Influence Of Geometric Nonlinearity Research Articles

A Comprehensive Investigation of Linear and Nonlinear Beam Models on Flexible Wind Turbine Blade Load Calculations

This study was performed to investigate the effects of structural nonlinearity and large deformations on the aeroelastic loads of flexible wind turbine blades. First, a blade structural analysis model was established using the geometrically exact beam (GEB) theory. Subsequently, the blade element momentum (BEM) theory was corrected using the geometrically exact method leading to the development of a geometrically exact blade element momentum (GE-BEM) model. The results from the GE-BEM model indicated that flapwise deformations always reduce blade fatigue loads, while torsional deformations decrease fatigue loads under low wind speeds but increase them under high wind speeds. Finally, the linear Euler–Bernoulli beam and the GEB were compared to explore the influence of geometric nonlinearity on the blade aeroelastic loads, which revealed that the Euler beam model underestimates the blade loads. The simulations that used the GEB model produced torsional root twist fatigue loads that were 57.49% greater than those generated when the Euler beam model was used. Furthermore, the flapwise bending moment fatigue loads at the root were 8.24% greater than those obtained by the Euler beam model. The smallest discrepancy between the results of the two models was 7.26%, and it corresponded to the edgewise fatigue load.

A nonlinear numerical scheme to investigate the influence of geometric nonlinearity on post-flutter responses of bridges

A nonlinear numerical scheme to investigate the influence of geometric nonlinearity on post-flutter responses of bridges

Nonlinear Performance of Steel Tube Tower in Ultra-High Voltage Transmission Lines under Wind Loads

As complex, statically indeterminate structures, transmission towers are subject to complex forces and are usually simplified into truss structures that only consider the effects of axial force. When the load and deformation of a tower are small, it is reasonable to carry out analysis according to the linear elasticity theory. However, the height of an ultra-high voltage (UHV) transmission tower is significantly large, meaning that the calculation result according to the current elastic analysis method often has a large deviation from the actual stress of the structure. With the influence of the bending moment at the end of the member, a numerical model is established considering the influence of geometric nonlinearity and material nonlinearity in this paper. The stress distribution characteristics and development law of UHV transmission towers in linear and nonlinear stress states are analyzed and studied. The real tower test and elastoplastic ultimate bearing capacity analysis show that the elastoplastic analysis is closer to the actual tower. The UHV steel pipe tower designed according to the linear elasticity and small deformation theory has a large safety margin under the design load, resulting in a significant waste of materials. Under the action of heavy load, the tower exhibits strong nonlinearity, and the influence of geometric and material nonlinear factors should be fully considered when designing the structural components in UHV transmission towers.

Nonlinear vibration of the sandwich beam with auxetic honeycomb core under thermal shock

The nonlinear thermally induced vibration (TIV) characteristics of sandwich beams with auxetic honeycomb cores under general boundary conditions are studied. Based on first-order shear deformation theory, the dynamic governing equations are obtained through Hamilton principle, in which geometric nonlinearity and temperature dependence are considered. The temperature field along the thickness is calculated by finite element method and nonlinear TIV responses are solved via Newton-Raphson-Newmark method. The effects of temperature dependency, thermal shock forms, geometric nonlinearity, thicknesses of beam and face-sheet, boundaries and honeycomb geometrical parameters are studied. Results show that the reduction of the absolute inclined angle of the auxetic honeycomb can weaken the TIV responses. The influence of geometric nonlinearity on quasi-static and dynamic responses depends on the thermal shock form. Thermal buckling is the necessary condition for the occurrence of the TIV in clamped beams with immovable ends. Moreover, the research provides some design references to suppress the TIV responses of the sandwich beam with auxetic honeycomb core.

Various beam and shell models for long slender tools in the area of HSC milling

AbstractHigh‐speed‐cutting) milling is an extensively used production process in tool‐making and mold‐making industries. For the purpose of a self‐balancing tool, a hollow shaft is used and filled partially with a fluid. This talk presents different beam and shell models for the investigation of nonlinear vibrations. Therefore, different theories are compared with respect to the influence of geometrical nonlinearities, spin‐softening as well as stress‐stiffening, and also shear deformation. Additionally, a stochastic Wedig–Dimentberg approach is presented for the simulation of a spatial distributed unbalance. Starting with the nonlinear kinematics for the tool‐deformation Hamilton's principle is evaluated for the variational formulation of each model. Regarding to the shear deformation, the theories of Euler–Bernoulli and Ehrenfest–Timoshenko (beam models) as well as Kirchhoff–Love and Mindlin–Reissner (shell models) are used. In the following up, the variational formulation is discretized under usage of a global Ritz approach on the one hand, and on the other hand with a local finite element (FE) discretization. Afterward, the governing system of differential equations is solved and discussed. Different results of rotating and nonrotating tools are presented, which show the available options of each theory and also their limits. In particular, results of the eigenfrequencies including their stochastic distribution, stationary deformation, stability behavior, and various time solutions are shown.

Influence of geometric nonlinearity on static and dynamic response of flexible beam

The flexible beam theory is widely applied in engineering, due to that many engineering structures can be regarded as flexible beam. For the flexible beam under large rotation, researches have shown that consideration of geometric nonlinearity is necessary: beam deflection will be erroneously larger or diverge without consideration of geometric nonlinearity. The reason lies on the dynamic stiffening effect caused by geometric nonlinearity. The dynamic stiffening effect of flexible beam under large rotation is well studied already, however, most studies only focus on flexible beam with constant cross section and rarely considers flexible beam without rotation. In view of this, a flexible beam with variable and twisted cross section is adopted to analyze the influence of geometric nonlinearity, and the response of flexible beam without rotation or static response is also analyzed. The results of dynamic beam deflection with and without consideration of geometric nonlinearity is compared, the results of static beam deflection under different load is also compared. On the basis of result comparison, the influence of geometric nonlinearity on static and dynamic response of flexible beam is then explained.

On Nonlinear Spatial Vibrations of Rotating Drill Strings under the Effect of a Fluid Flow

In this article, the development and subsequent numerical analysis of a nonlinear mathematical model of the drill-string dynamics taking into account the effect of a drilling fluid flow and the gravitational energy of the system is carried out. Spatial lateral vibrations of the drill string modeled as a rotating elastic rod are studied. The developed nonlinear model generalizes and refines the well-known linear models of rod vibrations with the considered effect. The obtained numerical results demonstrate the influence of geometric nonlinearity, the gravitational energy of the drilling system, additional Coriolis and centrifugal forces as well as the parameters of the fluid flow on spatial vibrations of the drill strings. It allows for giving some recommendations on the choice of the drilling system parameters for ensuring safe drilling operations.

Nonlinear analysis of planar, H-shaped and U-shaped thin reinforced concrete shear walls

This paper presents and discusses the results of nonlinear finite element analysis (NL-FEA) of thin reinforced concrete shear walls. For this, an in-home developed shell structures NL-FEA program called CANECA was used. The materials modeling use the basis of the Modified Compression Field Theory and the geometric nonlinearity is evaluated using a Total Lagrangian Formulation. The influence of geometric nonlinearity and cyclic loading condition on an H-shaped shear wall behavior is discussed. From the obtained results, a higher influence of the cyclic loading condition is observed. Other two shear walls (simple planar and U-shaped) are also analyzed. Their geometry and reinforcement are modified in order to observe the influence of these parameters on the structural behavior, including the case of slender shear walls. The performed analysis on the two shear walls showed good agreement with the numerical response obtained in the NL-FEA program VECTOR4. The obtained numerical ultimate loads were much higher than the original structure design load and the slenderness ratio was insufficient to characterize the ultimate structural behavior. The results from this study can contribute for a better understanding on the structural behavior of thin reinforced concrete shear walls, and serve as guidance for future studies and normative developments.

Development of the Dynamic Response of Curved Bridge Deck Pavement Under Vehicle–Bridge Interactions

Curved bridge is commonly used in highway viaducts and overpass, on which deck pavement plays a crucial role in dispersing wheel load and providing level driving surface. Due to the influence of geometric nonlinearity of curved bridge and vehicle–bridge coupling vibration, curved bridge deck pavement (BDP) is subjected to a complex mechanical state. To study the dynamic response of the curved BDP under complex vehicle–bridge interaction (VBI) condition, this paper proposes an original dynamic analysis scheme. The BDP and bridge structure are simulated by the finite element method and the vehicle is simulated as a multi-body system (MBS); together they are integrated into a coupled system model. The numerical results are consistent with the experimental data. The dynamic responses of the proposed scheme are about 10–20% larger than those of moving constant forces, which indicates that the vehicle–bridge coupling vibration should be considered in the dynamic analysis of BDP. The parametric study shows that the vehicle weight can aggravate the response of the BDP; however, the effect of the vehicle speed on the deck pavement response and impact factor is not obvious. As road roughness classification and tire stiffness increase, the dynamic curve fluctuation of BDP is more obvious and the amplitude is larger. Through parameter sensitivity analysis, it can be concluded that vehicle weight has the greatest effect on the dynamic behavior of BDP, followed by vehicle speed and roughness, and tire stiffness has the least impact.

Influence of different material parameters on nonlinear vibration of the cylindrical skeleton supported prestressed fabric composite membrane

Abstract In order to study the influence of geometric nonlinearity and material parameters on the free vibration behavior of the cylindrical skeleton supported prestressed fabric composite membrane. In this paper, based on von Karman's large deflection theory and D’Alembert's principle, the governing equations of nonlinear viscous damped prestressed free vibration of frame supported anisotropic membrane structures were established. By using Galerkin and KBM perturbation method, the analytical expressions of frequency function, displacement function and mode shape of nonlinear free vibration were obtained. In order to verify the effectiveness and effective range of the method, the fourth order Runge-Kutta method was used for numerical calculation. The calculation examples of membrane material parameters were given. The calculation and analysis of different membrane prestress, different length width ratio, different rise span ratio and different material parameters (elastic modulus ratio, viscous damping and material density) were carried out. The results were compared with the numerical results obtained by Runge-Kutta method to verify the accuracy of the method. The research results of this paper provide a theoretical reference for the selection of membrane materials, the subsequent calculation of wind-induced stability of steel skeleton membrane structure and the design of wind-driven rain resistance.

Influence of Double-Limb Double-Plate Connection on Stable Bearing Capacity of Quadrilateral Transmission Tower

Transmission tower connection joint is an important connection component of the tower leg member and diagonal member. Its axial stiffness directly affects the stable bearing capacity of a transmission tower. The axial stiffness of the joint is mainly related to the connection form of joint. This paper takes the double-limb double-plate connection joint as the research object. Through the comparative study with the single-limb single-plate connection joint, the influence law of single-limb single-plate and double-limb double-plate joint on stable bearing capacity of quadrilateral transmission tower is studied from three aspects of model test, theoretical analysis and numerical simulation. Through the scale model test, it is found that the elastic stiffness of the double-limb double-plate joint is 3.12 times that of the single-limb single-plate joint, which can increase the bearing capacity of the joint by 26.1%. Through the energy method, the theoretical calculation expression of the stable bearing capacity of the quadrilateral tower considering the influence of the axial stiffness of the joint is derived. Compared with the effect of the single-limb single-plate connection joint, the double-limb double-plate joint can improve the stable bearing capacity of the quadrilateral tower by 15.6%. Considering the influence of geometric nonlinearity of tower and connecting joint, it is found that the double-limb double-plate connecting joint can improve the nonlinear stability bearing capacity of a transmission tower by 14.9%. The results show that the double-limb double-plate connection joint can not only improve the bearing capacity of the joint, but also greatly improve the stable bearing capacity of the tower. The research results can provide reference for the engineering application and design of double-limb double-plate connection joints.

Effects of Unbalanced Lamination Parameters on the Static Aeroelasticity of a High Aspect Ratio Wing

In this paper, in order to understand the influence of the unbalanced coefficient of composite laminates on the static aeroelasticity of high aspect wings, a series of numerical simulation calculations were carried out, and this work wants to provide some reference for the structural design of aircraft. Considering the influence of geometric nonlinearity, the unidirectional fluid-solid coupling calculation method based on loose coupling is used to control the change of unbalanced coefficient of laminates on the basis of layering angle, layering thickness, and layering region, so as to observe the changes caused to the wings. The relationship between the unbalanced coefficient and the constant thickness layup and the variable thickness layup with 0° and ±45° layup angles was studied, respectively. Then, the layup angle of 90° was added to study the influence of the unbalanced coefficient on the static aeroelasticity of the wing structure with the change of the layup angle and the different choice of layup region. The results show that the deformation is the smallest when the unbalanced coefficient is 0.5, and the deformation trend is evenly distributed along both sides when the unbalanced coefficient is 0.5. When the unbalanced coefficient is changed, adding the 90° layup angle can significantly reduce the overall deformation of the wing and show different sensitivity characteristics to different layup areas. The increase of the unbalanced coefficient makes the chordal displacement gradually change from linear distribution to nonlinear distribution along the spread direction, and the displacement will gradually decrease.

Assessment of Geometric Nonlinearities Influence On NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

Abstract This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

Research on a Prediction algorithm of Bridge Engineering Mechanics parameters based on Deep Learning

With the increase of the span of cable-stayed bridge, the influence of geometric nonlinear factors in engineering mechanics is becoming more and more obvious, so it is necessary to seek the construction alignment prediction method of long-span cable-stayed bridge considering the influence of geometric nonlinearity. In this paper, we analyze the basic principle and improvement measures of BP neural network algorithm, establish a prediction model with the help of Matlab language, and discuss its application in the construction control of long-span cable-stayed bridge. Taking a large span steel box girder cable-stayed bridge with a main span of 1088m as the engineering background, the rationality and feasibility of this method are verified, which provides a reference for the alignment control of the same type of bridge.

Influence of Base Deformations on Stability of Frame-Rod Structural Systems

Purpose of research. Investigation of changes in the critical parameters of stability of structural system elements, taking into account the geometric nonlinearity associated with the deformation of the “building-base” system. Methods. Under the influence of geometric nonlinearity associated with joint deformations of the “building-base” system, the longitudinal force of some racks ceases to contribute to the bifurcation of the rod [5-7, 9, 12, 13]. Therefore, at a certain value of strain ΔS, a single rack can go from active bifurcation to passive, which will cause structural and change the critical stability parameters of the entire system under consideration. This situation can lead to irreversible deformations and destruction of both the individual load-bearing element and the entire building. Results. Let’s consider a core structural system, the Central element of which is loaded with The RCR force, and the extreme elements are loaded with the RCR forces. (Fig. 1A). We find the critical parameters of the stability of the specified frame and the form of bifurcation of its compressed struts using the given equations depending on the load application coefficient α before and after stabilization of the base precipitation.Let’s analyze the bifurcation pattern of the frame elements before and after the base deformation at the maximum precipitation of the second and third pillars at the value of the load application coefficient α=0.8 at a time when the base deformations have not stabilized, the left and right pillars lose their stability passively, the Central one-actively (Fig. 3A). Analysis of the obtained calculation results showed that when the second column precipitation is 2.4 cm or more, the character of the entire structural bifurcation system changes. Conclusion. During the theoretical research, the behavior of the elements of the frame in question during the loss of stability before and after the occurrence of an emergency situation associated with the subsidence of the base of the supports of the first and second pillars was analyzed. The dependence of the critical value of the precipitation and the difference in precipitation on the load application coefficient α for the second and third pillars of the frame was derived. Analysis of the obtained calculation results showed that when the second column precipitation is 2.4 cm or more, the character of the entire structural bifurcation system changes.

Geometric nonlinear dynamic response of wind turbines with different power performance

As the size of wind turbine blades increases, the influence of geometric nonlinearity on aerodynamic, structural and design of blades becomes more and more serious. In this work, the efficient aero-elastic calculation of large flexible blades is studied. In order to solve the problem of efficient aeroelastic caculation of large flexible blades, this work applied the geometrically exact beam theory based on Legendre spectral finite element and coupled with the blade element momentum theory to establish the aero-elastic analysis model of large flexible blades. This model can efficiently calculate the deformation and load on the blade under aerodynamic loading and fully consider the influence of geometric nonlinearity caused by deformation on aeroelastic ability. Taking NREL 5MW and IEA 15MW wind turbines as examples, the linear and nonlinear dynamic responses of these two wind turbine blades are calculated. The result shows that the neglect of nonlinear effect will bring error. From 5MW wind turbine to 15MW wind turbine, the numerical error increased by 27.88%. The influence of geometric nonlinearity of blades on dynamic responses is analysed, which is of great significance to improve the design level of large-scale wind turbines.

МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ В ЗАДАЧАХ ГЕОМЕТРИЧНО НЕЛІНІЙНОЇ ТЕОРІЇ ПРУЖНОСТІ

Розв’язки багатьох важливих для практики задач, що виникають в сучасній техніці, не завжди можуть бути отримані традиційними методами теорії аналітичних функцій або за допомогою інтегральних перетворень. Це відноситься, наприклад, до контактних задач, в яких враховуються скінченні розміри області хоча б в одному напрямку, або досліджуються середовища з криволінійною анізотропією тощо. Засоби математичної теорії пружності виявляються не надто ефективними для дослідження таких задач. У цьому випадку доцільно використовувати досягнення теорії потенціалу. Застосування ж асимптотичних методів при цьому, навіть в складних випадках, дозволяє отримувати обґрунтовані наближені рівняння, уточнювати якісні закономірності і отримувати аналітичні розв’язки задач. У даній роботі представлене узагальнення методу збурень, яке дозволяє звести дослідження складних задач геометрично нелінійної теорії пружності (в плоскій та просторовій постановці) до послідовного розв’язання більш простих крайових задач теорії потенціалу. Геометрично нелінійна теорія пружності містить в собі деякі особливості, завдяки яким вона відрізняється від класичної (лінійної) теорії. Головна відмінність полягає в урахуванні різниці між геометрією недеформованого та деформованого станів досліджуваного тіла, коли мають місце переміщення, які викликають значні зміни геометрії тіла. При цьому рівняння рівноваги необхідно складати з урахуванням зміни форми і розмірів конструкцій. Врахування кінцевих деформацій, які при створенні математичних моделей веде до значних труднощів при розв’язуванні задач, але в той же час наближає модель до реальної проблеми. Метод збурень, що використовується для розв’язання нелінійних рівнянь у частинних похідних, має теоретичне і практичне значення. Він універсальний і може використовуватися для аналізу різних завдань математичної фізики. Розроблений підхід може бути застосований для вирішення завдань, в яких істотну роль грають залишкові деформації. Наприклад, згин тонких пластин і оболонок. У розглянутій модельній задачі вдалося виділити вплив геометричної нелінійності на напружено-деформований стан досліджуваного тіла. Саме тому результати представленої роботи мають як теоретичне, так і прикладне значення, а дослідження є актуальним.

Physical and geometrical nonlinear forced oscillations of beams

The paper presents a calculation method and the results of modeling the nonlinear forced planar oscillations of a beam. The calculation approach is based on the method of weighted residuals in the Galerkin form in combination with numerical methods of integration over time. A sequential analysis of elastic linear and geometrically nonlinear oscillations is performed and the case of irreversible deformation due to the occurrence of physically nonlinear creep strains is considered. To describe it, the Norton power law is used. Cases of hinge supported and a cantilever beam are considered. When solving the problem of a hinge supported beam, the sine system was used as the basis functions, and the Krylov functions were used for the cantilever beam’s problem. The results of numerical modeling are presented in the form of the dependence of the beam deflections on time and on the coordinate at a given point in time. The influence of geometric nonlinearity is demonstrated. The increase in deflection with time due to an increase in creep strains is analyzed.

Large amplitude vibrations of a deepwater riser conveying oscillatory internal fluid flow

A marine riser operated in deepwater could encounter harsh environmental conditions and exhibit complex vibration phenomena which require thorough investigation, especially using nonlinear geometric diagnosis. The aim of this paper was to propose a theoretical formulation for undertaking large amplitude vibration analysis of a deepwater marine riser conveying oscillatory internal fluid flow. The work-energy principle based on virtual displacement was utilized to formulate the riser mathematical model, accounting for internal strain energy and external work done. The geometric nonlinearity of the riser regarding extensible elastica theory was considered, which accounted for axial stretching and the large deformed curvature of the riser. The finite element method was utilized to form the equation of the motion system for solving numerical solutions. Based on Taylor's series expansion, the stiffness matrices with second-order nonlinear dynamic displacements of the riser were regarded in the equation of motion. The hydrodynamic ocean force modeled in terms of the squared riser velocity also yielded the nonlinear hydrodynamic damping matrix. The inertial force initiated by the pulsatile flow of transported fluid was taken into account as a harmonic oscillation representing the pump operation. Performing the Newmark time integration incorporated direct iteration on the equation of motion provided the nonlinear vibration response. A thorough parametric study was accomplished which investigated the influences of geometric nonlinearity, the forcing frequencies of a hydrodynamic wave, and an internal pulsatile flow on the large amplitude dynamic response characteristics of a deepwater riser.

Influence of geometric nonlinearity of rectangular plate on vibration reduction performance of nonlinear energy sink

The differences between the vibration reduction of a NES (nonlinear energy sink) on a nonlinear plate and a linear plate are compared, and the effect of NES on the nonlinear plate is mainly analyzed. The nonlinear equations of the plates connected to NES are derived and subsequently solved by the complexification-averaging method and least square method. The amplitude of the first mode of the nonlinear plate is several times higher than that of the linear plate under large excitation when the two plates are attached to identical NES. The amplitudes of the second mode of the two NES equipped plate are similar. However, super-harmonic resonance responses of the two systems are significantly different. The evolution of the higher branch responses in super-harmonic resonance frequency band of the second mode is analyzed, and found to be significantly different with respect to that in the primary resonance frequency band of the first mode.