateral cortex, and micromovements of the osteotomy wedge, were calculated.ResultsFor both loading types, the stresses in the implants were lower than the threshold values defined by the material strength. The stresses in the lateral cortex were smaller than the ultimate tensile strength of the cortical bone. The implants iBalance and Contour Lock allowed the smallest micromovements of the wedge, while the PEEKPower allowed the highest. There was a correlation between the micromovements of the wedge, obtained for the simplified loading of the tibia, and the more realistic loading of the lower limb at 15% of the gait cycle (Pearson’s value r = 0.982).ConclusionsAn axial compressive load applied perpendicularly to the tibia plateau, with a magnitude equal to the first peak value of the knee joint contact forces, corresponds quite well to a realistic loading of the tibia during the stance phase of normal gait (at 15% of the gait cycle and a knee flexion of about 22 degrees). However, this magnitude of the knee joint contact forces overloads the tibia compared to more realistic calculations, where the muscle forces are considered. The iBalance and Contour Lock implants provide higher rigidity to the bone-implant constructs compared to the TomoFix and the PEEKPower plates.

Need of different flapping styles for different flight phases of a flapping wing vehicle: A preliminary analysis

Flapping wing vehicles ranging from a large bird sized model to a tiny insect-sized model were made successfully. Still, there is a lot of scope for further research, since their natural counterparts outperform them in most of the flight aspects. The fact that the natural flyers change their flapping style for different flight phases is taken for investigation. Aerodynamic forces at a wing section are analyzed using the general blade-element approach. Using vector mechanics, contributions of the sectional lift and drag forces to the thrust, lift and side force of the vehicle are derived and non-dimensionalized. All the three were in terms of four non-dimensional parameters - the sectional lift to drag ratio, advance ratio, stroke plane orientation and instantaneous flapping angle. The variations of the three force components with the four non-dimensional parameters were plotted. Flapping style with minimized side force and maximized the thrust and lift production is considered as that of efficient flying. The results demand that the stroke plane orientation, speed and amplitude of flapping should be varied for different phases of flight for efficient flying.

Measured aerodynamic forces on a full scale 2MW turbine in comparison with EllipSys3D and HAWC2 simulations

Design loads on turbines are normally simulated with an aeroelastic model using an engineering BEM type model with the turbulent inflow generated with a turbulence model like the Mann model. There are several fundamental uncertainties in this approach, e.g. how well the unsteady induction in response to the turbulent flow is computed. However, within the last few years full 3D CFD rotor computations with turbulent inflow have been performed which can provide detailed insight into this complex load response. In the present work we present computations with the EllipSys3D solver on the 80m diameter NM80 turbine used in the DANAERO project where surface pressure measurements at four radial positions were conducted. The aerodynamic loads integrated from the pressure distributions have been derived and compared with computations by the aeroelastic code HAWC2. Overall a very good correlation is found by comparing PSD spectra of the measured sectional blade forces with HAWC2 simulations using specific flow input from the meteorology mast at six heights. In another comparison using purely turbulent inflow for the simulations on the NM80 rotor some deviations between the force spectra are found between EllipSys3D results and HAWC2 simulations at the inboard part of the blade and at high frequencies.

On the effect of blade deformations on the aerodynamic performance of wind turbine rotors subjected to yawed inflow

This work is aimed to investigate the effects of elastic blade deformations on the aerodynamics of large wind turbine rotors subjected to yawed inflow. Due to the increasing rotor size and advanced light weight blade designs, significant blade deflections can be observed on a regular basis for modern wind turbines. However, especially for complex flow situations like yawed inflow, the role of blade deformations is still not completely understood. In this paper, numerical simulations are conducted on the DTU 10 MW reference wind turbine to gain a better understanding of the involved phenomena. Results are obtained by two numerical methods of different fidelity. First, by the aero-elastic simulation tool FAST, which is based on the low fidelity Blade Element Momentum Theory (BEM) and makes use of common skewed wake correction models. Secondly, by a high-fidelity framework which couples the open-source Computational Fluid Dynamics (CFD) toolbox OpenFOAM with the in-house geometrically non-linear beam solver BeamFOAM. The evaluation of the results is based on the analysis of azimuthal variations of the sectional forces along the blade span and reveals a generally good agreement between the used numerical approach in terms of force amplitudes and variation phases. However, especially for cases of larger yaw angles, the BEM models clearly over-predict the variation amplitudes of the forces up to 40% in the outer blade part.

Implementation of an advanced beam model in BHawC

The implementation of a new structural beam model in the in-house aeroelastic tool BHawC is presented. The model is based on a recently published equilibrium based formulation of a beam stiffness matrix as well as a novel stiffness proportional damping formulation. The performance of the new beam implementation is assessed via modelling a commercial wind turbine. Four analyses are presented to illustrates the increased accuracy in recovered section forces and representation of the dynamic behaviour gained from the new structural model.

Fluid-structure coupled computations of the NREL 5 MW wind turbine by means of CFD

Abstract This paper presents a fluid-structure coupled simulation tool for high-fidelity simulations of wind turbine rotors. Coupling the open source Computational Fluid Dynamics (CFD) code OpenFOAM and the inhouse structural solver BeamFOAM, the developed tool allows the analysis of flexible wind turbines blades by means of CFD without a significant increase in computational costs. To demonstrate the capabilities of the coupled solver, the aero-elastic response of the NREL 5 MW reference wind turbine is computed for various conditions and specific results are compared to findings of other authors. The solver framework is then used to investigate the effect of blade deformations on aerodynamic key parameters such as power, thrust and sectional forces. It is shown, that the structural deformations have a clear influence on the aerodynamic rotor performance. Especially for the case of yawed inflow, significant implications can be observed in terms of loads and local induction factors. Compared to the fluid-structure coupled framework, the rigid CFD solver underpredicts the forces acting on the blades for most of the cases. Consequently, the presented results are expected to contribute to improve the correction models used in aerodynamic models of lower fidelity like those based on the Blade Element Momentum theory.

An efficient fiber beam-column element considering flexure–shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures

In this paper, a fiber beam-column element considering flexure–shear interaction and bond-slip effect is developed for cyclic analysis of reinforced concrete (RC) structures. The element is based on conventional displacement-based Timoshenko beam theory, where the transverse shear deformation is included, and adopts the fiber model to describe the section force–deformation behavior. In the fiber model, shear deformation is assumed to be uniformly distributed along the section and is only resisted by concrete, thus the multi-dimensional concrete damage model is used for concrete fibers and therefore flexure–shear interaction is reflected naturally at the material level. Meanwhile, to account for the significant bond-slip effect at critical regions, the anchorage slip of bars at these regions is analytically derived. Then it is used to modify the uniaxial stress–strain model for steel fibers by assuming that the total strain can be treated as the sum of the bar deformation and anchorage slip, therefore the bond-slip effect is implicitly but simply represented. To validate the proposed element, a series of RC member and structure tests under cyclic loading are simulated. The results indicate that the proposed element can predict cyclic responses of RC structures, and can be used as a reliable tool for analysis of RC structures.

RANSE-based simulation and analysis of scale effects on open-water performance of the PPTC-II benchmark propeller

This paper presents our numerical study of the scale effects on a tip-rake propeller, the PPTC-II, based on the RANS simulations using software FLUENT 6.3. The low Re option in SST k–ω model is adopted at model scale, together with fine prism grids to resolve the viscous sub-layer. At full scale, standard wall function is adopted. The scale-effect corrections yielded by our RANS simulations are compared with those obtained from the ITTC method. To explain the CFD results, an analysis of sectional forces is performed. To investigate how the tip rake influences propeller scale effects, the geometry of PPTC-II is modified by removing the tip rake only, and the RANS-predicted scale effects for the modified propeller, PPTC-II-m, are compared with those for the PPTC-II. The study indicates that the scale effect on propeller thrust can be as important as that on the torque; somehow the RANS- and ITTC-based predictions for full-scale efficiency agree quite well; the tip-rake reduces tip loading and tip vortex strength, and brings about large differences in the scale effects as compared with the propeller without tip-rake.

A robust frame element with cyclic plasticity and local joint effects

A robust elasto-plastic element is developed for analysis of frame structures. The element consists of a beam member with end joints with properties permitting representation of the effect of section forces in adjoining members, like axial forces. By use of the equilibrium formulation the deformations of beam member, plastic hinges and joints become additive and can be expressed in explicit form. The plastic deformations of the beam and the joints are represented by separate plastic mechanisms, described by the same generic cyclic plasticity format. This format is defined by an energy function, a yield surface, and a plastic flow potential for each plastic mechanism. In the cyclic plasticity model each component is characterized by the elastic stiffness, the yield capacity, the additional flexibility at initial yield, the ultimate capacity and a shape parameter describing the curvature of the hysteresis curve. The yield surface is represented by a recently developed generic format, combining the section forces into a homogeneous function of degree one and permitting smooth transition between regions with large and more moderate curvature. A robust return algorithm of approximately second order is developed, using a mid-step state to obtain representative information about the return path. The element is implemented in a co-rotational large-deformation computer program for frame structures. The formulation is illustrated by application to a couple of typical offshore frame structures, and comparison of different representations of the plastic effects illustrates the importance of a robust element with realistic representation of the cyclic plastic mechanisms.

Determination of dominant degradation mechanisms of RC bridge deck slabs under cyclic moving loads

In this paper, fatigue behaviors of RC bridge deck slabs which fail in an unexpected but widely observed punching shear failure mode under cyclic moving loads is analyzed following a fracture mechanics based theoretical method. This method is developed focusing on the propagation and failure along the critical punching shear cracks. From analysis, some key indicators of structural fatigue performances, including the fatigue crack growth of critical punching shear crack, stress evolutions of all materials and sectional forces, moments and crack mouth opening displacements (CMODs) due to all components along the critical punching shear crack cross sections and fatigue life, are obtained. These information are then based on to identify the dominant degradation mechanisms of RC bridge deck slabs subjected to cyclic loads, which provides meaningful and reliable references for the development of an efficient and accurate numerical method.

Experimental and theoretical study on the effect of inclined angle in the SCR pipe-in-pipe system

A novel method of pipeline pigging is that Coiled Tubing (CT) connected with a pig, and then CT is injected into the SCR to clean up pipelines. The CT needs enough axial force so that it would not be stuck in the SCR during the pipeline pigging operation. To analyze the axial load transfer characteristic, paper built the force analysis of the micro element on the straight and curved section, amended effective axial force and the friction between the CT and SCR, and built the mathematical model of SCR pipe-in-pipe system considering impacts of the coiled tubing's buckling. The axial force of the random micro section can be calculated through iterative method. In order to verify the correctness of the theory, the SCR pipe-in-pipe system's indoor platform was built. The experimental platform can study different effects which affect the CT's load transfer behavior within the unfixed SCR. The experimental results of two different phases which inclined angles were 2.0° and 30.0° show that CT's transfer efficiency of axial load is less than 85.0% in SCR pipe-in-pipe system, and it will increase with the inclined angle increasing. Through comparing experimental and theoretical calculation results, the mathematical model of SCR pipe-in-pipe system is validated. Paper calculated the axial force results on the inclined angle 2.0°, 10.0°, 18.0°, 26.0° and 30.0° by the theoretical mechanical model. The theoretical calculation results show that the transfer efficiency would increase with the increasing of the inclined angles. To ensure more axial force to be transferred to the CT's bottom-end, the inclined angle should be as big as possible. The above research can provide theoretical support to the SCR's pigging operation.

Two‐scale finite element modelling of reinforced concrete structures: Effective response and subscale fracture development

SummaryA two‐scale model is derived from a fully resolved model where the response of concrete, steel reinforcement, and bond between them are considered. The pertinent “effective” large‐scale problem is derived from selective homogenisation in terms of the equilibrium of reinforced concrete considered as a single‐phase solid. Variational formulations of the representative volume element problem are established in terms of the subscale displacement fields for the plain concrete continuum and the reinforcement bars. Dirichlet and Neumann boundary conditions (BCs) are imposed on the concrete (pertaining to uniform boundary displacement and constant boundary traction, respectively) and on the reinforcement bars (pertaining to prescribed boundary displacement and vanishing sectional forces, respectively). Different representative volume element sizes and combinations of BCs were used in FE2 analyses of a deep beam subjected to four‐point bending. Results were compared with those of full resolution (single‐scale). The most reliable response was obtained for the case of Dirichlet‐Dirichlet BCs, with a good match between the models in terms of the deformed shape, force‐deflection relation, and average strain. Even though the maximum crack widths were underestimated, the Dirichlet‐Dirichlet combination provided an approximate upper bound on the structural stiffness.

A model for quick load analysis for monopile-type offshore wind turbine substructures

Abstract. A model for quick load analysis, QuLA, of an offshore wind turbine substructure is presented. The aerodynamic rotor loads and damping are pre-computed for a land-based configuration. The dynamic structural response is represented by the first global fore-aft mode only and is computed in the frequency domain with phases using the equation of motion. The model is compared to the state-of-the-art aeroelastic code Flex5. Both lifetime fatigue and extreme loads are considered in the comparison. In general there is good agreement between the two models. Some deviations for the sectional forces are explained in terms of the model simplifications. The differences in the sectional moments are found to be within 10 % for the fatigue load case and 10 % for the extreme load condition.

Inelastic large deflection analysis of space steel frames using an equivalent accumulated element

This paper presents a new model to perform inelastic large deflection analysis of space steel frames depending on the spread of plasticity method. A stiffness matrix of a beam-column element with only two nodes and six degrees of freedom for each node is derived to represent the space frame member. The proposed matrix includes the effect of section yielding along the member as well as the effect of large deflection. Stiffness degradation at the cross-section due to yielded parts is calculated using a formula for the tangent modulus which is affected by the sectional internal forces. The proposed technique of accumulation of rigidity factors is submitted as a first step to get exact first order stiffness factors for a member with variable cross sections. The effect of large deflection is included by considering the axial force while deriving the stiffness factors. Both cubic and higher order shape functions are tried to produce an element that can represent the member without discretization. A finite element program based on stiffness matrix method is developed to predict the inelastic large deflection behavior of steel space frames using the derived stiffness matrix. The proposed finite element technique exhibits good correlation when compared with the conventional spread of plasticity model results. Verification by solving benchmarked steel structures is carried out. The analysis results indicate that the new model is accurate with simple equations and it achieves a significant improvement to the run time.

Seismic response analysis of piled raft with grid-form deep mixing walls under strong earthquakes with performance-based design concerns

A seismic response analysis of a piled raft foundation combined with cement deep mixing walls (DMWs), supporting a 12-story base-isolated building under strong earthquakes, was conducted using a three-dimensional finite element model. To evaluate the induced internal stresses in the DMWs against their capacity, a nonlinear elastic model with tensile and shear criteria was applied for the stabilized soil. In order to verify the deformation parameters of the DMWs and the soil, a numerical simulation was carried out using the moderate earthquake motion recorded during the 2011 Tohoku Earthquake. As the strong earthquake motion, Level 2 earthquakes with a mean return period of approximately 500 years were generated using two sets of phase data. Four numerical cases were conducted considering the effects of the presence of the DMWs on the seismic response of the piled raft system. Based on the dynamic analysis results, it is seen that the bending moments near the pile head were decreased significantly by the DMWs. This occurred because the amplification of the lateral ground displacements below the raft was restrained by the DMWs, and the shear force acting at the pile head was very small because the lateral external force acting at the bottom of the raft was carried mostly by the DMWs. It is also seen that the amplification of the acceleration response spectra of the raft with DMWs was substantially lower than that of the raft without DMWs in long periods of 1–2 s. This is probably due to the difference in the kinematic interaction effects between the foundation and the soft soil. Tensile and shear failure occurred in the DMWs, and the extent of the tensile failure was dominant. Nevertheless, it was found that the grid-form DMWs were quite effective for reducing the sectional force of the piles to an acceptable level, even if such partial failure occurred. The DMWs could be designed more rationally by following the principles of a performance-based design (PBD), because minor damage to DMWs can be tolerated under strong earthquakes provided that the required foundation performance has been satisfied.

Vortex Oscillations Around a Hemisphere-Cylinder Body with a High Fineness Ratio

Vortex unsteadiness around a hemisphere cylinder at angles of attack of 10–80 deg was studied using large-eddy simulation and dynamic mode decomposition. The cylinder body has a fineness ratio of 24.5 (length-to-diameter ratio). The results revealed that oscillations of leeward vortices exist over a forebody at the whole range of angles of attack in addition to vortex shedding at an afterbody. The vortex oscillations consist of antisymmetric modes (alternate oscillation) and symmetric modes (in-phase oscillation). The alternate vortex oscillations correspond to the most energetic modes and are responsible for fluctuating sectional side forces at the forebody that are greater than the ones from vortex shedding at the afterbody. The Strouhal numbers of both alternate vortex oscillations and shedding at angles of attack of 10–40 deg are similar with , whereas at angles of attack of 50–80 deg, the Strouhal numbers are apparently divided into two regimes: the vortex oscillations with at the forebody, and the vortex shedding with at the afterbody. The vortex shedding regions progressively move forward with increasing angles of attack, and accordingly the regions of vortex oscillations contract and eventually only exist near the nose at sufficiently high angles of attack. The computed frequencies are in good agreement with the measured values of hot-wire probes in previous experiments.

Dynamic Response of Shallow-Buried Small Spacing Tunnel with Asymmetrical Pressure: Shaking Table Testing and Numerical Simulation

A series of shaking table tests were designed and carried out to study the seismic behaviors of a shallow-buried small spacing tunnel with asymmetrical pressure. The key details to shaking table model test, including test equipment, model similarity relation, similarity constant, model box, physical model, layout of transducers, seismic waves, and loading system were presented. The numerical simulation of the shaking table test was also carried out by using a finite element simulation software. The results show that: (1) the Fourier spectrums in the vertical direction and horizontal direction are different at the same measuring point. The structure of tunnel transforms the Fourier spectrum of horizontal direction. (2) The stability of middle rock pillar is poor under seismic wave action. The anchor plays an important role in strengthening the stability of middle rock pillar. The dynamic strain of anchor has accumulative effect. (3) The numerical simulation results are in significant agreement with the shaking table test results. (4) Compared with type of seismic wave, peak seismic wave has a significant effect on acceleration response of tunnel. The peak acceleration response of the tunnel is linear with the peak seismic wave, in the horizontal direction. The peak acceleration response is nonlinear in the vertical direction. (5) The axial force of cross section at arch foot is larger than other position. The shock absorption effect of 10 cm seismic isolation layer is better than 5 and 20 cm.

Multi-point earthquake response of the Bosphorus Bridge to site-specific ground motions

The study presents the earthquake performance of the Bosphorus Bridge under multi-point earthquake excitation considering the spatially varying site-specific earthquake motions. The elaborate FE model of the bridge is firstly established depending on the new considerations of the used FEM software specifications, such as cable-sag effect, rigid link and gap elements. The modal analysis showed that singular modes of the deck and the tower were relatively effective in the dynamic behavior of the bridge due to higher total mass participation mass ratio of 80%. The parameters and requirements to be considered in simulation process are determined to generate the spatially varying site-specific ground motions. Total number of twelve simulated ground motions are defined for the multi-support earthquake analysis (Mp-sup). In order to easily implement multi-point earthquake excitation to the bridge, the practice-oriented procedure is summarized. The results demonstrated that the Mp-sup led to high increase in sectional forces of the critical components of the bridge, especially tower base section and tensile force of the main and back stay cables. A close relationship between the dynamic response and the behavior of the bridge under the Mp-sup was also obtained. Consequently, the outcomes from this study underscored the importance of the utilization of the multi-point earthquake analysis and the necessity of considering specifically generated earthquake motions for suspension bridges.

Seismic Performance Analysis of Continuous Rigid Frame Bridges in Expressway under Non-linear Interactions of Soil-Piles

Taking the three-span pre-stressed concrete continuous rigid frame bridge as an engineering example, MIDAS Civil was utilized to establish a spatial finite element model and the interaction between pile foundation and the soil was simulated by equivalent soil spring. In addition to analyzing shearing force, bending moment and stress of the primary beam's characteristic section under different loads, a response spectrum method and time history analysis were adopted to conduct seismic response analysis respectively. In this case, performance of the bridge could be comprehensively evaluated. Relevant analysis results indicate that internal force of the large-span pre-stressed concrete continuous rigid frame bridge is mainly induced by gravity and pre-stress of the structure; section stresses of the primary beam satisfy the corresponding specification and structural safety can be achieved in a state of operation. Moreover, computed results obtained by the response spectrum method is more conservative than those of the time history analysis. In terms of continuous rigid frame bridge, different seismic directions should be taken into consideration during structural seismic analysis at different construction stages.

Seismic Response of Tunnel Lining for Shallow-Bias Tunnel with a Small Clear Distance under Wenchuan Earthquake

In order to study the internal force characteristics of shallow-bias tunnel with a small clear distance in earthquake, a large-scale shaking table slope model test was designed, and the geometric scale was 1 : 10. In the model test, the Wenchuan (WC) seismic wave was used as the excitation wave. Then, the three-dimensional numerical model was established by using MIDAS-NX, and the reliability of the numerical model was verified by comparing the acceleration of the test results. The axial force, bending moment, and shear force of the tunnel cross section and longitudinal direction were calculated by the numerical model under different excitation directions included the horizontal direction (X), the vertical direction (Z), and the horizontal and vertical direction (XZ). The results show the following. (1) The internal force of right arch foot of left hole and the left arch foot of right hole is larger than other part of the tunnels because the distance between the two tunnels is smaller and they interact with each other. (2) The loading direction of single direction loading method is different and the variation trend of tunnel force are different, so the loading direction of seismic wave has a significant influence on the seismic force response of the tunnel. (3) All of the internal force values of tunnel lining under the seismic wave action in bidirection are larger than those in single direction. The value is not a simple superposition of two directions and has some coupling effect. The influence of the vertical seismic wave cannot be ignored in dynamic response research. These results improve the understanding of the rock slope with small spacing tunnel under seismic action.