Hybrid Finite Element Research Articles

Effect of MWCNTS on mechanical properties of woven fabric hybrid polymeric nanocomposites and finite element analysis of nanocomposite

Effect of MWCNTS on mechanical properties of woven fabric hybrid polymeric nanocomposites and finite element analysis of nanocomposite

Efficient and Rigorous Modeling of Light Scattering From Complex Plasmonic Nanostructures With Multiple Incident Excitations

Optical responses to incident lights with different incident directional angles or polarization angles are often of concern in the analysis of light scattering from plasmonic nanostructures. This leads to a multiple-excitation problem for the modeling and prediction of light scattering. An efficient and rigorous numerical method is presented to deal with this problem. In this method, the hybrid finite element and boundary integral (FEBI) formula is adopted to model the interior complex plasmonic materials and the exterior scattering space rigorously, and a low-rank compressed matrix factorization algorithm based on the FEBI framework is proposed to deal with the multiple-excitation problem efficiently. Numerical experiments are performed to illustrate the effectiveness of the proposed method.

Experimental and Hybrid FEM/Peridynamic Study on the Fracture of Ultra-High-Performance Concretes Reinforced by Different Volume Fractions of Polyvinyl Alcohol Fibers.

In this study, a series of three-point bending tests were carried out with notched beam structures made of polyvinyl alcohol (PVA) fiber-reinforced ultra-high-performance concrete (UHPC) to study the effect of volume fractions of PVA fibers on the fracture characteristics of the UHPC-PVAs. Furthermore, in order to meet the increasing demand for time- and cost-saving design methods related to research and design experimentation for the UHPC structures, a relevant hybrid finite element and extended bond-based peridynamic numerical modeling approach is proposed to numerically analyze the fracture behaviors of the UHPC-PVA structures in 3D. In the proposed method, the random distribution of the fibers is considered according to their corresponding volume fractions. The predicted peak values of the applied force agree well with the experimental results, which validates the effectiveness and accuracy of the present method. Both the experimental and numerical results indicate that, increasing the PVA fiber volume fraction, the strength of the produced UHPC-PVAs will increase approximately linearly.

Effects of installing concrete deck on noise radiation of steel box girders: Mechanisms, modeling, and analysis of influential factors

Steel–concrete composite box girder (SCC BG) is widely used in engineering because it can make full use of the tensile properties of steel and the compressive properties of concrete. However, research on the vibrational transmission and vibroacoustic response of the SCC BG is still relatively rare. In this study, a laboratory hammering test was performed to obtain the dynamic characteristics of a scaled specimen of an SCC BG before and after installing a concrete deck. The experimental results revealed that the vibroacoustic response was greatly reduced after the installation of concrete deck due to a reduction in the transmission of on-deck vibrations to the steel box girder. Following this, we introduce a model to predict the structural vibroacoustic response of the SCC BG based on the hybrid finite element–boundary element–statistical energy analysis method, and verify its accuracy through experiments. The accurately calibrated model is then used to study the characteristics of vibration transmission between plates of the SCC BG. The influences of the thickness of the concrete deck, concrete material, and degree of shear connection on vibroacoustic responses of the SCC BG are also discussed.

Seismic assessment of masonry vaults by means of an advanced hybrid FEM-DEM modeling strategy

The current work presents a hybrid Finite Element Method and Discrete Element Method (FEM-DEM) strategy, which combines classical finite and discrete element methods in a common tool, and illustrates its capabilities in reproducing the real behavior of masonry during experimental quasi-static tests and seismic actions. The numerical implementation is available in the open-source LMGC90 code. In this hybrid approach, anisotropic damageable deformable blocks interact each other through contact joints governed by frictional cohesive behaviors. The DEM framework permits large displacements, rotations, and complete detachments of the blocks, which is usually neglected with FEM models. A comparative work is developed with a focus on the advantages and disadvantages of the hybrid model with respect to FEM micro- and macro-modeling (aka block based description or continuous homogeneous description), and DEM using rigid blocks. In this regard, validations through experimental benchmarks are achieved and the results of a diagonal compression test are discussed. Then, the main application performed in this work concerns the seismic assessment of a masonry cross vault. The key aspect of the numerical results concerns the ability of this approach in providing realistic prediction of failure mechanisms, which are relevant for retrofitting works, according to the real cracking pattern, considering the real stereotomy of the masonry and large deformations.

Conditions for minimum stiffness of proportionally loaded structures

During proportional loading of structures a significant re-arrangement of stresses may occur. It may result e.g. in the transition from a softening to a stiffening structure. This may even be the case for constant material stiffness. Since the terms stiffening structure and softening structure are lacking universally accepted definitions, it is not astonishing that the search for conditions for minimum stiffness of proportionally loaded multi degree of freedom structures has so far attracted very little attention. Presentation of such a condition, in the framework of the Finite Element Method (FEM), is the task of this publication. It is based on a linear eigenvalue problem that renders complex eigenvalues and eigenvectors possible. The point of inflection in the real part of the complex section of a specific eigenvalue function is shown to mark the load-level of minimum stiffness of a proportionally loaded structure. Complex eigenvalues require the indefiniteness of both real symmetric coefficient matrices of the underlying linear eigenvalue problem. In the given case, the first one depends on a dimensionless load parameter, whereas the second one is obtained by specialization of the first one for the onset of loading. These matrices are established with the help of a special hybrid finite element, available in a commercial FE program. The proposed condition for minimum stiffness of proportionally loaded structures is verified numerically. The results obtained in a parameter study of the investigated structure are found to agree well with the ones following from an alternative condition for the transition from a softening to a stiffening structure. This condition is based on a mechanically objective arc length in the form of a representative displacement of the structure.

A numerical investigation into the influence of the surfactant injection technique on the foam flow in heterogeneous porous media

We propose a sequential algorithm to investigate the influence of surfactant injection on foam-induced mobility reduction in two-phase liquid–gas flows in highly heterogeneous porous media. A foam model in local equilibrium is adopted in this context, assuming non-Newtonian foam behavior. A fractional flow formulation based on global pressure that includes the surfactant in the liquid phase is adopted, resulting in a system that couples elliptic and hyperbolic equations. These equations are split into two sub-systems that group equations of the same kind and are solved employing a sequential numerical algorithm that combines a locally conservative hybrid finite element method to approximate the hydrodynamics of the system with a central-upwind finite volume method for the transport equations. The resulting spatial discretized system is approximated in time by applying a multi-step, implicit finite difference method. The hydrodynamics and hyperbolic problems are solved using a staggered algorithm in different time scales. Through comparison with experimental data and classical numerical methods, we validated the proposed methodology and demonstrated its ability to produce stable approximations with reduced numerical dissipation and computational cost. Then, we apply the sequential algorithm to compare the co-injection of the water–gas–surfactant with the Surfactant Alternating Gas (SAG) technique in two-dimensional flows in highly heterogeneous media. The numerical results suggest a better sweep efficiency using the SAG injection technique when compared with the co-injection approach for the equivalent amount of injected surfactant.

Modeling Sequences of Earthquakes and Aseismic Slip (SEAS) in Elasto‐Plastic Fault Zones With a Hybrid Finite Element Spectral Boundary Integral Scheme

AbstractWe present a coupled finite element spectral boundary integral framework for modeling sequences of earthquakes and aseismic slip on a 2‐D planar rate‐and‐state fault with off‐fault visco‐plastic response in the plane strain approximation. The model resolves both slow aseismic deformation and inertia effects during rapid slip. As an application, we perform two sets of simulations with different choices of cohesion to explore the co‐evolution of fault slip, bulk plasticity and local stress fields. The first set implements a relatively large value of the cohesion parameter, which results in limiting inelastic strain accumulation to dynamic rupture phases. The second set implements a smaller cohesion, allowing for plastic strain to accumulate in both seismic and aseismic phases. For the first model, our results indicate that the extent and distribution of plastic strain depend on the angle of maximum compressive principal stress. At larger angles, inelastic strain accumulates on the extensional side of a dynamically propagating rupture. At smaller angles, the extent of plasticity is limited to the compressional side of the domain. At smaller cohesion values, off‐fault plasticity may occur during aseismic slip, which alters the nucleation characteristics and earthquake sequence pattern. Furthermore, our results at lower cohesion values indicate that plastic strain accumulation may occur in both the extensional and compressional sides of the off‐fault bulk even at higher angles of maximum compression. This produces damage patterns that deviate from the traditional off‐fault fan‐like distribution observed in dynamic rupture simulations and emphasizes the significance of long‐term deformation in interpreting observations.

Efficient simulation of stochastic seismic response of long-span bridges in river valleys using hybrid BEM-FEM

Determining ground motions is essential for seismic analysis of long-span bridges located at complex sites. However, there is a lack of earthquake records for local site conditions. Thus, this study focused on the effect of local site conditions on the stochastic response of long-span high-pier rigid frame bridges crossing a valley with an overlying water layer. For this purpose, a hybrid boundary element and finite element method (BEM-FEM) is proposed to investigate the stochastic seismic response of long-span bridges at such a complex site. First, a simulation method for 3-D spatially varying ground motions ascribed to wave scattering from irregular surface topography, sedimentary soil, and water layers was established based on the BEM combined with the spectral representation method. Furthermore, the statistical properties of the bridge response were explored based on the FEM and Monte Carlo simulations. The advantage of this work is that it reveals how the seismic wave propagation in this particular valley topography and water layer affects the stochastic response of the bridge considered. Moreover, the results indicate that seismic wave scattering leads to a significant energy redistribution of the input waves in the tri-directions related to the surface location, and a decrease in the coherency loss functions at all frequencies. Owing to this change, the peak ground accelerations (PGAs), bridge response means, and response variability are doubled. The beneficial effect of the water layer on the PGAs is weakened, while the adverse effect of hydrodynamic pressure dominates. The parameter analysis results demonstrate that a 10-m-deep sedimentary soil layer produces a 47% increase in the internal force of the pier bottom. The solid-liquid dynamic coupling effect should be accurately quantified for bridges located at saturated sites. Considering the local site conditions, the coefficient of variation (COV) of the response of the pier top exceeded 0.3, indicating strong randomness.

Vibroacoustic response of a high-speed train extruded profile under fluid-induced vibration

The wall pressure fluctuation caused by a turbulent boundary layer is an important source of noise and vibration in high-speed trains. Considering that railway vehicles are usually made of extruded profiles, a simple and reliable model is needed to predict the vibroacoustic characteristics of extruded profiles excited by a TBL in the early stages of design. A hybrid finite element and statistical energy analysis model is established for computing the vibroacoustic response of finite-sized panels excited by a TBL. In the hybrid model, the wall pressure fluctuation of the TBL is modelled in the wavenumber domain. The panels are modelled using FEs, and acoustic waves in the fluid space below the panels are modelled using SEA. The TBL wall pressure acting on the top surface of the panels is resolved into equivalent nodal forces with discretization of the structure using FEs, achieved by calculating the cross-spectrum matrix of the wall pressure in the spectral domain and using jinc functions with smooth boundary and symmetric properties as shape functions. The reciprocity between direct and reverberant fields couples the acoustic fields to the structure. Once the response of the hybrid model is determined, sound transmission through the panels can be calculated. By following the procedures outlined in this paper, the range of wall pressure model selection for TBL has extended and reduced computational time and provides a basis for the acoustic optimization design of extruded profiles.

Improvement of HCF life of automotive safety components considering a novel design of wheel alignment based on a Hybrid multibody dynamic, finite element, and data mining techniques

The main aim of the present study is to improve the High-Cycle Fatigue (HCF) life of automotive safety components subjected to multi-input random non-proportional loading. A case study was conducted on the automotive knuckle as one of the high-critical mechanical components of the suspension and steering systems. The steering knuckle is subjected to the highest road- and steering-induced random loads that are exerted on several points (i.e., joints of knuckle with lower control arm, steering linkage, and Macpherson strut). Moreover, incorrect adjustment of wheel angles increases the intensity of road loads. In this regard, previous studies have shown that wheel angles affect the service time of this component. In the present study, the authors attempted to present a novel design of wheel alignment to reduce the intensity of 3D stress components, and subsequently, to increase the fatigue life of the steering knuckle. To this end, a Hybrid multibody dynamic, finite element, and data mining techniques was used. Accordingly, different load histories extracted through Multi-Body Dynamics (MBD) analysis of a full vehicle model were applied on various joints of this component. Next, a transient dynamic analysis was performed, and the time histories of 3D stress fields were obtained in the critical zone. The fatigue life of the component was predicted using the Critical Plane Method (CPM) via employing the Rain-flow cycle counting technique and Miner-Palmgren damage accumulation rule. Finally, the results of Taguchi Sensitivity Analysis (TSA) were used to investigate the effect of wheel primary angles, including Camber and Toe, on the fatigue life of the cast iron knuckle. Moreover, Response Surface Method (RSM) was utilized to optimize the wheel alignment, and the cyclic lifetime of the component was compared under the pre- and post-optimization process. The results reveal that knuckle life improves by 33.66% using the optimum settings of wheel alignment.

Dynamic behavior and retrofitting of RC frame building under vehicular bomb explosion

Although the terrorist explosion attacks on critical buildings caused by the Vehicle-Borne Improvised Explosive Device (VBIED) are low-probability events, the blast-induced progressive collapse of buildings generally lead to the catastrophic consequences of the events. Through the high-fidelity hybrid finite element (FE) model and numerical simulations, this work aims to get a deep insight into the progressive collapse behavior of high-rise reinforced concrete (RC) frame buildings under blast loadings induced by VBIED, as well as the feasibility of two blast-resistant external retrofitting measures, i.e., fiber reinforced polymer (FRP) and steel plate (SP). Firstly, the applicability of the hybrid FE modelling approach, element types and size, material models and parameters, as well as numerical algorithms, i.e., multi-material Arbitrary Lagrangian-Eulerian (MM-ALE) and Fluid-Structure Interaction (FSI), are fully validated by comparing with the explosion tests on 1/4-scale bare and prototype FRP/SP-retrofitted RC frame structures, respectively. Then, a twelve-story RC frame building is designed following the Chinese regulations, and the corresponding hybrid FE model is established. The failure modes and progressive collapse process of building under the explosions of cargo vans bomb (equivalent TNT of 1814 kg) specified by Federal Emergency Management Agency are numerically examined. Furthermore, the effectiveness of FRP/SP-retrofitted frame columns is assessed quantitatively. It derives that, the SP-retrofitted building is not collapsed for both the scaled distance of 1.0 and 0.55 m/kg1/3; by retrofitting FRP warps, the collapse of entire buildings can be prevented with the scaled distance of 1.0 m/kg1/3, while the progressive collapse of the retrofitted building occurs with a scaled distance of 0.55 m/kg1/3. The present work could provide helpful references for the blast-resistant evaluation, design and retrofitting of the as- and newly-built RC building structures.

Three-dimensional probabilistic assessment of tunneling induced structural damage using Monte-Carlo method and hybrid finite element model

Probabilistic assessment methods can be used to estimate engineering demand parameters under significant uncertainty, such as in the assessment of building damage due to tunneling. This paper develops a new empirical, theoretical and finite element hybrid three-dimensional model, in which the soil–structure interaction is considered and window and door openings are modeled explicitly, to achieve a reasonably fast and accurate damage prediction. The proposed model is embedded in a Monte-Carlo based probabilistic assessment approach, so that the building damage probabilities under different input uncertainty can be computed. Typical methods to quantify the input uncertainty in tunnel-soil–structure interaction practice are suggested. The probabilistic assessment method and a variance-based (Sobol’s) sensitivity analysis are implemented with a computer program that runs in higher-performance computing clusters, and demonstrated with two case studies. The significance of the soil–structure interaction effect and three-dimensional building effect are studied.

A Combined Machine Learning and Model Updating Method for Autonomous Monitoring of Bolted Connections in Steel Frame Structures Using Vibration Data

This research paper presents a novel structural health monitoring strategy based on a hybrid machine learning and finite element model updating method for the health monitoring of bolted connections in steel planer frame structures using vibration data. Towards this, a support vector machine model is trained with the discriminative features obtained from time history data, and those features are used to distinguish between damaged and undamaged joints. An FE model of the planer frame is considered where the fixity factor (FF) of a joint is modeled with rational springs and the FF of the spring is assumed as the severity level of loosening bolts. The Cat Swarm Optimization technique is further applied to update the FE model to calculate the fixity factors of damaged joints. Initially, the method is applied to a laboratory-based experimental model of a single-story planer frame structure and later extended to a pseudo-numerical four-story planer frame structure. The results show that the method successfully localizes the damaged joints and estimates their fixity factors.

Influence of assembly stress on ultimate load carrying capacity of transmission towers

In recent years, for the influence of all kinds of natural disasters, the transmission tower’s collapsing or line’s damage presents a growing trend. The influence of assembly stress in transmission towers is often ignored when people analyze the accidents. To study the actual influence of assembly stress, the production process of assembly stress should be summarized and simulated. Find out the method to calculate and simulate assembly stress by using the finite element analysis software. Trussed beam hybrid finite element model is built. The ultimate load carrying capacity with the influence of assembly stress is studied. The position which is unfavorable for dimension error is determined through the variation of bar quantity and the position of dimension error. It founds that influence of assembly stress is small when there is only one pole existing size error in the transmission towers and the size error should small than 1% of the pole’s length; When there are a number of poles which are located at the tower leg existing size error will produce great influence on the Ultimate load carrying capacity of the transmission towers.

Two-dimensional basin-scale seismic site effects in the Kitimat Valley, British Columbia, Canada: A practical example of using a fast hybrid FE/BE method

The two-dimensional (2-D) basin-scale seismic site response of the Kitimat valley, located in the North Coast region of British Columbia, Canada, was investigated. The valley was subjected to a synthetic ground motion corresponding to a realistic local crustal earthquake of moderate magnitude consistent with the prevailing seismic hazard in the Kitimat region. SiteQUAKE, a fast hybrid finite element (FE)/boundary element (BE) numerical code was used for analyses, in which linear and equivalent-linear soil behavior models were implemented. The near-field (the sedimentary basin infill) and far-field (surrounding bedrock) were modeled by the FE and BE methods, respectively. Responses at different locations along a cross-section were compared with the input motion to illustrate the importance of basin effects. By dissociating the peak ground responses affected by the sub-surface topography (basin emptied of its infill) and by the presence of the sediment infill, it was shown that one-dimensional (1-D) analyses can either underestimate or overestimate 2-D seismic responses, highlighting their inability and insufficiency to correctly address basin effects.

A robust upwind mixed hybrid finite element method for transport in variably saturated porous media

Abstract. The mixed finite element (MFE) method is well adapted for the simulation of fluid flow in heterogeneous porous media. However, when employed for the transport equation, it can generate solutions with strong unphysical oscillations because of the hyperbolic nature of advection. In this work, a robust upwind MFE scheme is proposed to avoid such unphysical oscillations. The new scheme is a combination of the upwind edge/face centered finite volume method with the hybrid formulation of the MFE method. The scheme ensures continuity of both advective and dispersive fluxes between adjacent elements and allows to maintain the time derivative continuous, which permits employment of high-order time integration methods via the method of lines (MOL). Numerical simulations are performed in both saturated and unsaturated porous media to investigate the robustness of the new upwind MFE scheme. Results show that, contrarily to the standard scheme, the upwind MFE method generates stable solutions without under and overshoots. The simulation of contaminant transport into a variably saturated porous medium highlights the robustness of the proposed upwind scheme when combined with the MOL for solving nonlinear problems.

Transient rotordynamic thermal bow (Morton effect) modeling in flexure-pivot tilting pad bearing systems

The Morton effect (ME) is a thermally induced rotodynamic instability problem frequently reported in the fluid film bearing system. The temperature difference across the journal circumference may cause large spiral, synchronous vibration. Earlier ME modeling approaches rarely focus on the flexure-pivot bearing (FPB), significantly disproportionate to its wide application. Hereby, the transient ME prediction algorithm is proposed based on a high-fidelity thermo-elasto-hydrodynamic FPB model. A hybrid finite element analysis is adopted to evaluate the entire rotor thermal bow profile including the rotor midspan. The algorithm is benchmarked with experiments and applied to a realistic compressor model. Simulations confirm the proneness of the FPB system to the ME instability, and reveal the ME sensitivity to the bearing-rotor configuration and operation conditions.

Micromechanisms and Characterization of Low-Velocity Impact Damage in 3D Woven Composites.

Low-velocity impact (LVI) damage of 3D woven composites were experimentally and numerically investigated, considering different off-axis angles and impact energies. The impact responses were examined by LVI tests, and the damage morphology inside the composites was observed by X-ray micro-computed tomography (μ-CT). Yarn-level damage evolution was revealed by developing a hybrid finite element analysis model. The results show that the impact damage has significant directionality determined by the weft/warp orientation of the composites. The damage originates at the bottom of the impacted area and then expands outwards and upwards simultaneously, accompanied by in-plane and out-of-plane stress transfers. The straight-line distributed weft/warp yarns play an important role in bearing loads at the beginning of loading, while the w-shape distributed binder warp yarns gradually absorb impact deformation and toughen the whole structure as the loading proceeds. The effect of directional impact damage on post-impact performance was explored by performing compressing-after-impact (CAI) tests. It is revealed that the CAI properties along principal directions are more sensitive to the low-velocity impact, and the damage mode is significantly affected by the loading direction.

Hybrid High-Order and Weak Galerkin Methods for the Biharmonic Problem

We devise and analyze two hybrid high-order (HHO) methods for the numerical approximation of the biharmonic problem. The methods support polyhedral meshes, rely on the primal formulation of the problem, and deliver $O(h^{k+1})$ $H^2$-error estimates when using polynomials of order $k\ge0$ to approximate the normal derivative on the mesh (inter)faces. Both HHO methods hinge on a stabilization in the spirit of Lehrenfeld--Sch\"oberl for second-order PDEs. The cell unknowns are polynomials of order $(k+2)$ that can be eliminated locally by means of static condensation. The face unknowns approximating the trace of the solution on the mesh (inter)faces are polynomials of order $(k+1)$ in the first HHO method which is valid in dimension two and uses an original stabilization involving the canonical hybrid finite element, and they are of order $(k+2)$ for the second HHO method which is valid in arbitrary dimension and uses only $L^2$-orthogonal projections in the stabilization. A comparative discussion with the weak Galerkin methods from the literature is provided, highlighting the close connections and the improvements proposed herein. Additionally, we show how the two HHO methods can be combined with a Nitsche-like boundary-penalty technique to weakly enforce the boundary conditions. An originality in the devised Nitsche's technique is to avoid any penalty parameter that must be large enough. Finally, numerical results showcase the efficiency of the proposed methods and indicate that the HHO methods can generally outperform discontinuous Galerkin methods and even be competitive with $C^0$-interior penalty methods on triangular meshes.