Substructuring Technique Research Articles

A space-time mixed finite element method for reduced fracture flow models on nonmatching grids

This paper is concerned with the numerical solution of the flow problem in a fractured porous medium where the fracture is treated as a lower dimensional object embedded in the rock matrix. We consider a space-time mixed variational formulation of such a reduced fracture model with mixed finite element approximations in space and discontinuous Galerkin discretization in time. Different spatial and temporal grids are used in the subdomains and in the fracture to adapt to the heterogeneity of the problem. Analysis of the numerical scheme, including well-posedness of the discrete problem, stability and a priori error estimates, is presented. Using substructuring techniques, the coupled subdomain and fracture system is reduced to a space-time interface problem which is solved iteratively by GMRES. Each GMRES iteration involves solution of time-dependent problems in the subdomains using the method of lines with local spatial and temporal discretizations. The convergence of GMRES is proved by using the field-of-values analysis and the properties of the discrete space-time interface operator. Numerical experiments are carried out to illustrate the performance of the proposed iterative algorithm and the accuracy of the numerical solution.

Entanglement and Bell inequalities with boosted tt¯

The Large Hadron Collider provides a unique opportunity to study quantum entanglement and violation of Bell inequalities at the highest energy available today. In this paper, we will investigate these quantum correlations with top quark pair production, which represents a system of two-qubits. The semileptonic top pair channel has a factor of 6 increase in statistics and easier reconstruction with respect to the dileptonic channel. Although measuring the spin polarization of the hadronic top quark is known to be challenging, our study indicates that it is feasible to reconstruct the spin density matrix of the two-qubit system using an optimal hadronic polarimeter. This is achieved with the aid of jet substructure techniques and NN-inspired reconstruction methods, which improve the mapping between subjets and quarks. We find that entanglement can already be observed at more than the 5σ level with existing data, and violation of Bell inequalities may be probed above the 4σ level at the HL-LHC with 3 ab−1 of data. Published by the American Physical Society 2024

Evaluation of shear bond strength based on substructure materials and ceramic veneering techniques.

Bilayered restorations have both the strength of the substructure material and the esthetics of the veneer material; however, they should have appropriate bonding between the two materials. This study aimed to evaluate the shear bond strength (SBS) according to the substructure material and veneering technique used in bilayered restorations. The experimental group was divided into four groups (n = 15 per group) based on the substructure materials (cobalt-chromium [Co-Cr] alloy and 3 mol% yttrium-stabilized tetragonal zirconia polycrystal [3Y-TZP]) and veneering techniques (pressing and layering). Veneering was performed with disk shape (diameter: 5mm, height: 2mm) on a substructure using each veneering technique. Shear stress was applied to the interface of the substructure and the veneering ceramic using a universal testing machine. The shear bond strength, according to the substructure and veneering technique, was analyzed using a two-way analysis of variance with a post-hoc Tukey's honestly significant difference test. The failure mode was observed, and the surface was analyzed using a scanning electron microscope and energy-dispersive spectroscopy. The shSBS of the Co-Cr alloy and 3Y-TZP substructure was not different (p > 0.05); however, the pressing technique showed a higher SBS than the layering technique (p < 0.05). The SBS did not differ depending on the veneering technique in the Co-Cr alloys (p > 0.05), whereas the SBS in the pressing technique was higher than that in the layering technique for 3Y-TZP (p < 0.05). In the layering technique, the Co-Cr alloy showed a higher SBS than 3Y-TZP (p < 0.05). In the failure mode, mixed failure occurred most frequently in all groups. Extensive elemental interdiffusion was observed through the opaque layer in the Co-Cr alloy, regardless of the veneering technique. In 3Y-TZP, a wider range of elemental interdiffusion was observed in the pressing technique than in the layering technique. In bilayered restorations with a 3Y-TZP substructure, the pressing technique yielded higher bonding strength than layering. Using the layering technique, 3Y-TZP showed a lower SBS than the Co-Cr alloy. In bilayered restorations using 3Y-TZP as a substructure, the veneering technique and thermal compatibility of the materials must be considered.

Experimental nonlinear model of a set of connecting elements in view of nonlinear modal coupling

The development process of mechanical systems involves the evaluation of its modes of vibrations in the frequency range of interest. In general, a linear modal analysis is sufficient to determine whether the system can operate in dynamic conditions. However, in some cases the assembly is composed of many subsystems connected through nonlinear connections which make the response depend on the amplitude and frequency of the excitation. In those cases, Linear Normal Modes (LNMs) are not sufficient to fully describe the dynamics of the system and Nonlinear Normal Modes (NNMs) must be used. Using substructuring techniques it is possible to treat nonlinear joints as independent subsystems. However, a reliable nonlinear model is needed to use this approach. The experimental characterization is the only way to correctly estimate the nonlinear behavior of the connection. Thus, the aim of this work is to develop and validate the experimental characterization to build an experimental nonlinear modal model of a strongly nonlinear element that can be used to connect different linear subsystems and can be regarded as a localized source of nonlinearity. The NNMs identification is performed using the single-point single-harmonic phase resonance method, and the experimental nonlinear modal model of the NLCE is obtained by retaining only the first harmonic term of each NNM in order to get nearly uncoupled modal equations.

Study of High-Transverse-Momentum Higgs Boson Production in Association with a Vector Boson in the qqbb Final State with the ATLAS Detector.

This Letter presents the first study of Higgs boson production in association with a vector boson (V=W or Z) in the fully hadronic qqbb final state using data recorded by the ATLAS detector at the LHC in proton-proton collisions at sqrt[s]=13 TeV and corresponding to an integrated luminosity of 137 fb^{-1}. The vector bosons and Higgs bosons are each reconstructed as large-radius jets and tagged using jet substructure techniques. Dedicated tagging algorithms exploiting b-tagging properties are used to identify jets consistent with Higgs bosons decaying into bb[over ¯]. Dominant backgrounds from multijet production are determined directly from the data, and a likelihood fit to the jet mass distribution of Higgs boson candidates is used to extract the number of signal events. The VH production cross section is measured inclusively and differentially in several ranges of Higgs boson transverse momentum: 250-450, 450-650, and greater than 650GeV. The inclusive signal yield relative to the standard model expectation is observed to be μ=1.4_{-0.9}^{+1.0} and the corresponding cross section is 3.1±1.3(stat)_{-1.4}^{+1.8}(syst) pb.

Comparison of substructuring methods with interface reduction

For complex dynamical systems, substructuring techniques can be applied to simulate the large system more efficiently by handling it as a collection of smaller components. In order to couple these components, the description of the interface between components is very important. Classic substructuring techniques, such as the Craig-Bampton method, reduce the interior modes of the system, but don’t reduce the interface description. This can cause unnecessary degrees of freedom kept in the final assembled model. While there have been a few substructuring methods published that do include some amount of interface reduction, they are much more rare and even more rarely applied in practice. Therefore, the goal of this work is to survey these techniques and compare them with a new, line-based orthogonal polynomial interface reduction technique. These methods will be applied to a set of example problems in order to determine their validity and convergence compared to the full model.

Estimation of Joint Parameters Using Frequency-Based Substructuring Techniques

This study presents frequency-based substructuring (FBS) techniques and an identification method for predicting joint parameters. Two FBS techniques, FBS-1 and FBS-2, were derived by assuming pseudomasses at the joint nodes between adjacent substructures. It is estimated that the main reason for the discrepancy with the analytical FRFs is the difficulty in describing the low-frequency responses owing to the assumed pseudomasses of the substructures. Although the FRF curve based on the FBS-2 technique is very close to the analytical FRF curve up to the first resonance frequency, some inconsistencies occur thereafter. It is analyzed that the FRFs up to the first resonance frequency can be utilized for data expansion methods and system identification techniques. Paying attention to this result, this study also provides an identification method to estimate the joint parameters based on the FRF variation. Its validity is illustrated using a numerical example.

An explicit substructuring method for overlapping domain decomposition based on stochastic calculus

In a recent paper [7], a hybrid supercomputing algorithm for elliptic equations has been proposed. The idea is that the interfacial nodal solutions solve a linear system, whose coefficients are expectations of functionals of stochastic differential equations confined within patches of about subdomain size. Compared to standard substructuring techniques, such as the Schur complement method for the skeleton, the hybrid approach produces an explicit and sparse shrunken matrix—hence suitable for substructuring again. The ultimate goal is to push strong scalability beyond the state of the art by leveraging the potential for parallelisation of stochastic calculus. Here, we present a major revamping of that framework, based on the insight of embedding the domain in a cover of overlapping circles (in two dimensions). This allows for efficient Fourier interpolation along the interfaces (now circumferences) and—crucially—for the evaluation of most of the interfacial system entries as the solution of small boundary value problems on a circle. This is both extremely efficient (as they can be solved in parallel and by the pseudospectral method) and free of Monte Carlo error. Stochastic numerics are only needed on the relatively few circles intersecting the domain boundary. In sum, the new formulation is significantly faster, simpler, and more accurate while retaining all of the advantageous properties of PDDSparse. Numerical experiments are included for the purpose of illustration.

On the experimental dynamic substructuring of rotating machine foundations

The dynamic behavior of a rotating machine consists not only of the response of the shaft, but it also contains information of all supporting structures and equipment interacting with the rotor. These support structures, also named foundations, can add substantial influence on the machine operational behavior, hence it becomes necessary to dynamically characterize its components. This study presents the application of substructuring techniques in assembling a supporting structure model for a rotating machine and presents a novel formulation of the mixed coordinates method, which is used to connect rotor and foundation. This foundation model is validated against the actual physical foundation and provides an efficient way to analyze and optimize the behavior of such systems. The robustness of the substructuring technique is demonstrated by comparing the responses of the global system solved with both the dynamically assembled and experimentally measured supporting structures in free-free and clamped conditions. The simulations reveal important phenomena of the complete system, including the presence of structural modes in the Campbell diagrams and in displacement responses. The technique allows flexibility in the design of numerical foundations without requiring physical mounting and measurements.

The combined influence of bond–slip and joint-shear in the seismic upgrading via externally-attached BFRP-bar reinforced precast sub-frames

Earthquake causes severe damage to building structures, and seismic upgrading is an important solution to enhance the capacity of existing buildings. In recent years, the externally-attached substructure technique has received broad attention, which upgrades the existing buildings on the system level and proves to be prominently effective in the overall performance. In this paper, the authors develop an externally-attached BFRP-bar reinforced precast concrete sub-frame for seismic upgrading. In the Section 2, the working principles of the novel externally-attached technique are introduced. In the Section 3, the critical issues and simulation strategies of the novel externally-attached technique are proposed (i.e., bond–slip and joint-shear effects). In the Section 4, the generation approach of stochastic nonstationary excitations is given, and in the Section 5, the application examples via three concrete frames are analyzed. In general, the research verifies the effectiveness of the proposed externally-attached BFRP-bar reinforced precast concrete sub-frame for upgrading. The individual influence of bond–slip or joint-shear will apparently increase the drift ratio and lower the upgrading performance. Meanwhile, the combined influence of bond–slip and joint-shear is important in consideration, which will further affect the upgrading performance and enlarge the structural demands. Ignoring the combined influence of the two critical issues in analysis or incorporating only one factor in design will overestimate the structural behaviors and underestimate the potential risks after the externally-attached upgrading. In a sense, the research provides an important reference for the further investigation of the combined influence of bond–slip and joint-shear in the seismic upgrading.

Predicting the acoustic response of a cylindrical shell immersed in an underwater waveguide using a substructuring technique

Sound radiation from structures in an underwater waveguide presents a challenging underwater acoustics problem typically resolved with numerical methods. This can be computationally inefficient and limited to low-frequency analysis. Hybrid approaches improve on these limitations by combining numerical methods with analytical solutions. This study utilises a substructuring technique called the condensed transfer function approach (CTF) and a decoupling technique called the reverse condensed transfer function approach (rCTF). The hybrid CTF-rCTF approach builds systems by coupling and decoupling simpler subsystems. Each subsystem is represented at the junction interfaces, described by condensed transfer functions (CTFs) that can be analytically or numerically determined. These CTFs are decomposed into orthonormal condensation functions (CFs), for example, gate or exponential functions. To demonstrate the potential of CTF-rCTF, the acoustic response of an infinitely long cylindrical shell under line-distributed load and immersed in an underwater waveguide composed of an upper free surface and lower rigid floor is predicted. This system is built from an underwater waveguide decoupled with a fluid volume and coupled with an excited shell that takes place of the decoupled fluid. Acoustic pressures received in the fluid domain are predicted and verified against an analytical solution. It is particularly shown that using exponential functions as the CFs improves the prediction quality compared to gate functions.

Physical modelling of a harp from Central Africa.

Central Africa harps are string instruments, often anthropomorphic, serving an essential cultural role. Compared to pedal harps, their body is small in size with a soundboard mainly made of animal skin and a neck made of a wood beam. In this paper, a physical model is developed as a tool for assessing the specificities of these musical instruments, from a vibro-acoustic perspective. The modeling strategy is based on the modal Udwadia-Kalaba formalism which is a multibody substructuring technique. Input modal parameters of the body and the strings are experimentally identified and the main steps of the estimation procedures are detailed. The reliability of the physical model is investigated via the comparison between simulated and experimental data for several plucking configurations. Different hypotheses are assessed such as the string/neck coupling which proves to strongly influence the dynamic response of the body when there is a coincidence between string and neck modal frequencies. The inclusion of geometrical nonlinearities proves to be of major importance, even for a weak plucking, as it allows qualitative representation of double frequency terms in the simulations. Overall, physical simulations of the soundboard motion are in good agreement with measurements indicating characteristic features of the instrument are captured.

On the robust experimental multi-degree-of-freedom identification of bolted joints using frequency-based substructuring

Modeling joint dynamics is the bottleneck for precise predictive models of machines. Bolted joints are especially relevant due to their common use in mechanical engineering. Stiffness and damping properties of bolted joints are highly influenced by contact parameters (geometry, surface treatment, preload, …). For high amplitude vibrations, when non-appropriate joint closure is present, even frictional effects can play a role.Substructuring techniques offer a lean solution for isolating dynamical or quasi-static components of joint dynamics. It may be used for an identification of linearized contact parameters for multiple degrees of freedom (dofs). The main limitation of the method is finding a robust workflow to guarantee a proper controllability and observability of the desired joint dynamics, as well as dealing with disturbance/noise in the measurements.In this contribution a robust procedure for the identification of a bolted joint using frequency-based substructuring is presented for a contact in an experimental scenario. The dynamics of the joint are isolated from the assembled system using different substructuring techniques treating the joint as a quasi-static or dynamic component. A simple physical model of the joint is parametrized from the experimental joint dynamics. A validation of the methodology is given by using the identified joint parameters on a modified assembled system.

Application of Substructure Techniques to Syntactic Metal Foams in a Finite Element Environment

The presented work focuses on the development of a novel method that can numerically describe the properties of metal matrix syntactic foam (MMSF) with low memory requirements and short computational times without losing the properties of the interior structure. In this paper, we propose a novel method that avoids using the homogenization technique and instead rearranges stiffness matrices and constructs specific substructures to perform the overall construction. The two-dimensional cases are discussed in order to focus on the methodology itself. First, the reductions and structural design with solid mesh structures were performed, and then the model was applied on structures filled with iron hollow spheres. So far, the method has been used to evaluate small deformations to see how suitable the subspace technique is for describing metal foams. Aluminum was used as the matrix material, as it is one of the most common materials for MMSFs. The optimal parameters were searched that resulted in the shortest running time for the given construction. Since in the proposed substructure technique only the displacement values at the boundary points are computed, a back-calculation step for each selected substructure was performed to see the interior deformations in the vicinity of an iron hollow sphere.

Dynamic substructuring for mechanical systems with frequency-dependent materials using a POD-based model reduction method

Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. Contrary to classical modal reduction techniques (Craig-Bampton, MacNeal) where the normal modes basis must be enriched to account for damping effects, the methodology presented here takes advantage of the Golla–Hughes–McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The Lagrange multipliers are finally employed to couple the reduced system to a host structure, as made in popular dynamic substructuring techniques. This method has two major advantages. First, substantial savings are achieved by the judicious combination of GHM and POD techniques. Second, the reduced system takes the form of a constant matrix of small size which permits to preserve confidentiality.

A suggested dynamic soil – structure interaction analysis

In this paper, a new methodology for time domain analysis of buildings on raft foundations considering soil – structure interaction is proposed. Sub-structuring technique is used to separate the building as super-structure and the underneath soil as sub-structure. The super-structure can be modeled using any numerical method. However, in this paper the super-structure is modeled via the BEM to consider the real interaction area between column and slabs. The dynamic load is considered as an earthquake acceleration record that can be transformed to equivalent dynamic loads acting on the super-structure floors. The sub-structure is analyzed using the dual reciprocity boundary element method as closed domain. New iterative coupling technique is proposed between the super and sub-structures to reduce the computational effort and required storage. An example is presented to demonstrate the strength and the practicality of the proposed methodology.

Hybrid simulation of a steel dual system with buckling‐induced first‐story column shortening: A mixed control mode approach

AbstractThis paper presents a hybrid simulation (HS) with a proposed substructuring technique that captures the effect of first‐story column local buckling and axial shortening on the frame behavior. The HS is applied to examine the seismic response of a two‐dimensional seven‐story, two‐bay steel dual system. The experimental substructure consists of a full‐scale interior column and beam cruciform subassemblage, including a moderately ductile first‐story built‐up box column and two I‐shaped beams. Under combined axial and lateral loads, local buckling can occur near the column base, resulting in column shortening. The specimen is loaded through a four‐degree‐of‐freedom (DOF) mixed‐mode control (three displacement‐ and one force‐control) actuation system that simplifies the actual complex boundary conditions of the frame structure. To account for column shortening in the HS, a new approach consisting of a set of fictitious equivalent forces applied to columns in the numerical model to achieve compatible displacements with the experiment is implemented. Shortening of the two exterior columns in the model is simulated through finite element analysis using the computer program ABAQUS in an attempt to capture the redistribution of axial loads with column shortening. The test results confirm that the proposed modeling and control methods successfully integrate the experimental substructure and ABAQUS simulation into the HS, resulting in a more realistic frame response that captures the effect of column shortening in the analysis. The moderately ductile built‐up box column is verified to perform well in near‐fault earthquake loadings.

A model considering the longitudinal track–bridge interaction in ballasted railway bridges subjected to high-speed trains

AbstractIn this paper, a dynamic interaction model of the coupled system of railway bridge, foundation, subsoil, ballast, track, and high-speed train is presented, with special emphasis on the longitudinal interaction between the track and the bridge structure, taking into account the flexibility of the ballast. After a description of the model of this interaction system, the equations of motion are given separately for each subsystem. The discretization of the bedded rails is performed by two different approaches. In the first approach, the deflection of the rails is expanded into the eigenfunctions of a finitely long bedded beam representing the rails. In the second, simplified approach, the track response is represented by a superposition of the static deflection of the infinitely long bedded beam due to a concentrated load. The coupling of the bridge structure with the track is achieved by a component mode synthesis technique, which in the first approach leads to a representation of the equations of motion in state-space. A discrete substructure technique is used to couple this subsystem with the train model. The two presented strategies are verified by comparison with results of a finite element model of this interaction system. Several application examples reveal the influence of the horizontal track–bridge interaction and other modeling parameters on the dynamic bridge response.

Training artificial neural networks using substructuring techniques: Application to joint identification

The dynamic properties of assembled structures are governed by the substructure dynamics as well as the dynamics of the joints that are part of the assembly. It can be challenging to describe the physical interactions within the joints analytically, as slight modifications, such as static preload, temperature, etc. can lead to significant changes in the assembly’s dynamic properties. Therefore, characterizing the dynamic properties of joints typically involves experimental testing and subsequent model updating. In this paper, a machine-learning-based approach to joint identification is proposed that utilizes a physics-based computational model of the joint. The idea is to combine the computational model of the joint with dynamic substructuring techniques to train the machine-learning model. The flexibility of dynamic substructuring permits the enforcement of compatibility and equilibrium conditions between the component models from the experimental and numerical domains, facilitating the development of machine-learning models that can predict the dynamic properties of joints. The proposed approach provides an accurate data-driven method for joint identification in real structures, while reducing the number of measurements needed for the identification. The approach permits the identification of a full 12-DoF joint, enabling the coupling of 3D dynamic models of substructures. Compared to the standard decoupling approach, no spurious peaks are present in the reconstructed assembly response. The proposed approach is validated numerically and experimentally by reconstructing the assembly response and comparing the results with known assembly dynamics.

Exploring Higgs-photon production at the LHC

We have investigated the signal for physics beyond the Standard Model via Higgs plus photon final state, hitherto unobserved at the LHC, in the framework of Standard Model Effective Field Theory. Using the relevant dimension-6 operators, we probe two distinct classes of interactions, based on the Lorentz structure of Higgs couplings to gauge bosons and fermions. To begin with, constraints on the Wilson coefficients of these operators have been derived from existing experimental data. We then focus on the hadronic decay of the Higgs boson to two bottom quarks in the boosted regime, leading to a high pT fat-jet recoiling against a hard photon. Following a CMS Run II search for a heavy resonance decaying into a Higgs boson and a photon, a detailed signal and background analysis for this channel has been done and limits on the relevant Wilson coefficients have been obtained. By performing a cut-based analysis, we identify some kinematic observables that distinguish between signal and SM background. Minimum values of the Wilson coefficients that will yield 3σ signal significance at the 14 TeV run of the LHC with 3000 fb−1 data, have been obtained. A multivariate analysis using a boosted decision tree and exploiting the jet substructure techniques further help to isolate the regions of phase space where the contribution of SMEFT driven signal is significantly enhanced. Finally, we briefly discuss the parameter dependencies and interpretations of the allowed values of the coefficients on a particularly interesting UV complete model namely, the Minimal Supersymmetric Standard Model.