Nonlinear Dynamic Finite Element Research Articles

An explicit time integration algorithm for linear and non-linear finite element analyses of dynamic and wave problems

PurposeThe purpose of this paper is to propose a new explicit time integration algorithm for solution to the linear and non-linear finite element equations of structural dynamic and wave propagation problems.Design/methodology/approachThe algorithm is completely explicit so that no linear equation system requires solving, if the mass matrix of the finite element equation is diagonal and whether the damping matrix does or not. The algorithm is a single-step method that has the simple starting and is applicable to the analysis with the variable time step size. The algorithm is second-order accurate and conditionally stable. Its numerical stability, dissipation and dispersion are analyzed for the dynamic single-degree-of-freedom equation. The stability of the multi-degrees-of-freedom non-proportional damping system can be evaluated directly by the stability theory on ordinary differential equation.FindingsThe performance of the proposed algorithm is demonstrated by several numerical examples including the linear single-degree-of-freedom problem, non-linear two-degree-of-freedom problem, wave propagation problem in two-dimensional layer and seismic elastoplastic analysis of high-rise structure.Originality/valueA new single-step second-order accurate explicit time integration algorithm is proposed to solve the linear and non-linear dynamic finite element equations. The algorithm has advantages on the numerical stability and accuracy over the existing modified central difference method and Chung-Lee method though the theory and numerical analyses.

Research on the simulation modelling of high‐voltage switchgear ring‐shaped spring contact force

In order to explore the simulation method of the contact force for the ring-shaped spring and provide the support for the design of high-voltage switchgear-rated current and mechanical operating power, the parametric equation was derived, based on NX software the three-dimensional model was built, considering the influence of contact, friction, and large deformation, the non-linear dynamic finite element simulation model for the process of assembling and operating was established, the stress, resistance force, and friction force at any moment were obtained by simulation, and the variation of resistance and friction force during contact insertion was analysed. The results show that during the mechanical operating process, the resistance force rapidly increased to the extreme value and then gradually decreased to a stable value of 238N, and the friction force quickly increased and then slowly rose to the steady value of 238N, which is consistent with the experience and proved the rationality of the simulation model. Finally, according to the Coulomb friction law, the contact force of the spring contact was calculated as 1190N.

BEHAVIOR OF REINFORCED CONCRETE SLABS UNDER ACCIDENTAL IMPACTS

Loads resulting from activities such as rock fall, heavy drop weights (for e.g. equipment's, heavy machines during installation), missile and aircraft interaction with slabs may results in loading intensity which have higher magnitude as compared to static loading. Based on the velocity of the impacting object at the time of contact, these activities may result in impact loading. Therefore, slabs designed should provide resistance to these accidental loading during their entire operational life. In this study, a dynamic non-linear finite element analyses were conducted to investigate the behavior of the reinforced concrete slabs subjected to high-mass low-velocity impacts. For this purpose, initially an already published impact test results were used to validate the numerical predictions. Following validation, a study was conducted to investigate the influence of the impact velocity on the behavior of the reinforced concrete slab. Based on the numerical investigation, it was found that the velocity of the impacting object has a significant influence on the behavior exhibited by slab under impact loading. Furthermore, it was also found that the behavior of slab under impact is both local and global. Local behavior is associated with the damage caused at the contact area of the slab and the impactor, whereas global behavior refers to the overall deformation of the slab when stress waves move away from the impact zone and travel towards the supports.

Axial crushing analysis of polyurethane foam-filled combined thin-walled structures: experimental and numerical analysis

Axial crushing behaviour of the polyurethane foam-filled aluminum cylindrical tubes with shallow spherical caps (combined thin-walled structures) is studied both experimentally and numerically. Non-linear dynamic finite element analyses were carried out to simulate the quasi-static tests. Satisfactory agreements were generally achieved between the finite element model and experimental deformed shapes, load–displacements, fold lengths and specific energy absorptions. Influence of important parameters such as semi-apical angle, length of cylindrical and spherical caps, diameter and density of foam filler was discussed and the results highlight the advantages of using foam-filled shell of the combined geometry as energy absorber.

Study on the calculation method for dynamic wind deflection of transmission line in strong wind area

In order to improve the design and early-warning accuracy for wind deflection of transmission line in strong wind area, it is necessary to calculate the dynamic wind deflection of transmission line in consideration of fluctuating wind effect. In this paper, the generation method for fluctuating wind velocity in consideration of spatial correlation is discussed, then the wind load on every element node of conductor is determined on the basis of the calculation formula for wind load, and finally the dynamic wind deflection angle of insulator and the dynamic wind deflection displacement of conductor is calculated by using the nonlinear dynamic finite element method.

Experimental and numerical simulation study of perforation effect of steel pipes subject to the impact loadings of ASC and LSC jets

The perforation effect of steel pipes subjected to the circular-shaped charge (ASC) and linear-shaped charge (LSC) jet were studied by experimental research, and the explicit nonlinear dynamic finite element computer code LS-DYNA was adapted to study the nonlinear responses of the steel pipes, which subjected to the impact of the two different jets, using Lagrangian-Eulerian coupling method. The deformation process and the stress of the steel pipes were described and analyzed, and the simulation results are in good agreement with the experiment data. The studies indicated that under the impact of ASC jet, the steel pipe got a circular incision and a deformation process of local perforation, flocculent shear lip forming and axial shock. Under the impact of LSC jet, the steel pipe got a ship-type incision and a deformation process of coupling of local perforation and dent, whole bending and radial shock. The formation of flocculent shear lip attributes to the radial stress concentration. Under the impact of LSC jet, the whole bending leads to the axial stretch and tearing of the cut tip, and there is a bigger radial plastic deformation area than the damage effect for the impact of ASC jet.

Simulation and experimental investigation of high-speed projectile impacting closed-cell aluminum foam

In order to analyze the impact acceleration of the projectile impacting the aluminum foam material, a dynamic non-linear finite element model of the projectile impacting the closed-cell aluminum foam experiment device was established and verified by the experiment. It is found that the numerical simulation results of projectile impact closed-cell aluminum foam are consistent with the change of experimental results. When the projectile impacts the homogeneous closed-cell aluminum foam, the impact acceleration is trapezoidal and the impact peak and pulse width are related to the density of the aluminum foam material. With the increase of the porosity of the aluminum foam, the peak value of the acceleration rises and the pulse width of acceleration decreases.

Development and assessment of efficient models for barge impact processes based on nonlinear dynamic finite element analyses

The impact of vessels straying out of control poses a serious hazard for bridge piers located in navigation waterways. In order to accurately predict the dynamic responses of the bridge piers subjected to barge impact and to design bridge piers which can resist such impact, the impact forces need to be accurately defined. Empirical formulas such as those provided by AASHTO Guide Specification are currently extensively used for predicting the equivalent static impact forces. Whilst such equivalent static methods cannot accurately reflect the actual dynamic phenomena in a barge impact event, sophisticated finite-element (FE) simulations are computationally expensive. This paper aims to establish a coupled model which can replicate the complex full barge impact model (FBIM) with sufficient accuracy. In this coupled model, the barge model is simplified into a mass-spring model (MSM) whilst the pier is modeled using discrete masses and discrete beam elements. The parameters introduced by MSM are determined using the proposed strategies in this paper. Linear elastic pier columns with fixed bases and cantilevered tops are employed to assess the prediction quality of the proposed coupled model for different impact scenarios.

Proposal of Failure Mode Map Under Dynamic Loading—Ratcheting and Collapse

Ratcheting, collapse, and fatigue are the probable failure modes which can occur under alternate dynamic loading like seismic loading. The objective of this study is to propose a failure mode map for rectangular beams by determining the conditions of occurrence of the ratcheting and collapse failure modes. The paper considers the analogy between thermal ratcheting and dynamic ratcheting. The nonlinear dynamic finite element method was used to analyze a rectangular beam model for different loading conditions. The results were plotted on a nondimensional primary and secondary stress parameter graph similar to the Bree diagram for thermal ratcheting. The similarity between thermal load and dynamic load was observed. The main difference between thermal and dynamic loading is the effect of the frequency of dynamic loading on the occurrence of ratcheting and collapse. Experimental observations of ratcheting have been obtained and are used for comparison to validate the analytical predictions. From the above results, a failure mode map has been proposed which can evaluate the occurrence conditions of ratcheting and collapse under dynamic loadings.

Nonlinear seismic analysis of a high-pier, long-span, continuous RC frame bridge under spatially variable ground motions

Many very large bridges with high piers and long spans are under rapid construction in mountainous regions especially in Western China. However, the current seismic design methods in China are based on a code which only applies to bridges with span up to 150 m. To evaluate the risk of the inapplicable design method and the influence of spatially variable ground motions (SVGM) on the seismic response of very large bridges, a high-pier, long-span, continuous RC frame bridge is numerically studied. This study considers whether multiple support excitation can be simplified into specific uniform excitation cases while guaranteeing the conservative seismic demands for this bridge. Non-stationary SVGM on both bedrock and the surface of multiple soil layers are simulated including wave passage effects, coherency effects and site amplification effects. The nonlinear dynamic finite element model of the bridge is analysed for two groups of earthquake motions, namely group 1 - bedrock and group 2 - ground surface excitations. Each group contains three different excitations, i.e. i) multiple support excitation ii) the largest and iii) the smallest accelerations from the SVGM. The relative displacements, internal force responses and ultimate damage modes are obtained and compared. For this bridge the uniform ground motion input with the largest accelerations provides conservative seismic demands for most structural components when the site amplification effect is not considered (group 1). However, for the ground surface motions, where site amplification needs to be taken into account (group 2), in several cases the uniform ground motion with the largest accelerations results in lower response than that predicted when considering SVGM. The present results indicate that only when the bridges are located on ideal simple topography where site effects have little influence, the uniform excitation with the largest accelerations taken from the SVGM may be an alternative input for seismic analysis. However, for bridges on complex terrain, where site effects can significantly amplify the ground motions at the bedrock, SVGM need to be applied as input for the seismic analysis. As spatial variability of input motion is not a mandatory requirement in the Chinese bridges design code, these results suggest that the existing design code for very large bridges should be modified accordingly.

Physics Based Methodology for the Estimation of Bearings' RUL: Physics-Based Models, Diagnostic Methods and Experiments

Rolling element bearing (REB) is one of the basic mechanical components in a rotating machinery. REBs’ remaining useful life (RUL) estimation allows not only to assess time for maintenance actions but also can prevent a critical failure of the mechanical system. Usually, REB damage occurs in two stages, damage initiation and damage propagation. In the current work, it is assumed that spall is generated on the surface of the raceway during the initiation stage. The spall generation process is modeled based on continuum damage mechanics with the representation of material grain structure and implemented using a Finite Element (FE) software. The results of the model are in a good agreement with published theoretical and experimental data. However, after the first spall formation, the bearing might be fully operational for millions of cycles. For estimation of the bearing RUL it is important to understand the damage propagation process. The material behavior at the trailing edge of the spall during the rolling element (RE) impact is analyzed. The analysis is carried out by using a hybrid modeling approach. This approach integrates non-linear dynamic modeling and FE simulations. The paper also includes a discussion on the ongoing research and the methodology for the development of the prognostic method. Implementation of the proposed methodology has the potential to provide a complete estimation of the bearing’s RUL: from first spall formation to the un-operational bearing.

A nonlinear dynamic finite-element analyses of the basketball-related eye injuries

Eye injuries from blunt forces and penetrating objects can cause morbidity, disability, and blindness. Most of these injuries are preventable not only by understanding the detail of injury, but also by portraying the role of the ball’s characteristics. Basketball can induce severe forms of injuries to the eye. This study was aimed at performing a numerical analysis through the fluid–structure interaction on ocular trauma. Balls with different diameters, elastic moduli, and pressures were shot to the eye. Injury in terms of the stresses and deformations in each component of the eye was computed at ~ 0.72 mm deformation in the apex of the cornea. By increasing the diameter of the ball from 20 to 26 cm the stress in the eye components, excluding the aqueous body, vitreous body, and extraconal fat, increased. Stresses of 2.68 and 3.19 MPa were observed in the cornea under the ball diameters of 20 and 26 cm, respectively. Conversely, the elastic modulus and pressure of the ball in the defined range showed no considerable role on the stress in the eye components. The results revealed the importance of the ball size compared to the elastic modulus and pressure in the stress accumulation as a result of ocular trauma.

Modelling UHPFRC tension behavior under high strain rates

The advantages of Ultra High Performance Fiber Reinforced Concrete (UHPFRC) under static loads suggest it is a promissory material to withstand dynamic and especially extreme loads. However, the available results concerning dynamic behaviour of UHPFRC under high strain rates are still rather limited and there are some aspects that require further analysis and the development of numerical tools. A numerical model for UHPFRC is presented and applied to the simulation of high strain tension tests in this paper. The tension tests were performed in a Modified Hopkinson Bar with different strain rates and they include UHPFRC using different contents and orientations of smooth straight steel fibers. The numerical model is based on the modified mixture theory and takes into account the behaviour of the matrix and the fibers and the fiber/matrix sliding using a meso-mechanic pull-out model. The model was implemented in a non-linear dynamic finite element explicit code that constitutes a useful numerical tool for the design and analysis of structures made of this material. High strain rate tension tests were numerically simulated. The comparison of numerical and experimental results allows calibrating the material properties, validating the model and analysing the strain rate dependence of the composite and the contribution of each of the component materials and the pull-out mechanism. Tension dynamic amplification of UHPFRC is mainly due to the Ultra High Performance Concrete (UHPC) matrix and the pull-out mechanism. The dynamic amplification of the fibers pull-out mechanism is lower than that of the matrix and increases with fiber inclination.

Comparison of ultrasonic wire bonding process between gold and copper by nonlinear structure analysis

Wire bonding is one of the most important processes which connected the chip and lead frame in microelectronics packaging. Due to the expensive price of gold, copper wire and aluminum wire gradually become the substitutes of gold wire in the process of bonding. Meanwhile, changes in the materials result in a series of problems, such as violent wear of capillary and less reliable production on account of its higher Young modulus. However, the tiny range of parameter values for stable process makes it difficult to do experiment. In order to observe the process of thermalsonic bonding and find out the influence of new material in bonding stage, a transient nonlinear dynamic finite element framework is developed in this paper. A comprehensive parametric study which includes different thickness of bond pad and material of bond wire were conducted in this research to improve the reliability of wire bonding. The comparison between copper and gold wire bonding process on the third generation LEDs is introduced. As a result, this numerical simulation framework is of great importance to the development of LEDs packaging.

Numerical investigation of nonlinear fluid–structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid–structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

Structural Optimization for Roof Crush Test Using an Enforced Displacement Method

A roof crush test has been utilized to reduce passengers’ injuries from a vehicle rollover. The Federal Motor Vehicle Safety Standards (FMVSS) 216 and the Insurance Institute for Highway Safety (IIHS) perform actual vehicle tests and evaluate the vehicle’s ratings. Nonlinear dynamic response structural optimization can be employed not only for achievement of a high rating but also minimization of the weight. However, the technique needs a huge computation time and cost because many nonlinear dynamic response analyses are required in the time domain. A novel method is proposed for nonlinear dynamic response structural optimization regarding the roof crush test. The process of the proposed method repeats the analysis domain and the design domain until the convergence criteria are satisfied. In the analysis domain, the roof crush test is simulated using a high fidelity model of nonlinear dynamic finite element analysis. In the design domain, a low fidelity model of linear static response structural optimization is utilized with enforced displacements that come from the analysis domain. Correction factors are employed to compensate the differences between a nonlinear dynamic analysis response and a linear static analysis response with enforced displacement. A full-scale vehicle problem is optimized with a constraint on the rigid wall force from the analysis in the design domain.

Mechanical response of a lined pipe under dynamic impact

Abstract An experimental and numerical investigation on the mechanical response of a lined pipe (compound pipe) under a dynamic impact is presented. The influence of the impact energy has been studied in terms of the depth of the dent formed, and of the strains and residual stresses. To this end, a three-dimensional explicit dynamic non-linear finite element model has been developed and successfully validated against the results of impact-test experiments conducted on pipes made of AISI 10305 steel, with and without the AISI304 stainless steel liner. The validation was made by comparing numerically computed strains with those measured by strain gauges, as well as in terms of permanent deformation. The model is then utilized to evaluate the residual stresses, the amount of energy dissipation and the velocity of impact process as a function of different pipes (i.e. with or without liner) and of the free drop heights.

Research and application of reaming subsidence control in horizontal directional drilling

In the reaming operation of horizontal directional drilling, a centralizer is often attached to a reaming-bottomhole assembly (R-BHA) to change the reamer side force. This can address the problem of large-diameter reamer subsidence. However, there is no scientific basis for how to attach the centralizer in the R-BHA. In this paper, an equation for the reamer side force in a two-centralizer R-BHA is derived, based on three moment equations. Then, using the Drucker-Prager criterion as a rock constitutive relation and the shear criterion for predicting damage initiation, a nonlinear dynamic finite element model is established using the finite element method (FEM). In addition, the trajectory of the reamer and the failure of the drilling tools are analyzed. The study results show that the combination of the analytical and finite element methods can effectively improve the installation accuracy of the centralizer. The attachment range of the centralizer can be quickly determined by a simple calculation of the analytical method, and the FEM (with high computational precision) can be used to analyze the subsidence control capacity of the R-BHA in detail. Application to a field case demonstrates the feasibility of the method, and the study conclusions provide a scientific basis for the centralizer attached to the R-BHA, which is important for controlling reaming subsidence.

A nonlinear dynamic corotational finite element model for submerged pipes

A three dimensional finite element model is built to compute the motions of a pipe that is being laid on the seabed. This process is geometrically nonlinear, therefore co-rotational beam elements are used. The pipe is subject to static and dynamic forces. Static forces are due to gravity, current and buoyancy. The dynamic forces exerted by the water are incorporated using Morison’s equation. The dynamic motions are computed using implicit time integration. For this the Hilber-Hughes-Taylor method is selected. The Newton-Raphson iteration scheme is used to solve the equations in every time step. During laying, the pipe is connected to the pipe laying vessel, which is subject to wave motion. Response amplitude operators are used to determine the motions of the ship and thus the motions of the top end of the pipe.

A 3D FEM model for floating wind turbines support structures

The relevance of the interaction between the structural stiffness and the wind turbine dynamics are well known by the industry from decades of expertise. However, the novel floating concepts are commonly designed by tools that disregard the individual structural stiffness of the elements which compose the floating platform. Usually, these elements are treated as rigid body elements in the design process. However, their flexibility can be relevant in the long time structural life assessment, particularly for the fatigue assessment. Then, a structural analysis that includes the dynamic effects over the deformation of the structure is required. The paper proposes a model that integrates the instantaneous deformation of the structure by a nonlinear dynamic Finite Element Analysis (FEA) computation in a fully coupled Offshore Wind Turbine (WT) model in the time domain.A 3D hydro-aero-servo-elastic coupled numerical model in time domain for structural analysis of floating or bottom fixed structures has been developed at the UPC-BarcelonaTech. The code integrates the forces exerted by the waves and currents as well as the aerodynamic loads, including the wind turbine, and the mooring system. For the hydrodynamic loads the Morison’s equation is used to compute waves and current forces. Both Airy (regular and irregular) and Stokes 5th order wave theories are implemented. The mooring system can be computed in a quasi-static way or considering their fully dynamics. The aerodynamic loads are computed with AeroDyn standalone module from NREL, which is coupled to the FE model. The structure is discretized with one-dimensional beam finite elements, in which the formulation considers small strains as well as large motions under the implementations of the Euler beams theory. With this approach, the dynamic interaction between the wind turbine and the structure, as well as the effects on the internal forces are implicitly coupled in the formulation.A comparison of the Windcrete concrete SPAR concept experimental Response Amplitude Operators (RAO) against the numerical results are presented, as well as some results from simulations under normal operation conditions.