Large Deformation Effects 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 large deformation multiphase continuum mechanics model for shock loading of soft porous materials

AbstractA large deformation, coupled finite‐element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain‐rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one‐dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed‐form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain‐rate, and (iii) showing differences in deformations between a single‐phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain‐rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single‐phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain‐rate loading of soft porous materials. It was discovered that explicit, adaptive time‐stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time‐stepping schemes for shock‐like loadings. Shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

Research on the breakage and fractal characteristics of calcareous sand

Calcareous sand is widely used in coastal engineering and island construction, which has the characteristic of easy crushing. A series of ring shear and one-dimensional compression creep tests were carried out for the crushing evolution under the influence of large deformation and time length effects. The mechanical characteristics and deformation properties of the single-graded specimens were analyzed, focusing on the crushing characteristics, and fractal properties under the action of different shear displacements, stress levels, initial gradations and creeping motion effects. The results show that the fractal dimension is positively correlated with crushing, the increase of shear displacement, stress level, and initial mean particle size has a facilitating effect on crushing. Under large deformation conditions, this promoting effect gradually tends to slow down, and the characteristic of limit fractal exists. The creep behavior reflects the continuous deformation characteristics of calcareous sand, and the specimen as a whole is still in the stage of crushing development, and the effect of time duration on the fractal is limited.

Experimental and Numerical Study on Dynamic Response of Foam-Nickel Sandwich Panels under Near-Field Blast Loading.

The explosion products, such as shock waves, fragments and heat energy formed by explosion, act on the plate structure, which may cause structural damage, material failure and even phase transformation of material. In this paper, the damage mechanism and protective effect of near-field blast load on sandwich structure based on foam-nickel core material were studied. Firstly, the near-field explosion test was conducted to investigate the blast response of the foam-nickel sandwich structure subjected to blast shock from 8701 explosive at near-field position. The deformation characteristics and stress history of the sandwich structure on the acting location of blast load were carefully investigated via experimental methods. A finite element model of near-field explosion was established for effective numerical modelling of the dynamic behaviour of the sandwich structure using the explicit dynamics software ANSYS/LS-DYNA for more comprehensive investigations of the blast shock response of the sandwich structure. The finite element model is reasonable and validated by mesh independence verification and comparing the simulated response behaviour to that from the experimental results for the sandwich structure subjected to near-field blast load. On this basis, the damage mechanism and protection effect of the near-field explosion impact on foam-nickel cores with different density and porosity are simulated more systematically. The investigated results from the experiments and a series of numerical simulations show the large deformation effect due to the extensive energy absorption, which suggests that the sandwich structure based on foam-nickel core material may be expected to become a new choice of protective structure under near-field blast load.

Determining the Soil Modulus for Use in Soil–Pipe Interaction Modeling

Research and engineering practice for the earthquake, landslide, or tunneling response of underground pipelines has focused on large ground deformation (LGD) effects, recognizing that LGD often causes the most serious local damage in buried pipelines. The adjacent soil reaction that develops as the pipe moves, i.e., soil–pipe interaction, is of key importance in the response of underground pipelines subject to LGD. A finite-element elastoplastic model can be used to analyze the soil–pipe interaction, and the model requires a soil modulus to simulate the force versus displacement behavior. In the simulation of soil–pipe interaction, a secant modulus associated with high stress and strain should be used in the finite-element model rather than an initial tangent modulus. This research provides a strain-compatible secant modulus that can be used in a finite-element analysis (FEA) of soil–pipe interaction for lateral, upward, downward, and oblique pipe movements. The favorable comparison between the experimental data and the FEA using the strain-compatible secant modulus implies that the proposed approach is suitable to predict soil–pipe behavior under large ground deformation.

Influence of Single External Store on Geometrical Nonlinear Flutter of High-aspect-ratio Wings

High-altitude and long-endurance UAVs, distributed electric propulsion aircraft and large passenger aircraft often use high-aspect-ratio wings, which have obvious geometric nonlinear large deformation effect, and are usually arranged with a certain number of external stores, which have an impact on their geometric nonlinear aeroelastic characteristics. Based on the “quasi-linear” hypothesis, the updated Lagrange incremental finite element method and doublet-lattice method are used to perform the geometrically nonlinear static aeroelastic analysis, and the mass, stiffness and aerodynamic matrices of large deformation are updated, and the geometrically nonlinear flutter characteristics of high-aspect-ratio wings are calculated. The influence of the position and mass of the external store on geometrical nonlinear flutter characteristics of high-aspect-ratio wing structure is investigated. Results show that the change of the position and mass of the external store causes the relative position between the elastic axis and the center of gravity of the wing, and the wing’s large deformation equilibrium state to change, resulting in differences in the stiffness characteristics of the wing and the natural vibration frequency of the equilibrium state, thus affecting the wing flutter characteristics. When a single external store is installed near the wing root, changing the mass and direction of the store has no significant effect on the geometric nonlinear flutter characteristics of the wing. The improvement of wing flutter speed is most obvious when the hanging point is moved to the leading edge of the wing near 0.65 times the wingspan.

A Mixed Model Representing Accurately the Inelastic Behavior of Multi-storey Buckling Restrained Braced Frames

Seismic structural fuses such as buckling restrained braces (BRBs) are highly nonlinear members that need a detailed finite element model (FEM) to represent their actual behavior. On the other hand, making detailed model for the whole building from solid or shell elements to be consistent with the model of BRBs would require expensive computational time and large storage space especially when performing nonlinear time history analysis (NTHA). Therefore, a mixed FEM is developed in this research so that the solid elements are used for the core plate and the restraining system only. The non-yielding segments of the BRBs and the conjoined girders and columns are simulated using beam elements with nonlinear material properties while the effect of large deformations is taken during analysis and this was able to represent plastic hinge formation, plastic rotations and residual displacements in such members. A beam-solid transfer mechanism is developed to properly transfer forces between the non-yielding segments of BRB and the inner solid plate. The core plate is connected to the surrounding restraining system with contact elements to simulate the normal and frictional forces generated upon contact based on the penalty algorithm. This model was validated using the data and the results of an experimental work mentioned in the literature where very good agreement was achieved. Thereafter, a rehabilitation study for the SAC 9-storey building was performed. The results showed how the BRBs work as structural fuses during earthquakes and confirmed the ability of the model to represent inelastic behavior of multi-story BRBFs.

Curvature Correction of a Notched Continuum Robot Based on a Static Model Considering Large Deformation and Friction Effect

Continuum robots are often used as wrist joints in medical robots because of their high dexterity and flexibility. Especially, the notched continuum robot (NCR) is used in the miniaturized wristed surgical robot. The Piecewise Constant Curvature (PCC) assumption is often used in the design of NCR. However, due to the friction effect, ideal PCC is difficult to achieve. Static analysis is a necessary means to correct the curvature of NCR. The static modeling of NCR is often based on the theory of small deformation. However, this cannot obtain accurate solutions at large bending angles. In this paper, a static model of a triangular-notched continuum robot is proposed. It presents a curvature correction method of NCR, considering large deformation. In addition, the friction effect is considered in the correction of PCC. The static model is derived from the end notch. Based on the Coulomb friction model, the recurrence relationship of the force on the cable is obtained. Then the elliptic integral solution corresponding to the large deformation assumption is calculated. The deformation parameters of the NCR are obtained by numerical iteration. Finally, the capability and validity of the static model proposed in this paper are verified in the experiment. This paper is of great significance for establishing an accurate static model for curvature correction and design of the notched continuum robot.

Theoretical analysis and application research on local toggle energy dissipation device

The toggle-brace-damper system (TBDS) can obviously improve the energy dissipation efficiency of a damper by amplifying its deformation. The small deformation solution is widely used to characterize the amplification capacity of the TBDS. However, the parameters of the small deformation solution are not mutually independent. Furthermore, as the small deformation solution is a constant, it cannot comprehensively characterize the mechanism of the TBDS. These drawbacks hinder a more in-depth study of the TBDS mechanism. In addition, the existing TBDS requires a large building space, which adversely affects the layouts of doors and windows. In view of the problems above, a space-saving local toggle-brace-damper system (LTBDS), as an extended form of the TBDS, is proposed. The displacement amplification factor considering the large deformation effect is derived. The variation law of this amplification factor with the lateral displacement is clarified. The local toggle energy dissipation device (LTEDD), which consists of two identical and symmetrically arranged LTBDSs, is recommended to overcome the LTBDS’ amplification capacity asymmetry. The effects of the geometric parameters on the amplification capacity of the LTEDD are clarified. A geometric optimization method to improve the amplification capacity of the LTEDD is proposed based on the estimation of the maximum lateral displacement of the LTEDD under earthquakes. To estimate the maximum lateral displacement of the LTEDD and calculate the additional damping ratio contributed by the LTEDD damping system, the storey drift utilization ratio is proposed, and the calculation method is derived and verified. Finally, the case analysis verifies the feasibility of the LTEDD and the effectiveness of the optimization method.

Global and local modeling for inter‐wire fretting in multi‐wire copper conductors

AbstractSubmarine power cables (SPC) are vulnerable to fretting, wear, and fatigue due to the dynamic environment, particularly at end connectors and junctions or other discontinuities, such as seabed features. This paper presents a finite element methodology for global and local analysis of fretting between copper conductors in multi‐strand cables. The salient inter‐wire fretting variables, such as relative slip and contact pressure, almost impossible to measure experimentally, are identified here via the three‐dimensional, global multi‐wire model, which includes frictional contact and large deformation effects. Local 2D and 3D representative models, typical of laboratory‐scale fretting test configurations, are adopted, with fretting boundary conditions derived from the global model fretting variables, for detailed micro‐scale resolution of fretting contact. A critical‐plane, multiaxial fretting‐fatigue life methodology is implemented to quantify fretting‐fatigue life. The effects of lay angle, contact size, wire diameter, friction, and slip are investigated. It is shown that, in general, increasing lay angle, contact size, wire diameter, and friction lead to reduced life. A key novel contribution of the paper is identification of the fretting fatigue relationships between representative local 2D (Hertzian) and 3D (crossed cylinder) modeling, via matching contact pressure, and global multi‐wire contacts. A rationalization of the relative contact size effects associated with transverse‐ and longitudinal‐type contacts in such applications is also presented.

Enhancement in Rejected Heat from Heat Sinks Using High Flexible Winglets with Large Deformation and Low Blockage Effect

This paper presents an original concept of using high flexible flapping vortex generator in a heat sink for airside heat transfer augmentation. The proposed thin winglet, made with an elastic sheet, is responsible for increasing the cooling rate and mixing quality performance in laminar convection airflow. This study focuses on the excessive bending of the flapping winglet and reducing its blockage effect and pressure drop. This novel concept is demonstrated using a numerical simulation of the flow field with a coupled Fluid-Solid-Interaction technique in transient conditions. The continuity, momentum, and energy equations for forced convection airflow are solved by the finite element method using the COMSOL Multi-physics. Numerical results reveal high amplitude for the flapping vortex generator while under a large deformation and bending. This behavior leads to flow mixing with a small blockage effect due to the deformed aerodynamic shape of the winglet. The present findings show that the high flexible winglet enhances the rejected heat by 100%, with a 33% decrease in pressure drop compared to the rigid vortex generator at the same air velocity.

Band gap tuning through microscopic instabilities of compressively loaded lightened nacre-like composite metamaterials

Large deformation effects give the opportunity for tuning and manipulating the dynamic properties of periodic microstructured materials, including those related to vibration control and band gap phenomena. We investigate the wave propagation properties in bioinspired nacre-like composite metamaterials subjected to uniaxial loading processes, also considering the onset of instabilities at the microscopic and macroscopic scales. The dynamic response of a new 2D lightened brick-and-mortar microstructure containing periodically arranged cavities is investigated, by analyzing the propagation of elastic waves superimposed on a deformed state by means of a Bloch-wave analysis. The band gap properties of the proposed advanced metamaterial were investigated in terms of spectral quantities as a function of the main geometrical parameters and of the level of applied deformations. Numerical results have shown that the elastic wave propagation is strongly influenced by the prestress state inducing microscopic instability, thus providing new opportunities to design periodic bioinspired composite metamaterials characterized by wave absorption capabilities as a function of microstructural evolution.

Spatial Rigid-Flexible-Liquid Coupling Dynamics of Towed System Analyzed by a Hamiltonian Finite Element Method

An effective Hamiltonian finite element method is presented in this paper to investigate the three-dimensional dynamic responses of a towed cable-payload system with large deformation. The dynamics of a flexible towed system moving in a medium is a classical and complex rigid-flexible-liquid coupling problem. The dynamic governing equation is derived from the Hamiltonian system and built-in canonical form. A Symplectic algorithm is built to analyze the canonical equations numerically. Logarithmic strain is applied to estimate the large deformation effect and the system stiffness matrix will be updated for each calculation time step. A direct integral solution of the medium drag effect is derived in which the traditional coordinate transformation is avoided. A conical pendulum system and a 180° U-turn towed cable system are conducted and the results are compared with those retraced from the existing Hamiltonian method based on small deformation theory and the dynamic software of Livermore software technology corp. (LS-DYNA). Furthermore, a circularly towed system is analyzed and compared with experimental data. The comparisons show that the presented method is more accurate than the existing Hamiltonian method when large deformation occurred in the towed cable due to the application of logarithmic strain. Furthermore, it is more effective than LS-DYNA to treat the rigid-flexible-liquid coupling problems in the costs of CPU time.

Large deformation effects on the combustion structure of a hydrogen/air rich premixed flame

The effects of large flame deformation on the premixed flame combustion structure were studied by means of a 2-D numerical experiment with detailed chemical kinetics and accurate transport properties, in which a high-speed unburnt gas volume was injected into a stationary hydrogen-air premixed flame of equivalence ratio 4.5. It was found that an extraordinarily high fuel consumption rate appears in the course of the gas volume penetration into the premixed flame. Full use of the numerical data was made to understand the cause of this phenomenon. It was found that enthalpy accumulation that takes place when the flame merges plays a key role: an increase in high-temperature unburnt O2 produced by the accumulated enthalpy accelerates the productions of OH and O, leading to the acceleration of H2-consuming reactions. A similarly extraordinarily high fuel consumption rate in a turbulent rich premixed flame has previously been observed in the 3-D simulation of a hydrogen jet lifted flame, and therefore the mechanism found in this study may be one of the key mechanisms to understand in the behavior of turbulent premixed flames.

Theoretical analysis and optimization of toggle-brace damper for cable tray system

The cable tray system, one type of non-structural components, may suffer severe damage and even fall in case of earthquakes, causing interruptions to post-earthquake operations and even injuries or casualties. This paper introduces a toggle-brace damper (TBD) into the cable tray system to control its seismic response and damage. However, owing to the large deformation/rotation effect in the TBD equipped cable tray system, the traditional design method based on small deformation assumption is no longer applicable. The new deformation calculations of suspension frame and TBD subjected to displacement loading are established combining the optimization technique and the geometry relationship, respectively. After then, an optimization design method for connecting location of the damper brace is proposed, considering the installation errors, deformation constraints, and loading process. With the aid of numerical analysis, it is found that the large deformation effect and in-plane installation errors have considerable influence on the damping magnification function. Compared with typical seismic resistant elements such as the steel brace, diagonal- and chevron-brace damper, the proposed optimal TBD can dissipate more energy and effectively suppress the vibration of cable tray system.

Electromechanical Model-Based Adaptive Control of Multilayered Dielectric Elastomer Bending Actuator

Abstract Dielectric elastomer (DE) possesses attributes such as large deformation and fast response. As a typical DE actuating structure, the multilayered DE bending actuator (MDEBA) is lightweight and can actuate in relatively low voltage without a rigid frame and pre-stretch. These attributes arouse wide research interest in the MDEBA on the application of soft robots. However, due to its large deformation and nonlinear electromechanical dynamics, the control of MDEBA remains highly challenged. Considering the large bending deformation and gravity effect, we develop an electromechanical dynamic model-based control strategy, which can adaptively compensate for the parameter uncertainties during the actuation of MDEBA. Experimental results validate that this control strategy provides highly enhanced control performance compared to the proportional integral derivative (PID) controller. The electromechanical modeling method and dynamic control strategy may guide the further study of MDEBA, soft robots, and flexible devices.

Analysis of steel tank shell deformation and its impact on further utilisation

Recent research in thin-walled structures and steel structures has demonstrated that, in addition to internal forces and membrane stresses of shells, initial deformation and imperfection components should also be considered when calculating design cases. This paper presents a numerical analysis of a steel water tank with an initial deformation of the shell, which is used in an industrial plant for technological purposes. The steel water tank is a typical type of thin-walled structure for which initial deformation may be important. In the numerical example, a round symmetrical steel tank 2.70 m high is analysed under two states: with an undeformed shell and a deformed shell. The complicated interaction between the initial deformation and the vertical and horizontal stresses is analysed in detail. While the initial deformation of the shell may sometimes reduce stresses, in most cases, it substantially increases the overall stresses of the analysed steel water tank shell, up to 820% (for stresses in the horizontal direction) and up to 3554% (for stresses in the vertical direction). This means that initial large deformation and imperfections effects may play an important role not only in the design of industrial structures like silos and tanks but also for very specific slim, thin-walled structural elements.

Numerical simulation of application effect of FRP on torsional-flexural behavior of RC columns

Regarding to significant effects of torsional loads as well as axial and flexural loads on columns under earthquake loads, strengthening and confinement of the concrete columns with Fiber Reinforced Polymer (FRP) layers is accounted as an appropriate technique to enhance the torsional strength of the column. In the present paper, the numerical simulation of torsional performance of the columns, flexural and axial loads are simultaneously considered. The experimental results from the authors on columns with and without FRP reinforcement with different configurations are used to validate the numerical results. Finite element method and software ABAQUS are applied for simulation. The behavior of concrete is simulated using damaged plasticity model and the behavior of the steel is defined with coordination of yield and ultimate points using bilinear model. Whereas the cyclic loads are applied to the column, the kinematic hardening is used and also the effects of large deformations on the behavior are considered. Moreover, the nonlinear static analysis is applied and the displacement based loads are applied to the models in accordance with experimental loads. The numerical and experimental results are compared and shows less than 5% error.

Investigation of optimum compaction pattern in dynamic compaction operation using numerical simulation of adjacent impacts

ABSTRACT In this study, dynamic compaction in sandy soil has been simulated using a three-dimensional numerical model, considering a cap plasticity model and the large deformation effects. Two different approaches for modelling the tamper impact were considered. After simulation of impact at one point, three-dimensional modelling of two and three adjacent impacts was performed to investigate the effect of various parameters on the amount and extension of improvement in the overlap area. The results of analyses indicate that if the grid spacing in the first phase of dynamic compaction is considered equal to four times the tamper diameter and the impact energy of the second phase equal to or more than 85% of the first phase, the required improvement in the soil mass can be uniformly created until the desired depth.

Influence of Liquid Isoprene Rubber on Strain Softening of Carbon Black Filled Isoprene Rubber Nanocomposites

The reinforcement of rubbers by nanoparticles is always accompanied with enhanced dissipation of mechanical energy upon large deformations. Methods for solving the contradiction between improving reinforcement and reducing energy dissipation for rubber nanocomposites have not been well developed. Herein carbon black (CB) filled isoprene rubber (IR)/liquid isoprene rubber (LR) blend nanocomposites with similar crosslink density (ve) are prepared and influence of LR on the strain softening behaviors including Payne effect under large amplitude shear deformation and Mullins effect under cyclic uniaxial deformation is investigated. The introduction of LR could improve the frequency sensitivity of loss modulus and reduce critical strain amplitude for Payne effect and loss modulus at the low amplitudes. Meanwhile, tuning ve and LR content allows reducing mechanical hysteresis in Mullins effect without significant impact on the mechanical performances. The investigation is illuminating for manufacturing nanocomposite vulcanizates with balanced mechanical hysteresis and reinforcement effect.