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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. [ABSTRACT FROM AUTHOR]

In this paper, we study the two-fold algebra based on the n-standard fuzzy number theoretical system as a special type of two-fold fuzzy algebras, where we study the elementary properties of the algebraic operations defined over this system. Also, we prove many results that describe the relations between two-fold substructures and sub-algebras defined by fuzzy number theoretical systems. On the other hand, we provide many different examples to explain our results. [ABSTRACT FROM AUTHOR]

This paper presents frequency response function (FRF) expansion techniques that minimize the difference between the analytical and predicted FRF matrices to satisfy the FRF constraints. The measured FRF relationships at a small number of locations were used as constraints. The expansion method is useful for estimating the rotational FRFs that are difficult to measure or apply using frequency-based substructuring (FBS) techniques. The validity of the proposed method, including the effects of external noise, was confirmed using numerical examples. An FBS algorithm was also derived by incorporating the FRFs of each substructure, and the compatibility conditions were transformed into FRFs with pseudomasses at the joint nodes. A discrepancy between the FRFs of the synthesized system estimated using the proposed method and the analysis results of the entire system was observed in the numerical example, and the reasons for the discrepancy were investigated and discussed. It is estimated that the proposed FBS method can be enhanced by combining it with other dynamic substructuring techniques and supplementing additional information, such as measured FRFs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An effective and flexible method for encoding ambiguous data is using cubic sets. The concept of incline algebraic substructure is considered and is interlinked with the notation of the cubic set to define cubic subincline. The sense of cubic sub incline of algebra is established with relevant results. Additionally, the results such as homomorphic image, preimage, cartesian product and level sets of cubic sub incline are worked out in this study, and several of its associated findings were looked into. [ABSTRACT FROM AUTHOR]

Machine tools are permanently exposed to complex static, dynamic and thermic loads. This often results in an undesired displacement of the tool center point (TCP), causing errors in the production process and thus limiting the achievable workpiece quality. Recent research efforts try to counter these effects by process‐parallel solutions utilizing machine internal data. Therefore, fast simulation models are a fundamental requirement. Here, model order reduction (MOR) becomes crucial. The resulting low‐dimensional models are required for various applications, e.g., in digital twins, the correction of thermally induced errors at the TCP during the production process as well as for lifetime calculations in predictive maintenance. In this contribution, we present a strategy of MOR for a coupled thermo‐mechanical model with a nonlinear subsystem and moving loads, using the example of a feed axis with nonlinear machine components. Applying tailored substructuring techniques, we are able to separate the linear and nonlinear system components. This allows to apply classic linear MOR methods to the much larger linear part, whereas the small nonlinear part is kept, and thus enables drastically reduced computing times. The relative movement is considered by a switched system approach. Transient thermo‐mechanical interactions of the feed axis are calculated in a final investigation, comparing the performance of the resulting reduced‐order model and the original one. [ABSTRACT FROM AUTHOR]

This work introduces an efficient methodology for: (i) predicting dynamic responses across a broad frequency band for large-scale, highly complex structures, and (ii) forecasting their high-frequency response using associated low-frequency information. Structures of interest are characterized by a large number of degrees of freedom (DOFs) and numerous local vibration modes that couple, within the frequency range of interest, with long-wavelength global elastic modes. Given this complexity, high-fidelity numerical models present a significant computational burden, and a reduced-order modeling (ROM) approach was developed by the authors using substructuring techniques. However, despite its enhanced efficiency, this ROM remains prohibitive for tasks such as uncertainty quantification (UQ). Moreover, given the limitations on the number of training samples used for machine learning tasks, the "small-data" challenge is not easily addressed by traditional machine learning paradigms. Another obstacle for this class of problems is the large number of input parameters and response quantities of interest. This high-dimensional setting exacerbates the small-data challenge for UQ and, more generally, for the development of predictive models. This paper presents a novel implementation of the Probabilistic Learning on Manifold (PLoM) method, which is adept at handling small datasets for both supervised and unsupervised learning. Even with scarce data, PLoM can identify the low-dimensional manifold inherent in the training dataset. Subsequently, projected Itô sampling—a stochastic sampling method—facilitates the generation of samples constrained to the manifold, thereby augmenting the training data. Nonparametric conditioning is then used to infer the joint distribution of a subset of the observables, conditional on another subset having been observed. The focus of this paper is particularly on a multi-level spent nuclear fuel canister, and we infer the statistical properties of high-frequency dynamics, encoded as a frequency response function (FRF), from low-frequency observations of the FRF. [ABSTRACT FROM AUTHOR]

Plate-like structures form the essential components of diverse engineering systems, such as building floors, aircraft wings, wind turbine blades, etc. Detection of early onset of damage/s and prevention of sudden catastrophic failures during operation are necessary for maintaining and enhancing the safety standards of such high-dimensional and intricate systems. To detect anomalies in high resolution within the structure, the employment of a high-dimensional support model parameterized with damage attributes becomes imperative within a model-based assessment framework. Further, to support the estimation of consequent high-dimensional parameter sets, the traditional structural health monitoring methods require dense instrumentation over the entire structure for accurate damage location and severity assessment. Targeting an overall cost reduction in the implementation and subsequently circumventing the augmented cost of computation, this article employs a robust Interacting Particle Kalman filtering (IPEnKF)-based approach for health estimation of plate-like structures that is capable of monitoring only a manageable subdomain of interest while being independent of the rest of the domain. Eventually, this approach allows stage-wise health estimation of complex plate-like structures under the limitation of instrumentation. The proposed approach has been validated through both numerical simulations and real experiments on a scaled model of the plate roughly representing the NASA CRM wing, idealized as a trapezoidal Mindlin plate divided into independent substructures. The proposed method employs the IPEnKF algorithm to estimate each substructure independently by modifying the process model by injecting output towards achieving robustness against unknown substructure boundary forces. By using this subdomain estimation approach, the sensor requirement has been reduced by 60% while maintaining 95% accuracy in damage detection and assessment. Additionally, computational costs have been significantly reduced due to the algorithm's ability to independently monitor the system at its substructure level without depending on the rest of the structure. The method also exhibits excellent reliability, with minimal false alarms. The results emphasize the algorithm's robustness and the essential role of sensor placement in improving the accuracy of damage identification. • Feasibility of stage-wise parameter estimation for plate-like structures is studied. • The proposed framework eliminates the need for interface force computations. • Substructuring technique contributes to significant instrumentation cost savings. • Numerical and experimental studies support applicability to complex real structures. [ABSTRACT FROM AUTHOR]

A two-degree-of-freedom (two-DOF) equation of motion was derived in the frequency domain using a substructuring technique for efficiently calculating the in-structure response spectrum (ISRS) considering equipment–structure interaction. The model of the primary structure was condensed into a mechanical impedance function and combined with the equipment represented by a single-degree-of-freedom oscillator in the frequency domain. This condensed two-DOF system is applied to the efficient calculation of the ISRS considering the equipment–structure interaction without repeated analysis of the coupled model with full DOFs. This coupled analysis procedure was applied to a finite element model of an auxiliary building in a nuclear power plant to validate both the accuracy and impact on the equipment response. Finally, the adequacy of three representative decoupling criteria on the necessity of coupled analysis was investigated by applying those criteria to the auxiliary building example. [ABSTRACT FROM AUTHOR]

In this paper, the collocation spectral method (CSM) combined with domain decomposition method is developed to solve the radiative transfer equation in two-dimensional irregular domains. Three benchmark problems consist of the square enclosure, the L-shaped enclosure and the square enclosure with a centered obstruction are solved and compared with the published data to validate the ability of present developed method. The comparison shows good agreements and indicates that the method has a good accuracy for all problems. Then, the performances of influence matrix technique and iterative substructuring technique to exchange the radiative information between subdomains are compared. It is found that, in the serial computations, the computational cost of influence matrix technique is hundreds of times more expensive than that of iterative substructuring technique. The high cost of influence matrix technique is due to that the radiative intensity is a high dimensional variable with angular dependence, and tremendous subproblems have to be solved to construct the influence matrix. Finally, the modified CSM with domain decomposition, in which the radiative intensity is decomposed into three components, the real wall-related one, the virtual shared interface-related one, and the medium-related one, is proposed. The first two components are solved analytically, and the last one is still solved by the CSM. With such treatments, the computational cost is slightly increased, but the ray effect originated from step-change temperature of medium or step-change optical parameters can be effectively mitigated. Besides, the modified CSM with domain decomposition can also avoid the ray effect due to shadowing singularities. But it should be noted that, in such case, the ray effect due to inhomogeneous spatial distribution of source term may emerge. In conclusion, the CSM combined with domain decomposition is a good alternative method for thermal radiation calculation in complex geometry which can be decomposed into regular subdomains. [ABSTRACT FROM AUTHOR]

In this study, virtual product development method for reducing vibration and noise is proposed for designing at the concept development stage of a vehicle. To this end, the vibration characteristics of the system are predicted through the Lagrange-multiplier frequency-based substructuring technique. The concepts of contact, blocked and transmitted force, and force transmissibility were used for determining the improvement subsystem or combination of subsystems when using the modular platform. Moreover, after the subsystems to be improved were determined, Artificial Neural Network was used as a method of predicting vibration characteristics according to the change of design variables. To verify this, the prediction of the blocked force was performed by changing the young's modulus of the simplified substructure. Finally, the reduction in response was confirmed by applying the blocked force of the simplified subframe to the simplified structure, and a vehicle development process using a database at the concept setting stage is proposed. [ABSTRACT FROM AUTHOR]

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Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena. [ABSTRACT FROM AUTHOR]

The wind-induced fatigue damage is an important reason for the structural deterioration of transmission tower-line systems. The study of the fatigue damage of transmission towers is a basic requirement to ensure their normal service. To simulate the fatigue damage evolution occurring in the joints of the tower, a verified hybrid multiscale finite element (FE) model is first developed by concurrent modeling and substructuring techniques. Second, a fatigue damage model based on continuum damage mechanics is calibrated by conducting a fatigue crack initiation experiment and integrated into the FE material model by subroutines technique. Third, an improved Bayesian updated probability density evolution method (BUPDEM) with higher efficiency is proposed based on the Kriging method. Finally, based on the multiscale FE model and the damaged material model, the strategies for stochastic analysis of fatigue damage of transmission tower-line systems are proposed together with a numerical example for illustration. The results of the example show a good accuracy of the proposed BUPDEM. [ABSTRACT FROM AUTHOR]

Dynamic sub-structuring technique is often employed to determine the structural dynamics of the large complex structural system. This technique reduces the complexity of numerical models obtained during structural analysis and eventually helps obtain accurate, efficient, and cost-effective model reduction. In this paper, Craig–Bampton method is adopted to evaluate the performance of model reduction. The structural system is considered to be an assembly of sub-systems and these sub-systems are called component modes. Vibration mode for each component is determined separately and is used to get overall dynamics of the whole structural system. The components at interface degrees of freedom satisfy the compatibility conditions of the interconnected components. Natural frequency of each components is determined, using the free-free condition and the fix condition. Durability of the test specimen is estimated by sine sweep test under 30 Hz and 50 Hz. Experimental data are combined with the sub-structural components to get an efficient model of the system. Krylov reduction technique is introduced in this paper to obtain the tactile response. The wind turbine blade is discretized to nodes and elements. The discretized blade consists of solid shell elements with 11,376 elements and tetra solid volume elements having 35,598 elements and the approximate spacing between two nodes is 5 mm. The finite-element model is reduced to sub-structure model with 8937 super-elements. Furthermore, this sub-structure model is reduced to 12 super-elements with 2 at the tip of the blade and 10 at the other end using Krylov reduction. [ABSTRACT FROM AUTHOR]

Featured Application: The methodology presented in this work can be applied to develop reliable scientific codes, and specifically codes for the finite element analysis of finite periodic structures. In this paper, we follow the Test-Driven Development (TDD) paradigm in the development of an in-house code to allow for the finite element analysis of finite periodic type electromagnetic structures (e.g., antenna arrays, metamaterials, and several relevant electromagnetic problems). We use unit and integration tests, system tests (using the Method of Manufactured Solutions—MMS), and application tests (smoke, performance, and validation tests) to increase the reliability of the code and to shorten its development cycle. We apply substructuring techniques based on the definition of a unit cell to benefit from the repeatability of the problem and speed up the computations. Specifically, we propose an approach to model the problem using only one type of Schur complement which has advantages concerning other substructuring techniques. [ABSTRACT FROM AUTHOR]

The paper proposes an approach for the efficient model order reduction of dynamic contact problems in linear elasticity. Instead of the augmented Lagrangian method that is widely used for mechanical contact problems, we prefer here the linear complementarity programming (LCP) method as basic methodology. It has the advantage of resulting in the much smaller dual problem that is associated with the governing variational principle and that turns out to be beneficial for the model order reduction. Since the shape of the contact zone depends strongly on the acting outer forces, the LCP for the Lagrange multipliers has to be solved in each time step. The model order reduction scheme, on the other hand, is applied to the large linear system for the displacements and computed in advance by means of an Arnoldi process in combination with the Craig–Bampton substructuring technique. In terms of computational effort the reduction scheme is very appealing because the contact constraints are fully satisfied while the reduction acts only on the displacements. As major benefits, the model order reduction preserves the nodes in the contact zone and does not require any snapshot data. A careful performance analysis closes the paper. [ABSTRACT FROM AUTHOR]

A new semi-analytical approach to analyze the dynamic response of railway bridges subjected to high-speed trains is presented. The bridge is modeled as an Euler–Bernoulli beam on viscoelastic supports that account for the flexibility and damping of the underlying soil. The track is represented by an Euler–Bernoulli beam on viscoelastic bedding. Complex modal expansion of the bridge and track models is performed considering non-classical damping, and coupling of the two subsystems is achieved by component mode synthesis (CMS). The resulting system of equations is coupled with a moving mass–spring–damper (MSD) system of the passing train using a discrete substructuring technique (DST). To validate the presented modeling approach, its results are compared with those of a finite element model. In an application, the influence of the soil–structure interaction, the track subsystem, and geometric imperfections due to track irregularities on the dynamic response of an example bridge is demonstrated. [ABSTRACT FROM AUTHOR]

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. • Experimental identification of nonlinear normal modes of strongly nonlinear elements. • New concept design of a nonlinear connecting element. • Quantification of super-harmonics contributions of the response around resonance. • Validation of the identified model of the strongly nonlinear element. [ABSTRACT FROM AUTHOR]

Modularization of complex structures allows for faster, higher quality, and more cost-effective design. However, sharing information about the geometry and materials of the modules presents a security risk when multiple companies are involved in the project. In such cases, an equivalent model can be developed for secure sharing purposes. The equivalent model should be able to predict the nonlinear geometrically behaviour of the module. This paper aims to develop a nonlinear equivalent model for substructures based on a combination of the Craig-Bampton technique and model order reduction. The paper provides explicit formulas for constructing the reduced-order matrices of the equivalent model based on third-order and fifth-order modal polynomial approximations. The ability of the equivalent models to simulate the geometrically nonlinear static displacements of structures is evaluated through two numerical examples of beam structures. • The accuracy of the nonlinear reduced-order models for substructures was evaluated. • The third-order equivalent model yields accurate results for flat or slightly curved structures. • The fifth-order equivalent model yields accurate results for structures with large curvatures. [ABSTRACT FROM AUTHOR]

The inverse dynamics method is applied to the investigation of dynamical behavior of a parallel manipulator. The substructure technique is used for creating a differential-algebraic system of equations that describes motion of the Stewart-Gough platform. The system of equations is modified into a set of linear differential equations for the determination of the solution of the inverse dynamics problem. A computational algorithm is developed to solve the inverse dynamics of the manipulator. Several trajectories of the moving platform are simulated as a result of the inverse dynamics problem of the Stewart-Gough platform according to the substructure technique. [ABSTRACT FROM AUTHOR]

In the context of simulations of coupled thermal enclosures, we present here a substructuring technique adapted to the amalgam reduced‐order modal model (AROMM). This technique consists of splitting the geometry into different zones. A modal model is then applied to each zone, and the coupling of the resulting models is performed via a thermal contact resistance. This technique allows the consideration of physical thermal resistances between different components of the geometry, as well as the making of fictitious cuts within a continuous domain, when its large size causes difficulties in obtaining the global reduced model. Applied to the simulation of a simplified component of a liquefied natural gas carrier, the use of a sub-structured model with 200 modes allows an access to the whole temperature field with a maximum difference near 1 K and an average difference of the order of 0.2 K, compared with a conventional Lagrange finite-element model of shell type, which requires 60 times longer calculation. [ABSTRACT FROM AUTHOR]

The vibrations produced by an agricultural machine are transmitted to the seat of the tractor operator and must comply with the limitations imposed by international and national regulations. An agricultural machine is generally composed of a tractor that can be linked to different machines required to perform a large number of agricultural tasks. In this paper, substructuring techniques are proposed to investigate the dynamics of the agricultural machine and to evaluate the resulting vibration exposure to the tractor driver in different configurations of the machine. These techniques allow one to couple reduced-order models or experimental models of the component subsystems to obtain the response of the whole system. In the results, the vibration exposure of the tractor operator is evaluated for different configurations of the agricultural machine, by observing the frequency response function (inertance and transmissibility) and the transient response to a given excitation. In conclusion, these techniques allow one to investigate a large number of different configurations and a wide range of operating conditions with a light computational burden and without asking the manufacturers to share sensitive design details. [ABSTRACT FROM AUTHOR]

Purpose: The Craig–Bampton method is a substructuring technique that reduces the number of internal degrees of freedom of substructures by approximations, using a set of truncated vibration modes. It is useful for structural designs with many degrees of freedom. This work aims to develop substructuring through the Craig–Bampton method for free vibration analysis on planar frames according to the frequency range of interest. Methods: The finite-element models of different substructures were assembled. Thus, the degrees of physical freedom were reduced according to the frequency range of interest. The reduced-order models were coupled. Thus, the physical response was obtained. Detailed calculation and the algorithm flowchart are provided. Conclusions: The study of frame dynamics using the present method in different frequency ranges of interest was presented and validated with the results of a commercial software. It was possible to clarify the coupling formulations of the component mode synthesis, as well as the amount of reduction of the number of equations provided by the method, reaching less than 4% of the complete model, for the considered cases. [ABSTRACT FROM AUTHOR]

The reinforcing members are often added on an existing structure to improve stiffness of the structure up to required level. In general, the design targets for the reinforcing members need to be allocated for their designs. However, since the members are additively designed, it is difficult to predict behavior of the reinforcing members and their influence on the existing structure. Therefore, allocating the design targets is challenging task, and the targets based on engineering experience and intuition can lead to the repetitive design cycles. This paper proposes a method for determining target stiffness of a reinforcing member which makes an existing structure achieve the required performances. To utilize individual models of an existing structure and the reinforcing members in a design, the system of equations of the assembled structure is decomposed by using a substructuring technique. Additional boundary conditions are imposed on the interfaces between the structure and members to ensure consistency between models, and the target stiffness of the member is defined by using the boundary conditions. The optimal target stiffness and design of the members are determined through the use of a multidisciplinary design optimization technique, analytical target cascading. This method is applied to a simple portal frame and a body-in-white with reinforcing member of a vehicle manufactured by Hyundai Motor Company. By using the optimal target stiffness, reinforcing member of any shape can be designed independently and at little cost, without access of the existing structure model. [ABSTRACT FROM AUTHOR]

A modified electromagnetic topology (EMT) simulation scheme for the interactions of an electromagnetic wave with an aperture and with cables of an electrical system beyond the aperture is described. The modified EMT simulation scheme addresses a concept in dealing with an aperture node of the topological circuitry without having to specify the details of the entire electrical circuitry. The results of the modified EMT simulation scheme have been validated through experiments for aperture/wave interactions and the induced currents on the cable near the aperture. The aperture transfer functions, obtained for both the simulation and experimental cases, have shown the characteristic response similar to that of the high-pass filter with a cutoff frequency. The simulated and measured currents on a cable, placed behind the aperture, resulted in good agreement with each other, providing the good validation of the modified EMT simulation scheme. Under this scheme, any change in topological circuitry can be handled easily in the substructural levels without having to consider an entire system. Consequently, the effects of various types of aperture interactions on the entire system can be reinvestigated via simply remodeling of topological interaction nodes in substructural levels. [ABSTRACT FROM AUTHOR]

In this paper, we follow the Test-Driven Development (TDD) paradigm in the development of an in-house code to allow for the finite element analysis of finite periodic type electromagnetic structures (e.g., antenna arrays, metamaterials, and several relevant electromagnetic problems). We use unit and integration tests, system tests (using the Method of Manufactured Solutions—MMS), and application tests (smoke, performance, and validation tests) to increase the reliability of the code and to shorten its development cycle. We apply substructuring techniques based on the definition of a unit cell to benefit from the repeatability of the problem and speed up the computations. Specifically, we propose an approach to model the problem using only one type of Schur complement which has advantages concerning other substructuring techniques.

Vulnerability analysis of engineering structures is an important aspect of risk assessment. It involves the probability that the structure meets or exceeds various set damage conditions under the influence of different risk levels. In order to quantitatively analyze the vulnerability of the typical bridge substructure under debris flow, four vulnerability curves with different damage levels under debris flow impact are obtained by numerical simulation of 150 damage conditions with the aid of three-dimensional finite element analysis software. The results show that the vulnerability curves of debris flow established in this paper are well fitted with data of numerical simulation. The acceleration is fastest in the middle of the curve, and high-intensity debris flow is more likely to cause high-level damage of bridge structure. By using the vulnerability curves established in this paper, the damage probability distribution under a certain debris flow intensity and damage control points of bridge substructure can be further obtained, which provides a basis for disaster prediction, risk management and reliability analysis of transportation system. The method and model presented can provide a reference for the vulnerability analysis of other types of structures under debris flow. [ABSTRACT FROM AUTHOR]

In this paper, a novel static condensation method is extended to mechanisms and structures with internal joints. The formulation is framed inside the static reduction techniques in a similar way to the classic Guyan–Iron reduction. A new class of joint nodes is added to the existing classes of inner and boundary nodes to consider joint constraints inside the compatibility conditions. Within the set of joint nodes, a reduced subset of independent nodes can be individuated to perform the static reduction. A simple connection rule is provided to determine the independent nodes of a mechanical system composed of rigid bodies, flexible components and joints. The inner and boundary nodes are then expressed in terms of the independent joint nodes to form a new transformation matrix able to reduce the stiffness and mass matrices of the original system without connections. Joint stiffness and external forces are also included in the final reduction process. Finally, two examples prove the efficiency and demonstrate the equivalence and compatibility of the proposed method with other static reduction techniques in order to create a unique substructuring framework. [ABSTRACT FROM AUTHOR]

In this study, an efficient three-stage method is proposed for damage detection of large-scale space structures by employing forward substructuring approach, modal strain energy and enhanced bat algorithm (EBA) optimization. EBA is a modified version of BA that is proposed in this paper and used a passive congregation operator to improve the performance of standard BA. In the first stage, the global structure is divided into manageable substructures. The stiffness matrices of independent substructures are obtained based on Kron's substructuring method. Then a modal strain energy-based index is employed to precisely locate the eventual damages of the structure. In the third stage, damage severities are estimated via EBA using the second-stage results. To demonstrate the ability of the proposed method for detection of multiple structural damages, large-scale space structures with different types of damage scenarios are considered. The results show that the proposed method can detect the exact locations and severity of damages highly accurate in space structures. [ABSTRACT FROM AUTHOR]

Dynamic substructuring is a technique to simplify the analysis of complex structures. The vibrational problems of the constituent substructures are analysed and solved individually and their solutions are then assembled to form the global solution. In experimental dynamic substructuring, at least one of the constituent substructures is identified experimentally. The coupling interfaces are commonly simplified in such syntheses, which can result in poor prediction quality in many applications. The transmission simulator was introduced to address this problem. Transmission simulators are well-modelled parts attached to the interface of the substructures to be coupled. This allows for distributed interfaces and a relaxation of the coupling conditions by using the transmission simulator's analytical modes as a basis for the coupling equations, at the cost of adding a decoupling step to the substructuring problem. In this paper, the transmission simulator method is translated to the state-space substructuring domain. The methodology is applied to the Society for Experimental Mechanics' substructuring focus group's Ampair A600 test bed in form of experimental-analytical substructuring. The Ampair wind turbine's hub is used as the transmission simulator and is modelled with finite elements while the three blades, individually attached to the real hub, are experimentally identified. The three experimental blade hub systems are then coupled and two finite element hubs decoupled from the system, using the derived method. Finally, this system is compared to a directly measured hub with three blades by means of frequency response functions and modal properties. [ABSTRACT FROM AUTHOR]

Abstract 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. Highlights • A new method to accurately model the stiffness of 2D welded steel joints based on surrogate modelling • Substructuring techniques to condense full finite element model to a 4-node cruciform element • Modal decomposition techniques to reduce the number of variables and develop the design space • Kriging method and Support Vector Machine Regression to generate the surrogate models [ABSTRACT FROM AUTHOR]

Abstract A dynamic model to study the coupled longitudinal and transverse vibrations of a submarine elastic propeller-shaft-hull system is developed using the FRF-based substructuring method (FBSM). The total system is firstly modeled as two substructures: the elastic propeller-shaft subsystem and the hull shell. For the former substructure, the elastic propeller is modeled by using harmonic blade array elements and the shafts are assumed to be Timoshenko beams, while the latter one is modeled using traditional finite element method. After that, the two substructures are synthesized using FBSM. The modes, the natural frequencies and the coupled longitudinal and transverse vibration characteristics of the propeller-shaft subsystem, the hull shell, and the total system are analyzed. An experiment studying the dynamic characteristics of a large-scale submarine experimental setup is processed and compared with the numerical results, which shows great consistency. Finally, a further discussion is carried out focused on how the bearing stiffness affects the coupled vibration characteristics of the total system. Highlights • The dynamic model of an elastic propeller-shaft-hull system is developed using FBSM. • The elastic propeller is modeled by using harmonic blade array elements. • The vibration behaviors of the substructures and total system are simulated and compared. • Experiment is performed to validate the coupled vibrations of the substructures and total system. • Coupled vibration analysis using FBSM is of reasonable accuracy and high efficiency. [ABSTRACT FROM AUTHOR]

Abstract This work presents a generalized topology optimization approach for the design of hierarchical lattice structures with the development of an Approximation of Reduced Substructure with Penalization (ARSP) model. The structure is assumed to be composed of substructures with a common lattice geometry pattern. Unlike conventional homogenization-based designs assuming the separation of scales, this work considers two different yet connected scales. Each substructure is condensed first into a super-element with a reduced degrees of freedom and is associated with a density design variable indicating the material volume fraction. The density design variable is linked to a lattice geometry feature parameter. A surrogate model is particularly built with the aid of proper orthogonal decomposition and diffuse approximation, mapping the density to super-element stiffness matrix. The derivative of super-element matrix with respect to the associated density can therefore be evaluated efficiently and explicitly. The super-element matrix is further augmented with a penalized density to control the structural complexity. The optimality criteria method is used for the update of design variables. Numerical examples show that both the size and the lattice pattern of substructure have essential influences on the design, indicating the necessity of performing connected hierarchical modeling and design. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract A new coarse space for domain decomposition methods is presented for nodal elliptic problems in two dimensions. The coarse space is derived from the novel virtual element methods and therefore can accommodate quite irregular polygonal subdomains. It has the advantage with respect to previous studies that no discrete harmonic extensions are required. The virtual element method allows us to handle polygonal meshes and the algorithm can then be used as a preconditioner for linear systems that arise from a discretization with such triangulations. A bound is obtained for the condition number of the preconditioned system by using a two-level overlapping Schwarz algorithm, but the coarse space can also be used for different substructuring methods. This bound is independent of jumps in the coefficient across the interface between the subdomains. Numerical experiments that verify the result are shown, including some with triangular, square, hexagonal and irregular elements and with irregular subdomains obtained by a mesh partitioner. [ABSTRACT FROM AUTHOR]

This paper presents an efficient and extensive exploratory search for lightweight side-door intrusion-bar assembly design concepts using the approach previously developed by the author. The study aimed to discover latent dependence or other relationships between the geometry based design input parameters and the performance objectives (strength and lightweight) to identify the best engineering concept designs. The utilisation of the adopted approach and the extended substructures in particular, allowed for more than 2.6 times more design alternatives to be explored in the same time frame, which significantly increased necessary confidence in the acquired discoveries since a priori hypothesis about factors or patterns of input parameters was absent. The Pearson product-moment correlation coefficient and the Spearman's rank correlation coefficient were used to discover any potential and latent relationships, and the effects significance plots were utilised to deduce the best settings for each parameter and construct a generalised preferred shape. [ABSTRACT FROM AUTHOR]

In this study, a new technique for discrete time system reduction is suggested which preserves the substructure of the higher order system in the reduced system. Motivated by various system reduction and optimization techniques available in the literature, the proposed technique is based on Cuckoo search which is used to obtain unknown elements of the reduced system with an error criterion minimization. The efficacy of the proposed technique is justified by reducing few benchmark systems and the obtained results are compared with other well-known order reduction methods existing in the literature. [ABSTRACT FROM AUTHOR]

Abstract As a massive explosion happens inside a building, a number of structural members (columns, beams, slabs and so on) are damaged or failed, along side with non-zero initial conditions (displacement, velocity, acceleration and so on), and the progressive collapse of the building structures is most likely to occur. However, limited research works about blast load effect of structural members inside a building can be found. In view of this, based on the substructure model, a new method for progressive collapse analysis of steel frames under blast load is proposed. First, the massive explosion scenario inside a building is introduced. Then, the substructure model within effective areas of blast influence is established. After that, the calculation method of non-zero initial conditions and initial damage for structural members is given, and finally the specific steps of the proposed method are described. By way of example of a steel frame with 5 stories in height, 4 bays in the longitudinal direction, 3 bays in the transverse direction, direct simulation method, alternative load path method and proposed method are all employed to simulate the progressive collapse process, respectively. Through the example analyses, it is shown that blast load effect of structural members cannot be ignored on the ground floor, and it can be ignored on the other floors by the effect of the reinforced concrete slab. The non-zero initial conditions and initial damage of structural members can be predicted well by the substructure model, and the proposed method is also reliable and accurate. Highlights • Lots of structural members have blast load effect under massive explosion scenario. • The explosive floor and its adjacent floors can be taken as the substructure model. • A new method for progressive collapse is proposed considering blast load effect. • Different methods are employed to simulate the progressive collapse process. • Blast load effect of the components on the other floors can be ignored by the slab. [ABSTRACT FROM AUTHOR]

In current design office practice, a commonly used modelling assumption is that the base of a building structure can be idealised with fixed support conditions, thereby neglecting any effects from soil-structure interaction (SSI). Various recent studies, however, have shown that the explicit consideration of SSI effects in seismic analysis of buildings structures may significantly affect the predicted seismic demands and resulting structural performance. This study addresses some key issues and practices in the area of SSI and its effects on the dynamic response and seismic performance of buildings. It is also intended to demonstrate the significance of considering SSI effects in structural modelling and analysis while providing key insights into practical applications in real projects. Using a forty storey example building, the effect of considering SSI on the predicted seismic performance is demonstrated. For the purpose of comparison, five detailed computer models (one without considering any SSI effects, two models with SSI modelled using indirect approach, and two models with SSI modelled using direct approach) of the example building were constructed and subjected to various input ground motions. It is observed that depending upon the modelling approach used, the consideration of SSI effects may affect the predicted seismic performance in varying degrees. Moreover, the direct modelling approach presented in this study may provide improved results compared to various approximate methods. [ABSTRACT FROM AUTHOR]

The Hurty/Craig-Bampton method in structural dynamics represents the interior dynamics of each subcomponent in a substructured system with a truncated set of normal modes and retains all of the physical degrees of freedom at the substructure interfaces. This makes the assembly of substructures into a reduced-order system model relatively simple, but means that the reduced-order assembly will have as many interface degrees of freedom as the full model. When the full-model mesh is highly refined, and/or when the system is divided into many subcomponents, this can lead to an unacceptably large system of equations of motion. To overcome this, interface reduction methods aim to reduce the size of the Hurty/Craig-Bampton model by reducing the number of interface degrees of freedom. This research presents a survey of interface reduction methods for Hurty/Craig-Bampton models, and proposes improvements and generalizations to some of the methods. Some of these interface reductions operate on the assembled system-level matrices while others perform reduction locally by considering the uncoupled substructures. The advantages and disadvantages of these methods are highlighted and assessed through comparisons of results obtained from a variety of representative linear FE models. [ABSTRACT FROM AUTHOR]

A parametric reduced-order model (PROM) was developed by using a free-interface coupling method. For dynamic substructuring, the accuracy of the free-interface assembly is generally higher than that of the fixed interface one in a low frequency range, since it considers free-interface normal modes and rigid-body modes of each substructures. Therefore, by using the free-interface coupling method, we can enhance the accuracy of the PROM developed previously, in particular, the one formulated with a primal assembly. One important characteristic to retain the efficiency of PROM in the free-interface assembly is that the interpolation of substructural modes should be discriminated considering the characteristics of the modes. In the present work, we newly suggest a strategy for interpolating free-interface mode according to the change of parameter values. To verify the accuracy of the proposed PROM, we investigated the accuracy of the eigenvalues with a high-dimensional parametric input space. [ABSTRACT FROM AUTHOR]

This paper reports new dislocation configurations responsible for cyclic hardening/softening behaviour of a directionally solidified nickel base superalloy after relaxation fatigue tests at 850 °C with hold durations of 1 and 5 min. Dislocation interactions in the gamma (γ)-matrix and the formation of new dislocation configurations during relaxation fatigue (RF) test with 1 min hold duration is responsible for the cyclic hardening behaviour, whereas, the coarsening of gamma prime (γ′)-precipitates are attributed to the cyclic softening behaviour during 5 min hold testing. [ABSTRACT FROM AUTHOR]