Substructure Approach Research Articles

New strategy of substructure method to model long-span hybrid cable-stayed bridges under vehicle-induced vibration

Hybrid cable-stayed bridges consist of steel and concrete bridge segments, of which steel–concrete joints are of great importance and raise strong research interest. Due to the limitation of the traditional methods, i.e., the member finite element (FE) method and Mixed Dimensional Coupling (MDC) method, the present study proposes a substructure method to model long span bridges. The current application of the substructure method is to extract some specific parts of the whole structure to refine and analyze them. Different from the routine substructure approach, here the entire structure is modeled in detail and divided into many substructures. All the substructures are then condensed into super-elements except the concerned part. The application of the method is then illustrated through numerical studies of the vehicle–bridge coupling vibration of the Jingyue Yangtze River Bridge with a main span of 816 m. The entire bridge is first divided into many substructures with a reasonable length. Among them, the concerned substructure with 23.8 m in length including the steel–concrete joint is modeled in detail but not formed into super-element, while all the other components are modeled in detail and formed into super-elements using the component mode synthesis (CMS) method. All the components including both the super-elements and non-super-elements are then assembled into a complete and fine full bridge model. Finally, the model is used for the vehicle-induced dynamic analysis under deterministic traffic flows. The results show that the joint works well, and the transition between the steel girders and concrete beams is very smooth.

Multi-level substructuring combined with model order reduction methods

In many fields of engineering problems linear time-invariant dynamical systems (LTI systems) play an outstanding role. They result for instance from discretizations of the unsteady heat equation and they are also used in optimal control problems. Often the order of LTI systems is a limiting factor, since it becomes easily very large. As a consequence these systems cannot be treated efficiently without model reduction algorithms. In this paper a new approach for the combination of model order reduction methods and recent multi-level substructuring (MLS) techniques is presented. Similar multi-level substructuring methods have already been applied successfully to huge eigenvalue problems up to several millions of degrees of freedom. However, the presented approach does not make use of a modal analysis like former algorithms. Instead the original system is decomposed in smaller LTI systems which are treated with recent model reduction methods. Furthermore, the error which is induced by this substructuring approach is analysed and numerical examples based on the Oberwolfach benchmark collection are given in this paper.

Identification of non-linear structural parameters under limited input and output measurements

In this paper, an algorithm is proposed for the identification of non-linear structural parameters under limited input and output measurements. The algorithm is based on the sequential application of extended Kalman estimator for the non-linear structural parameters and the least-squares estimation for the unmeasured excitation. First, the identification of small size non-linear structural parameters is studied. Then, based on the substructure approach, the algorithm is extended to identify large size non-linear structural parameters. Interconnection effect between adjacent substructures is accounted by considering the interconnection forces at substructural interfaces as ‘additional unknown inputs’ to the substructures. The general case that measurements at the substructure interfaces are not available is considered. Two numerical examples which identify non-linear hysteretic parameters of a four-story and an eight-story hysteretic shear-beam building subject to unmeasured excitation respectively, demonstrate the efficiency of the proposed algorithm.

Structural damage detection with limited input and output measurement signals

It is important but still challenging to detect structural damage with limited input and output measurement signals. In this paper, an algorithm is proposed for detecting structural damage with limited input and output measurement signals. The algorithm is based on sequential application of an extended Kalman estimator for the extended state vector of a structure and least-squares estimation of its unknown external excitations. Analytical recursive solutions for the identification of structural parameters and unknown excitations are derived. Such straightforward derivation and analytical solutions are not available in the previous literature. Structural damage can be detected from the degradation of the identified element stiffness. Numerical examples of detecting damage of some small size structural systems are used to demonstrate the performances of the proposed algorithm. Then, the algorithm is extended to detect structural damage of large size structural systems based on substructure approach. Inter-connection effect between adjacent substructures is considered by ‘additional unknown inputs’ to substructures. It is shown that the ‘additional unknown inputs’ can be estimated by the algorithm without the measurements of the substructure interface DOFs, which is superior to previous identification approaches. A numerical example of detecting structural damage of a large size truss illustrates the efficiency of the proposed algorithm.

Synthesis and chromatographic evaluation of molecularly imprinted polymers prepared by the substructure approach for the class-selective recognition of glucuronides

Two series of molecularly imprinted polymers (MIPs) for the class-selective recognition of glucuronides have been prepared by using lipophilic substructures of the target analyte as template molecule and potent host monomers against oxyanions, that are expected to establish a strong stoichiometric interaction with the single carboxylic group of the template. The polymers were tested as stationary phases in liquid chromatography for specific recognition. A preliminary investigation of the imprinting properties of eleven MIPs was carried out, by comparing the retention time of the template and of structurally related compounds on the MIP column with that on the corresponding non-imprinted polymer (NIP). The two polymers showing the best performance were selected to further test cotinine, mycophenolic acid, testosterone and their respective glucuronides as model compounds. The high specificity obtained against glucuronides and the different chemical structure of the parent drug make the two MIPs class-selective imprinted receptors, also suitable for SPE application.

A wave-based substructuring approach for concept modeling of vehicle joints

In highly competitive fields, such as the automotive industry, complex products must be innovated in short timeframes and at affordable costs. The need for simulation tools, able to steer and support the early design choices, pushes researchers to develop concept modeling techniques. In this paper, an innovative procedure, based on the wave-based substructuring (WBS) technology, is proposed to achieve a database framework for joint concepts, so that joint alternatives can be easily exchanged in concept modification and optimization studies. An industrial case study is analysed, where the proposed methodology is validated through static and dynamic FE analyses.

Identification of stiffness and damping characteristics of axial air-foil bearings

Air-foil bearings (AFBs) are self acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while the layer or layers underneath provide an elastic foundation. AFBs are currently used in many commercial applications, both terrestrial and in aerospace. AFBs provide a means to eliminate the oil system leading to reduce weight and enhanced temperature capability. Regardless of the application of the AFBs, the identification of the structural characteristics is important for successful design practice. In the present work, structural characteristics (stiffness and damping) of axial AFBs are indentified in the light of experimental results. Due to the initial high torque requirement of the AFB, the experimental setup using a single AFB is proposed instead of standard two-foil bearing setups. Experiments are carried out at maximum speed of 60,000 rpm. Sub-structuring approach is used for identification of the structural (stiffness and damping) characteristics of the AFB. The results have shown that the developed experimental procedure is able to identify the stiffness and damping characteristics of axial AFBs accurately.

Identification of Dynamical Contact Parameters for Spindle-Tool Holder Interface Based on the Receptance Coupling Substructure Approach

It is very crucial to accurately identify the parameters of contact dynamics in predicting the chatter stability of spindle–tool holder assemblies in machining centers. Fast and accurate identification of contact dynamics in spindle–tool holder assembly has become an important issue in the recent years. In this paper, the receptance coupling substructure approach is employed for identification the stiffness and damping of the interface in a simple manner, in which the frequency response function of the tool holder is derived from the Timoshenko beam finite elements model. A BT 50 type tool holder is adopted as an application example of the method. Although this study focuses on the contact dynamics at the spindle–tool holder interfaces of the assembly, the approach might be used for identifying the dynamical parameters of other critical interface.

Improving Parallel Substructuring Efficiency by Using a Multilevel Approach

This research adopted a multilevel substructuring approach to improve the efficiency of parallel substructure finite-element analysis. The multilevel approach employed in this work provides a simple way to parallelize the computational workload of solving the interface equation system and reduces the total time cost. Eight numerical examples of structural analysis were used to demonstrate the effectiveness of the multilevel parallel substructural method for nonlinear dynamic structural analysis. The scalability with respect to number of cores and problem sizes was investigated. The results showed that, compared with the ordinary single-level approach, the multilevel approach reduces up to 50% of the interface equation system solving time and improves the overall efficiency of parallel substructural method by up to 40% in the examples.

Experimental modal substructuring to estimate fixed-base modes from tests on a flexible fixture

Fixed boundary conditions are often difficult if not impossible to simulate experimentally, but they are important to consider in many applications. In principle, modal substructuring or impedance coupling approaches can be used to predict the fixed base modes of a system from tests where the system has some other boundary condition if the motion at the connection point can be measured, but this approach can be highly sensitive to imperfections in the experimental measurements. This work presents two alternatives that reduce the sensitivity to experimental errors, capitalizing on recent works where additional degrees of freedom are used to improve the robustness of substructure uncoupling. The system of interest is tested while mounted on a stiff fixture, where some modes of the fixture inevitably interact with those of the system of interest. The modes of the system–fixture assembly are extracted using a modal test and then a modal substructuring approach is used to apply constraints to eliminate the motion of the fixture. Two types of constraints are proposed, one based on the modes of the fixture and the other on a singular value decomposition of the fixture motion that was observed during the test. Neither approach requires an estimate of the displacements or rotations at the points where the system of interest is connected to the fixture. The methods are validated by applying them to experimental measurements from a simple test system meant to mimic a flexible satellite on a stiff shaker table. A finite element model of the subcomponents was also created and the method is applied to its modes in order to separate the effects of measurement errors and modal truncation. The proposed method produces excellent predictions of the first several modes of the fixed-base structure, so long as modal truncation is minimized. The proposed approach is also applied to experimental measurements from a wind turbine blade mounted in a stiff frame and found to produce reasonable results.

Embedment effects of flexible foundations on control of structures

In the design of controller for earthquake-excited building benchmark, it is common to inquire about the present relationships between controlled building performance and the considering soil–foundation–structure interaction (SFSI) effects for description of the earthquake excitation. The SFSI effects can drastically affect the response of the structures subjected to earthquake motion. The effects of embedment depth on the control of structures, under plane-strain conditions, have been studied by substructure approach for buildings supported by rigid foundations embedded into a homogeneous, isotropic and elastic half-space. It is assumed that control devices are installed on all the floors. It is concluded that deeply embedded structures may increase the energy dissipated by control devices for the case of considering SFSI effects than expected from the fixed-base model and decrease the H 2 norm of the system transfer function than control of structures with surface supported foundations. The effects are intensified for structures located on relatively soft soils. The inter-story drifts for control of squat structures with embedded foundations may reduce than the one controlled according to the fixed-base model, while it may increase the demand of inter-story drifts for the case of control of slender interacting systems. According to these results, considering SFSI effects on structural control can make some unexpected damages. Hence, for structures rested in or on soft soil that are controlled by active or semi-active control devices, SFSI effects in controller design should be considered.

Application of the EKE and LSE-UI Based Substructure Approach for Damage Detection with Limited Output Measurements

This paper presents an effort to apply the EKE (extended Kalman estimator) and LSE-UI (least squares estimation for unknown input) technique to detect structures damage with limited output measurements. This technique can be extended to detect structural local damage in complex structures based on substructure approach. Structural parameters and the unknown inputs are identified by a recursive algorithm based on sequential application of the extended Kalman estimator for the extended state vector and the least squares estimation for the unknown inputs. Only a limited number of measured acceleration responses of the benchmark structure subject to unmeasured excitation inputs are utilized. This structural damage detection method is applied to the ASCE SHM benchmark building to test its efficacy and provide a solution to the complex case of the Phase I benchmark problem. Damage detection results indicate that the proposed technique can detect and localize structural damage of the complex benchmark problem with good accuracy.

A Two-Step Numerical Method for Efficient Analysis of Structural Response to Blast Load

Even with modern computer power, detailed numerical modeling and simulation of structure response to blast loads are still extremely expensive and sometimes prohibitive because it is very time consuming and requires huge computer memory. Often compromise has to be made between simulation efficiency and simulation accuracy. A lot of research efforts have been spent on improving the computational efficiency. Most of these researches concentrate on simplifying the structures, such as simplifying a structure to an equivalent SDOF system, use smeared reinforcement steel and concrete model, use substructure approach to only model part of the structure in detail. Although these approaches under certain conditions yield reliable predictions, each of them has its associated limitations. Recently a two-step method was developed to improve the computation and modeling efficiency of structure response to blast loads. Instead of simplifying the structure, the proposed method calculates the structural responses in two steps. The first step calculates the structural responses in the loading phase and the second calculates the free vibration responses with the velocity profile of the structure at the end of the loading phase as initial conditions. Using a reinforced concrete beam as the example, it was found that the proposed method yields reliable predictions of the overall beam deflection and stress in longitudinal reinforcement bars with less than 10% computational time as compared to a detailed FE model simulation. However, the predicted stress in hoop reinforcements near the beam supports is not as good. In this paper, the method is improved by also including displacement response at the end of the forced-vibration phase as the initial conditions in the free vibration analysis. The same reinforced concrete beam is used. The results show that including the displacement initial conditions in the two-step method leads to an improved prediction of the beam responses. Parametric calculations are performed in this study by varying the blast loading amplitude and duration. Using the detailed FE model simulation results as benchmark, the prediction errors on various response quantities and savings on computational times of the proposed two-step method with respect to different blast loading scenarios are presented. The accuracy and efficiency of the proposed method in predicting structural responses and damage to blast loadings are demonstrated in this paper.

An iterative substructuring approach to the calculation of eigensolution and eigensensitivity

The eigensolutions and associated eigensensitivities of an analytical model are usually calculated at the global structure level, which is time-consuming or even prohibitive for large-scale structures. Several substructuring approaches have been proposed that divide the global structure into some manageable substructures and assemble parts of the eigensolutions and eigensensitivities of the substructures to recover those of the global structure. However, these approaches are not usually accurate, as only the lowest eigensolutions and eigensensitivities are retained and the higher modes are excluded. In this paper, a new iterative substructuring method is proposed to accurately obtain the eigensolutions and eigensensitivities of structures. With this new approach, the contribution of the higher modes to the reduced eigenequation is retained as a residual flexibility matrix in an iterated form, which allows the eigenvalues and eigenvalue derivatives to be obtained from the previous results. The eigenvectors and their derivative matrices can be calculated from a reduced eigenequation directly without iteration. Upon convergence, the iterative scheme reproduces the eigensolutions and eigensensitivities of the original structure exactly. The computational efficiency and numerical accuracy of the proposed method are verified by the applications to a cantilever plate structure and an actual super-tall structure.

A substructure approach to local damage detection of shear structure

SUMMARY We propose a substructure approach that allows for the local damage detection of a shear structure. This method requires only three sensors to identify localized damage in any story of a shear structure building. A substructure approach was used in this method to divide a complete structure into several substructures in order to significantly reduce the number of unknown parameters for each substructure so that damage detection processes can be independently conducted on each substructure. Thus, our method is suitable for use in a parallel and distributed damage detection system. Simulations and experiments on five-story buildings were conducted to test the feasibility of our proposed method. Copyright © 2011 John Wiley & Sons, Ltd.

A Substructuring Method for Model Updating and Damage Identification

Model updating of large-scale structures is time-consuming as the global system matrices need to be assembled continuously and the global eigensolutions and eigensensitivities are required in each iteration, even only a few elemental parameters need updating. In this paper, a substructuring approach is proposed to extract the substructural dynamic flexibility matrices from the measured modal properties of the global structure under the constraints of force compatibility and displacement compatibility. Thereafter the focused substructure is treated as an independent structure and updated directly using the traditional model updating method. It not only reduces the size of the analytical model involved in model updating but also decreases the uncertain parameters that need updating, thus resulting in a rapid convergence of the optimization process. Moreover, if a particular substructure needs updating, the measurement can be focused on the local area of the interested substructure only and the requirement of measurement on the entire structure is avoided. A laboratory tested frame structure is employed to illustrate the effectiveness and accuracy of the proposed method.

Identification of dynamic properties of radial air-foil bearings

Air-foil bearings (AFBs) are self acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while the layer or layers underneath provide an elastic foundation. Air-foil bearings are currently used in many commercial applications, both terrestrial and aerospace. Air-foil bearings provide a means to eliminate the oil system leading to reduce weight and enhanced temperature capability. Regardless of the application of the air-foil bearings, the identification of the dynamic characteristics is important for successful design practice. In the present work, stiffness and damping of radial air-foil bearings are indentified in the light of experimental results. Due to the initial high torque requirement of the air-foil bearing, the experimental setup using single air-foil bearing is proposed instead of standard two-foil bearing setups. Experiments are carried out at maximum speed of 60,000 rpm. Sub-structuring approach is used for identification of stiffness and damping properties of the air-foil bearings. The results have shown that the developed experimental procedure is able to indentify the stiffness and damping properties of radial air-foil bearings accurately.

Improved reduced order solution techniques for nonlinear systems with localized nonlinearities

This paper examines the modeling and solution of large-order nonlinear systems with continuous nonlinearities which are spatially localized. This localization is exploited by a combined component mode synthesis (CMS)—dynamic substructuring approach for efficient model reduction. A new ordering method for the Fourier coefficients used in the Harmonic Balance Method (HBM) is proposed. This allows the calculation of the slave dynamic flexibility matrix, using simple analytical expressions thus saving considerable computational effort by avoiding inverse calculation. This procedure is also capable of handling proportional damping. A hypersphere-based continuation technique is used to trace the solution, and hence track bifurcations since it has the advantage that the augmented Jacobian matrix remains square. The reduced system is also solved using a time-variational method (TVM) which generates sparse Jacobian matrices when compared with HBM. Several systems including those with parametric excitation and internal resonances are solved to demonstrate the capability of the proposed schemes. A comparison of these techniques and their effectiveness in solving extremely strong nonlinear systems with continuous nonlinearities is discussed.

Building frame - pile foundation - soil interaction analysis: a parametric study

The effect of soil-structure interaction on a single-storey, two-bay space frame resting on a pile group embedded in the cohesive soil (clay) with flexible cap is examined in this paper. For this purpose, a more rational approach is resorted to using the finite element analysis with realistic assumptions. Initially, a 3-D FEA is carried out independently for the frame on the premise of fixed column bases in which members of the superstructure are discretized using the 20-node isoparametric continuum elements. Later, a model is worked out separately for the pile foundation, by using the beam elements, plate elements and spring elements to model the pile, pile cap and soil, respectively. The stiffness obtained for the foundation is used in the interaction analysis of the frame to quantify the effect of soil-structure interaction on the response of the superstructure. In the parametric study using the substructure approach (uncoupled analysis), the effects of pile spacing, pile configuration, and pile diameter of the pile group on the response of superstructure are evaluated. The responses of the superstructure considered include the displacement at top of the frame and moments in the columns. The effect of soil-structure interaction is found to be quite significant for the type of foundation considered in the study. Fair agreement is observed between the results obtained herein using the simplified models for the pile foundation and those existing in the literature based on a complete three dimensional analysis of the building frame - pile foundation - soil system.

A substructure approach tailored to the dynamic analysis of multi-span continuous beams under moving loads

The paper deals with the dynamic analysis of multiply supported continuous beams subjected to moving loads, which in turn can be modelled either as moving forces or moving masses. A dedicated variant of the component mode synthesis (CMS) method is proposed in which the classical primary–secondary substructure approach (SA) is tailored to cope with slender (i.e. Euler–Bernoulli) continuous beams with arbitrary geometry. To do this, the whole structure is ideally decomposed in primary and secondary spans with convenient restraints, whose exact eigenfunctions are used as assumed local modes; the representation of the internal forces is improved with the help of two additional assumed modes for each primary span, while primary–secondary influence functions allow satisfying the kinematical compatibility between adjacent spans; the continuous beam is then re-assembled, and the Lagrange's equations of motion are derived in a compact block-matrix setting for both moving force and moving mass model. Numerical examples demonstrate accuracy and efficiency of the proposed procedure. An application with a platoon of high-speed moving masses confirms that the inertial effects neglected in the moving force model may have a significant impact in the structural response.