Substructuring Technique Research Articles

Using point symmetry in finite element analyses

This paper presents the conditions in which a large class of structural problems having a geometric and material type of symmetry, i.e. point symmetry, may be used as a half model to reduce the computational effort. This type of symmetry may be used in finite element modelling to analyze a large class of usual problems especially for linear (static and modal), and for nonlinear analyses when it is necessary to run huge models avoiding the more complex substructuring techniques. First, all the theoretical aspects are introduced and presented using simple 2D models and then a 3D approach is considered to include all six DOFs per node that may be used in a structural analysis. Then, a practical problem, having one plane of reflective symmetry and point symmetry is described and analyzed for linear static analysis considering two different finite element models: an approximate shell model and an accurate solid based model. For each of the two models, full, half due to the reflective symmetry, and then quarter models (due to the mixed reflective and point symmetries) were analyzed, and the advantages of considering point symmetry are presented.

Search for low mass vector resonances decaying into quark-antiquark pairs in proton-proton collisions at s=13 TeV

A search for low mass narrow vector resonances decaying into quark-antiquark pairs is presented. The analysis is based on data collected in 2017 with the CMS detector at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 41.1 fb$^{-1}$. The results of this analysis are combined with those of an earlier analysis based on data collected at the same collision energy in 2016, corresponding to 35.9 fb$^{-1}$. Signal candidates will be recoiling against initial state radiation and are identified as energetic, large-radius jets with two pronged substructure. The invariant jet mass spectrum is probed for a potential narrow peaking signal over a smoothly falling background. No evidence for such resonances is observed within the mass range of 50-450 GeV. Upper limits at the 95% confidence level are set on the coupling of narrow resonances to quarks, as a function of the resonance mass. For masses between 50 and 300 GeV these are the most sensitive limits to date. This analysis extends the earlier search to a mass range of 300-450 GeV, which is probed for the first time with jet substructure techniques.

Jet substructure at the Large Hadron Collider

Jet substructure has emerged to play a central role at the Large Hadron Collider, where it has provided numerous innovative ways to search for new physics and to probe the Standard Model, particularly in extreme regions of phase space. In this article we focus on a review of the development and use of state-of-the-art jet substructure techniques by the ATLAS and CMS experiments.

Search for Physics beyond the Standard Model in Events with Overlapping Photons and Jets.

Results are reported from a search for new particles that decay into a photon and two gluons, in events with jets. Novel jet substructure techniques are developed that allow photons to be identified in an environment densely populated with hadrons. The analyzed proton-proton collision data were collected by the CMS experiment at the LHC, in 2016 at sqrt[s]=13 TeV, and correspond to an integrated luminosity of 35.9 fb^{-1}. The spectra of total transverse hadronic energy of candidate events are examined for deviations from the standard model predictions. No statistically significant excess is observed over the expected background. The first cross section limits on new physics processes resulting in such events are set. The results are interpreted as upper limits on the rate of gluino pair production, utilizing a simplified stealth supersymmetry model. The excluded gluino masses extend up to 1.7TeV, for a neutralino mass of 200GeV and exceed previous mass constraints set by analyses targeting events with isolated photons.

Methods of Reflections: relations with Schwarz methods and classical stationary iterations, scalability and preconditioning.

The basic idea of the method of reflections appeared almost two hundred years ago; it is a method of successive approximations for the interaction of particles within a fluid, and it seems intuitively related to the Schwarz domain decomposition methods, the subdomains being the complements of the particle domains. We show in this paper that indeed there is a direct correspondence between the methods of reflections and Schwarz methods in the two particle/subdomain case. This allows us to give a new convergence analysis based on maximum principle techniques with precise convergence estimates that one could not obtain otherwise. We then show however also that in the case of more than two particles/subdomains, the methods of reflections and the Schwarz methods are really different methods, with different convergence properties. Using substructuring techniques from domain decomposition, we then show that the methods of reflections are classical block Jacobi and block Gauss-Seidel methods for the interface traces, and we derive new, relaxed versions of the methods of reflections with better convergence properties. We finally also introduce for the first time coarse corrections for the methods of reflections to make them scalable in the case when the number of particles becomes large. The substructured formulations permit the easy use of the methods of reflections as preconditioners for Krylov methods, and we illustrate scalability and preconditioning properties with numerical experiments.

Explicit–Implicit Co-Simulation Techniques for Dynamic Responses of a Passenger Car on Arbitrary Road Surfaces

To study the durability of a passenger car, this work investigates numerical simulation techniques. The investigations are based on an explicit–implicit approach in which substructure techniques are used to reduce the simulation time, allowing full vehicle dynamic analyses to be performed on a timescale that is difficult or impossible with the conventional finite element model (FEM). The model used here includes all necessary nonlinearities in order to maintain accuracy. All key components of the car structure are modeled with deformable materials. Tire–road interactions are modeled in the explicit package with contact-impact interfaces with arbitrary frictional and geometric properties. Key parameters of the responses of the car driven on six different kinds of test road surfaces are examined and compared with experimental values. It can be concluded that the explicit–implicit co-simulation techniques used here are efficient and accurate enough for engineering purposes. This paper also discusses the limitations of the proposed method and outlines possible improvements for future work.

Search for electroweak diboson production in association with a high-mass dijet system in semileptonic final states in pp collisions at s=13 TeV with the ATLAS detector

This paper reports on a search for the electroweak diboson ($WW/WZ/ZZ$) production in association with a high-mass dijet system, using data from proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV. The data, corresponding to an integrated luminosity of 35.5 fb$^{-1}$, were recorded with the ATLAS detector in 2015 and 2016 at the Large Hadron Collider. The search is performed in final states in which one boson decays leptonically, and the other boson decays hadronically. The hadronically decaying $W/Z$ boson is reconstructed as either two small-radius jets or one large-radius jet using jet substructure techniques. The electroweak production of $WW/WZ/ZZ$ in association with two jets is measured with an observed (expected) significance of 2.7 (2.5) standard deviations, and the fiducial cross section is measured to be $45.1 \pm 8.6(\mathrm{stat.}) ^{+15.9} _{-14.6} (\mathrm{syst.})$ fb.

Jet substructure measurements of interference in non-interfering SMEFT effects

The tails of diboson production at the LHC are sensitive to the interference between Standard Model and higher dimension operators parameterizing the effects of heavy new physics. However, helicity selection rules for the diboson scattering amplitudes set an obstruction to the na¨ıve interference contributions of dimension six operators, causing the total diboson rate correction’s leading contribution to cancel. In this case, carefully measuring the azimuthal decay angles “resurrects” the interference, recouping sensitivity to the “non-interfering” operators. We explore these signatures in detail, and find that the EFT uncertainties associated with higher-dimensional operators are uniquely well-suppressed by the construction of an asymmetry variable which is only generated by these non-interfering operators, relegating the effects of higher-dimensional, interfering operators to the same status as statistical errors in this observable. We perform a complete analysis of this azimuthal interference pattern in hadronic decays of W bosons using jet substructure techniques to tag the bosons and measure their azimuthal decay angles. This technique provides a valuable cross-check to purely-leptonic measurements of interference resurrection in diboson production.

Substructuring verification of a rear fuselage mounted twin-engine aircraft

Dynamic substructuring allows for the reduction of large complex structures into substructures to increase computational efficiency and to isolate the local dynamic behaviors of concern. However, errors such as truncation, continuity and rigid body mode errors still limit the applicability of this method experimentally. Additionally, the feasibility of implementing substructuring techniques on finite element models of multi-component fuselage structures has yet to be shown in the literature. The objective of this paper is twofold: first to introduce a feasible substructuring methodology that mitigates the experimental and multi-component limitations with current methods; and secondly, to investigate the modal properties and applicability of substructuring analysis on a rear fuselage mounted twin-engine aircraft. This configuration is not well understood in the literature despite having been shown to have increased interior cabin noise and vibration levels. Experimental validation of the computational model was first performed. A substructuring analysis of the validated computational model produced natural frequencies of the local and global modes that agreed within 6.47% on average, and pseudo-orthogonality terms greater than 0.89 for all modes considered. This methodology proved to be useful for generating an accurate representation of local modes within a global structure for the aircraft configuration studied. This will allow for future work to more thoroughly investigate the local modes using innovative design methods with confidence that the local modes will correlate with the global modes.

Experiments and simulations of an industrial assembly with different types of nonlinear joints subjected to harmonic vibrations

The structure Harmony-Gamma is a metallic assembly representative of an industrial structure for which the vibratory response is influenced by the apparition of nonlinear phenomena within two specific types of joints, the first corresponding to friction joints and the second to elastomer joints. Firstly, the paper presents the experimental procedure and results obtained for this structure. Secondly, a global methodology for modeling and simulation of the nonlinear vibrational response is set up.The experiments are performed for longitudinal and transverse swept sine experiments. First of all, swept sine experiments are performed at low excitation levels on the structure in order to update a linear finite-element model. Then, the evolution of the frequency response function is studied at increasing excitation levels in order to identify the contribution of the nonlinear effects on the global vibrational response of the system.The methodology for modeling and simulation consists of five steps. Firstly, a finite-element model of the structure is presented and updated in order to be representative of the structure when it is excited at low excitation levels. This model is then reduced using a hybrid sub-structuring technique. Thirdly, the nonlinear models of the friction and elastomer joints are added. The resulting optimization problem is solved by means of the Harmonic Balance Method (HBM) coupled with a Newton-Raphson continuation and a condensation process. Lastly, the simulation results are compared to the experimental results in order to validate the development of the finite element model for the nonlinear industrial structure Harmony-Gamma with nonlinear joints of different natures and to achieve a refined understanding of the nonlinear phenomena and their origin.

Frequency and intensity dependent dynamic responses of soil-steel pipe sheet pile (SPSP) foundation-superstructure system

Frequency and intensity dependent dynamic response behavior of soil-steel pipe sheet pile (SPSP) foundation and superstructure supported on it is studied in this work considering the soil-structure interactions (SSI) effect through experimental investigation by utilizing a physical scaled model of soil-SPSP foundation-superstructure (S-SPSP-S) system. The vertical shear resistance of SPSP foundation joint is assessed experimentally by using an element model of SPSP joint and the result satisfies the requirement laid in design code. The components of sub-structuring solution technique for dynamic response computation namely-the inertial interaction effect and the kinematic interaction effect are estimated through SPSP foundation head loading test and shake table experiment under 1-g conditions, respectively. Frequency and intensity dependent SPSP foundation head impedance functions (IFs) and effective foundation input motion (EFIM) are estimated from these experiments for inertial interaction and kinematic interaction, respectively. The total dynamic response of S-SPSP-S system is computed using the sub-structuring technique through superposition of the experimentally measured IFs and EFIM. The superimposed dynamic response is further compared with the experimental total dynamic response estimated from shaking table experiment with the model S-SPSP-S system. The comparison shows certain discrepancies particularly in resonance behavior of SPSP foundation system. The reason for such observed difference is the stiffness variation of SPSP foundation unit due to the nonlinear behavior of SPSP joint resulting from profound influence of superstructure mass. As a whole, the results and discussions presented in this paper will provide the reader a detail insight on the fundamental dynamic response behavior of S-SPSP-S system.

Evaluation of equivalent material properties of reinforced composites by a novel smoothed rebar element technique

Reinforced composite materials are widely used in industry and also have attracted the interest in academia due to their superior properties. The numerical methods are usually employed for evaluating the microscopic mechanical properties of composite materials. In this paper, an efficient numerical approach is developed by coupling the strain smoothing technique and the rebar element technique base on the framework of traditional finite element method. The proposed approach can be applied with the simple meshes, and it requires few degrees of freedom compared to the traditional finite element method, thus the computational time and storage requirement are significantly reduced. In addition, the quality of solutions with the distorted meshes can also be assured, and the coordinate mapping and the calculation of Jacobian matrix can be eliminated. On the other hand, the local strain/stress is captured by reanalysis with substructure technique. The superior performances of the proposed approach are numerically demonstrated with several numerical examples compared with the traditional finite element method, especially the distorted meshes can also yield reasonable results. Finally, the proposed approach is employed for the evaluation of the equivalent elastic properties of polymeric nano-composites material, which reaffirms that the present approach has good performance.

An optimized mesh partitioning in FEM based on element search technique

The substructuring technique is one of the efficient methods for reducing computational effort and memory usage in the finite element method, especially in large-scale structures. Proper mesh partitioning plays a key role in the efficiency of the technique. In this study, new algorithms are proposed for mesh partitioning based on an element search technique. The computational cost function is optimized by aligning each element of the structure to a proper substructure. The genetic algorithm is employed to minimize the boundary nodes of the substructures. Since the boundary nodes have a vital performance on the mesh partitioning, different strategies are proposed for the few number of substructures and higher number ones. The mesh partitioning is optimized considering both computational and memory requirements. The efficiency and robustness of the proposed algorithms is demonstrated in numerous examples for different size of substructures.

Search for resonant mathrm{t}overline{mathrm{t}} production in proton-proton collisions at sqrt{s}=13 TeV

A search for a heavy resonance decaying into a top quark and antiquark left(mathrm{t}overline{mathrm{t}}right) pair is performed using proton-proton collisions at sqrt{s}=13 TeV. The search uses the data set collected with the CMS detector in 2016, which corresponds to an integrated luminosity of 35.9 fb−1. The analysis considers three exclusive final states and uses reconstruction techniques that are optimized for top quarks with high Lorentz boosts, which requires the use of nonisolated leptons and jet substructure techniques. No significant excess of events relative to the expected yield from standard model processes is observed. Upper limits on the production cross section of heavy resonances decaying to a mathrm{t}overline{mathrm{t}} pair are calculated. Limits are derived for a leptophobic topcolor Z′ resonance with widths of 1, 10, and 30%, relative to the mass of the resonance, and exclude masses up to 3.80, 5.25, and 6.65 TeV, respectively. Kaluza-Klein excitations of the gluon in the Randall-Sundrum model are excluded up to 4.55 TeV. To date, these are the most stringent limits on mathrm{t}overline{mathrm{t}} resonances.

A semi-analytical method for vibrations of a layered transversely isotropic ground-track system due to moving train loads

The vibrations of a ground-track system subjected to moving train loads are investigated by using a semi-analytical method combining with the substructure technique. In the coupled system, the ground is modeled as a multi-layered transversely isotropic (TI) half-space, and the track is modeled as a three-layered beam structure, which consists of the rails, sleepers and ballast. The two substructures are coupled by the compatibility condition of vertical displacement at the ballast centerline. The displacement and stress responses of the layered TI ground due to the reaction of the track are then obtained by employing the stiffness method. And solutions in the physical domain are recovered by Fourier synthesis of the frequency-wavenumber domain responses. The proposed semi-analytical model has the merits of all parameters having explicit physical meaning, which is very convenient for engineering application, and of the accuracy being not affected by the layers’ thickness because of the exact dynamic stiffness matrix. The derived formulations are verified by comparison with the existing solutions for the isotropic medium that is a special case of the more general problem addressed. Numerical calculations are first performed for the case of a single wheel axle load moving at subsonic, transonic and supersonic speeds, and then for the case of the X-2000 high speed train of the Swedish National Railway travelling at a speed of 200 km/h. Numeric results show that the vibrations of the ground-track system can be very different when soil anisotropy is considered. And the variation of the TI parameters alters the resonance frequencies of the ground, which in turn alters the interaction between the track and ground.

Search for a heavy resonance decaying to a top quark and a vector-like top quark in the lepton + jets final state in pp collisions at sqrt{s} = 13,text {TeV}

A search is presented for a heavy spin-1 resonance mathrm {Z}' decaying to a top quark and a vector-like top quark partner text {T} in the lepton + jets final state. The search is performed using a data set of mathrm {p}mathrm {p} collisions at a centre-of-mass energy of 13,text {TeV} corresponding to an integrated luminosity of 35.9{,text {fb}^{-1}} as recorded by the CMS experiment at the CERN LHC in the year 2016. The analysis is optimised for final states arising from the text {T} decay modes to a top quark and a Higgs or mathrm {Z} boson (text {T} rightarrow mathrm {H} mathrm {t}, mathrm {Z} mathrm {t}). The event selection makes use of resolved and merged top quark decay products, as well as decays of boosted Higgs bosons and mathrm {Z} and mathrm {W} bosons using jet substructure techniques. No significant deviation from the standard model background expectation is observed. Exclusion limits on the product of the cross section and branching fraction for mathrm {Z}'rightarrow mathrm {t}text {T}, text {T} rightarrow mathrm {H} mathrm {t}, mathrm {Z} mathrm {t}, mathrm {W}mathrm {b} are presented for various combinations of the mathrm {Z}' resonance mass and the vector-like text {T} quark mass. These results represent the most stringent limits to date for the decay mode mathrm {Z}'rightarrow mathrm {t}text {T} rightarrow mathrm {t}mathrm {H} mathrm {t}. In a benchmark model with extra dimensions, invoking a heavy spin-1 resonance mathrm {G}^* , masses of the mathrm {G}^* between 1.5 and 2.3,text {TeV} and between 2.0 and 2.4,text {TeV} are excluded for text {T} masses of 1.2 and 1.5,text {TeV}, respectively.

Search for a W\u2032 boson decaying to a vector-like quark and a top or bottom quark in the all-jets final state

A search for a heavy W′ resonance decaying to one B or T vector-like quark and a top or bottom quark, respectively, is presented. The search uses proton-proton collision data collected in 2016 with the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb−1 at sqrt{s}=13 TeV. Both decay channels result in a final state with a top quark, a Higgs boson, and a b quark, each produced with significant energy. The all-hadronic decays of both the Higgs boson and the top quark are considered. The final-state jets, some of which correspond to merged decay products of a boosted top quark and a Higgs boson, are selected using jet substructure techniques, which help to suppress standard model backgrounds. A W′ boson signal would appear as a narrow peak in the invariant mass distribution of these jets. No significant deviation in data with respect to the standard model background predictions is observed. Cross section upper limits on W′ boson production in the top quark, Higgs boson, and b quark decay mode are set as a function of the W′ mass, for several vector-like quark mass hypotheses. These are the first limits for W′ boson production in this decay channel, and cover a range of 0.01 to 0.43 pb in the W′ mass range between 1.5 and 4.0 TeV.

Stiffness modelling of 2D welded joints using metamodels based on mode shapes

Connections are a key component of steel structures. Current methods of analysis of steel frames mostly rely on approximate joint models based on zero-length rotational springs or mechanical models of rigid bars and springs. A method is presented in this paper to accurately model the stiffness of 2D welded steel joints that is based on surrogate modelling. The joint modelling process starts by developing an accurate 4-node (12 degree of freedom) cruciform finite element from a complete finite element model using substructuring techniques. Then a modal decomposition of these matrices yields the eigenvalues and mode shapes that are used to develop the design points of the training and validation sets of the surrogate model. The modal decomposition leads to a reduced set of variables that accurately models the design space. A uniform Rectangular Grid of design sites is proposed. The Kriging method and Support Vector Machine Regression are used to generate the metamodels and predict the stiffness at untried sites. Both methods provide accurate results. Simulations of steel frames are performed to show the accuracy of the proposed surrogate modelling.

Search for heavy resonances decaying into two Higgs bosons or into a Higgs boson and a W or Z boson in proton-proton collisions at 13 TeV

A search is presented for massive narrow resonances decaying either into two Higgs bosons, or into a Higgs boson and a W or Z boson. The decay channels considered are mathrm{H}mathrm{H}to mathrm{b}overline{mathrm{b}}{tau}^{+}{tau}^{-} and mathrm{V}mathrm{H}to mathrm{q}overline{mathrm{q}}{tau}^{+}{tau}^{-} , where H denotes the Higgs boson, and V denotes the W or Z boson. This analysis is based on a data sample of proton-proton collisions collected at a center-of-mass energy of 13 TeV by the CMS Collaboration, corresponding to an integrated luminosity of 35.9 fb−1. For the TeV-scale mass resonances considered, substructure techniques provide ways to differentiate among the hadronization products from vector boson decays to quarks, Higgs boson decays to bottom quarks, and quark- or gluon-induced jets. Reconstruction techniques are used that have been specifically optimized to select events in which the tau lepton pair is highly boosted. The observed data are consistent with standard model expectations and upper limits are set at 95% confidence level on the product of cross section and branching fraction for resonance masses between 0.9 and 4.0 TeV. Exclusion limits are set in the context of bulk radion and graviton models:spin-0 radion resonances are excluded below a mass of 2.7 TeV at 95% confidence level. In the spin-1 heavy vector triplet framework, mass-degenerate W′ and Z′ resonances with dominant couplings to the standard model gauge bosons are excluded below a mass of 2.8 TeV at 95% confidence level. These are the first limits for massive resonances at the TeV scale with these decay channels at sqrt{s}=13 TeV.

Probing heavy charged Higgs boson at the LHC

Signature of heavier charged Higgs boson, much above the top quark mass, is investigated at the LHC Run 2 experiments, following its decay mode via top and bottom quark focusing on both hadronic and leptonic signal final states. The generic two Higgs doublet model framework is considered with a special emphasis on supersymmetry motivated Type II model. The signal is found to heavily affected by the huge irreducible backgrounds due to the top pair production and QCD events. The jet substructure technique is used to tag moderately boosted top jets in order to reconstruct charged Higgs mass. The simple cut based analysis is performed optimizing various kinematic selections, and the signal sensitivity is found to be reasonable for only lower range of charged Higgs masses for very high luminosity 3000 fb$^{-1}$ option. However, employing the multi-variate analysis(MVA) technique, a remarkable improvement in signal sensitivity is achieved. We find, the charged Higgs signal for the mass range about $300-600$ is observable with 1000 fb$^{-1}$ luminosity option. However, for more high luminosity option 3000 fb$^{-1}$, the discovery potential can be extended to $700-800$ GeV.