Substructure Approach Research Articles

Dynamic soil-structure interaction models for fragility characterisation of buildings with shallow foundations

Dynamic Soil–Structure Interaction (SSI), involving the coupling of structure, foundation and soil, is a crucial and challenging problem, especially when soil nonlinearity plays an important role. This paper shows the impact of adopting different SSI models on the assessment of seismic fragility functions. The linear substructure approach is initially adopted by implementing two different models, the first of which is one-dimensional and includes, between the foundation node and the ground, a translational elastic spring and a dashpot, whose stiffness and viscous damping are retrieved from the real and imaginary parts of the dynamic impedance at the first natural frequency of the structure. The second and more refined model is a Lumped-Parameter Model (LPM) accounting for frequency dependence of the impedance. In order to explore the sensitivity of fragility functions to the linearity assumption, an additional approach, including soil nonlinearities, is employed. A nonlinear footing macro-element is adopted to model the near-field behaviour by condensing the entire soil-foundation system into a single nonlinear element at the base of the superstructure. Energy dissipation through radiation damping is also accounted for. The superstructure response is simulated in all approaches as a simple nonlinear single-degree-of-freedom (SDOF) system. The comparison between the adopted approaches is evaluated in terms of their effects on the characterisation of fragility functions for unreinforced masonry buildings (URM) on shallow foundations.

A comparison of molecular representations for lipophilicity quantitative structure-property relationships with results from the SAMPL6 logP Prediction Challenge.

Effective representation of a molecule is required to develop useful quantitative structure-property relationships (QSPR) for accurate prediction of chemical properties. The octanol-water partition coefficient logP, a measure of lipophilicity, is an important property for pharmacological and toxicological endpoints used in the pharmaceutical and regulatory spheres. We compare physicochemical descriptors, structural keys, and circular fingerprints in their ability to effectively represent a chemical space and characterise molecular features to correlate with lipophilicity. Exploratory landscape continuity analyses revealed that whole-molecule physicochemical descriptors could map together compounds that were similar in both molecular features and logP, indicating higher potential for use in logP QSPRs compared to the substructural approach of structural keys and circular fingerprints. Indeed, logP QSPR models parameterised by physicochemical descriptors consistently performed with the lowest error. Our best performing model was a stochastic gradient descent-optimised multilinear regression with 1438 descriptors, returning an internal benchmark RMSE of 1.03 log units. This corroborates the well-established notion that lipophilicity is an additive, whole-molecule property. We externally tested the model by participating in the 2019 SAMPL6 logP Prediction Challenge and blindly predicting for 11 protein kinase inhibitor fragment-like molecules. Our model returned an RMSE of 0.49 log units, placing eighth overall and third in the empirical methods category (submission ID 'hdpuj'). Permutation feature importance analyses revealed that physicochemical descriptors could characterise predictive molecular features highly relevant to the kinase inhibitor fragment-like molecules.

Vulnerability analysis of bridge superstructures under extreme fluid actions

Vulnerability analyses of bridge structures affected by extreme flood or tsunami wave loads in terms of loading variability and structural and fluid characteristics are conducted. The numerical model is developed by a combined three-dimensional (3D)/two-dimensional analysis based on phase field theory and 3D solid modeling of the fluid and structural systems, respectively. Coupling effects between the fluid and structure are simulated by using a moving mesh method based on an arbitrary Lagrangian–Eulerian approach to take bridge deformability and moving wall conditions into consideration. The proposed model is implemented in a finite element formulation, whose solution is achieved through a substructuring approach by introducing projection map operators defined to connect the structural and fluid systems. Several wave load scenarios related to the initial impact or dam break phenomena depending on inundation and blocking ratios and Froude numbers are considered. The main aim is to quantify the dynamic amplification effects of the kinematic and stress variables produced by the external loads with respect to conventional static analyses. In addition, the influences of bridge deformations on the hydrodynamic loads and vice versa are also discussed in terms of fluid and structural characteristics.

An improved substructuring approach for dynamic modelling – The example of the ITER vacuum vessel

This study deals with the substructuring method that is adopted for treating complex structures, such as the ITER Tokamak, as an assembly of different components or substructures. This method uses basic mass and stiffness matrices combined with conditions representative of the geometrical compatibility along the substructure boundaries. This approach makes it possible to simulate the dynamic behaviour of the (complex) ITER Vacuum Vessel (VV), subjected to dynamic loading (e.g. seismic), by means of a simplified model (finite element discretization) with little loss of accuracy. In this framework, a simplified model of the ITER VV for use in global seismic analyses has been developed and implemented. In order to minimize the wavefront (and hence computational time), the simplified model is made of multiple superelements, each representing a part of the VV. Moreover, in order to reduce the number of Degrees of Freedom (DoFs) needed along the boundaries of the different substructures, a new approach has also been developed for the breakdown of the benchmark model.

Schur Complement-based Substructuring of Stiff Multibody Systems with Contact

Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.

A substructuring approach based on mechanical admittances to solve vibro-acoustic problems in the mid-frequency range

In the low frequency range, discretization methods such as the Finite Element Method are the preferred techniques to solve vibro-acoustic problems. The main limitation of such approaches is that the mesh needs to be refined when the frequency increases, leading to prohibitive calculation costs. This paper presents the Condensed Transfer Function (CTF) method for substructuring vibro-acoustic problems. The problem is split in several structural, acoustic or vibro-acoustic subsystems that are studied individually before being assembled. The vibro-acoustic behavior at the boundaries of the subsystems is expressed in terms of mechanical admittance for structures and acoustic impedance for fluid domains. A set of condensation functions is used as a basis to express the values at the boundaries. The coupling between subsystems is written through the continuity equations of mechanics. Compared to classical reduction methods such as Craig-Bampton, this approach does not require the prior knowledge of the modal basis of the subsystems. Also, the CTF method allows coupling subsystems that are described by different techniques, i.e., analytically, numerically or experimentally. The principle of the method will be recalled and example of applications will be given. In particular, numerical and experimental results on a stiffened cylindrical shell will be compared.In the low frequency range, discretization methods such as the Finite Element Method are the preferred techniques to solve vibro-acoustic problems. The main limitation of such approaches is that the mesh needs to be refined when the frequency increases, leading to prohibitive calculation costs. This paper presents the Condensed Transfer Function (CTF) method for substructuring vibro-acoustic problems. The problem is split in several structural, acoustic or vibro-acoustic subsystems that are studied individually before being assembled. The vibro-acoustic behavior at the boundaries of the subsystems is expressed in terms of mechanical admittance for structures and acoustic impedance for fluid domains. A set of condensation functions is used as a basis to express the values at the boundaries. The coupling between subsystems is written through the continuity equations of mechanics. Compared to classical reduction methods such as Craig-Bampton, this approach does not require the prior knowledge of the modal ba...

Assessment of dynamic soil-structure interaction effects for tall buildings: A 3D numerical approach

Soil-structure interaction (SSI) phenomena are typically studied in the frequency-domain using the substructure approach, involving several simplifications. In this study, SSI effects for a 20-storey building are studied numerically performing time-domain 3D non-linear dynamic analyses, using an elastoplastic nonlinear constitutive model for the soil. Three foundation systems - a relatively shallow, a deeply embedded and a pile foundation - and two soil profiles are investigated and compared. Specifically, relative merits of site amplification, kinematic interaction and inertial interaction are isolated, and the role of foundation deformability and local stratigraphy is highlighted. To isolate such features, the results of the complete 3D models are compared with those provided by 3D numerical analyses of the sole building, of the foundation-soil systems and of the free-field soil deposit.Numerical results show that, for tall buildings, an increase in foundation deformability leads to a decrease of the maximum base shear force (seismic demand), to a higher rigid rotation of the foundation, but not to appreciably higher displacements of the structure. Moreover, possible situations where a (decoupled) substructure approach can lead to a misinterpretation of SSI phenomena are highlighted, as in the case of deep foundations crossing very soft soil layers.In addition, the use of embedded pile elements was proven to be an effective strategy in reducing the computational cost when performing complex 3D simulations of dynamic SSI problems.

Adaptive tracking control for real-time hybrid simulation of structures subjected to seismic loading

Abstract Real-time hybrid simulation (RTHS) is an interesting method for studying the performance of structures subjected to dynamic loading. RTHS decomposes a structure into partitioned physical and numerical sub-structures that are coupled together through actuation systems. The sub-structuring approach is particularly attractive for studying large-scale problems since it allows for setting up large-scale structures with thousands of degrees of freedom in numerical simulations while specific components can be studied experimentally. Due to the RTHS system dynamics, there is an inevitable time delay that affects accuracy and stability of the simulation. Several tracking control algorithms have been proposed to compensate time delay and improve the accuracy, however, robustness still presents challenges to obtain successful simulation results. In this paper, a Conditional Adaptive Time Series (CATS) compensator is proposed based on the principles of the Adaptive Time Series compensator (ATS) for a benchmark problem that consists of a three-story shear frame with one degree of freedom (DOF) in a virtual RTHS (vRTHS) that considers numerical and experimental models subjected to earthquake loading. A recursive least square (RLS) algorithm is adopted for the parameter estimation of the controller to reduce computational efforts in the simulation. The performance and robustness of a first-order CATS controller is evaluated for different partitioned cases. It is shown that an adaptive compensation strategy is an effective approach for RTHS based on nine performance criteria due to its simple implementation and accuracy.

A review on dynamic substructuring methods for model updating and damage detection of large-scale structures

Substructuring methods possess many merits in model updating and damage identification of large-scale structures. With substructuring methods, a global structure is divided into a number of independent substructures. Only the substructures are repeatedly analyzed and the re-analysis of the global structure is thereby avoided. This article reviews widely used dynamic substructuring methods for model updating and damage identification of large-scale structures. These methods can be categorized into forward and inverse substructuring approaches. The former is a conventional process that assembles the vibration properties of each substructure to obtain the vibration properties of the global structure. The latter, on the contrary, disassembles the vibration properties of the global structure into those of the substructures. In each category, both frequency and time domain methods have been developed and will be reviewed.

An iterative reduced-order substructuring approach to the calculation of eigensolutions and eigensensitivities

Substructuring methods are efficient to estimate some lowest eigensolutions and eigensensitivities of large-scale structural systems by representing the global eigenequation with small-sized substructural eigenmodes. Inclusion of more substructural eigenmodes improves the accuracy of eigensolutions and eigensensitivities, whereas decreases the computational efficiency adversely. This paper proposes a new iterative reduced-order substructuring method to calculate the eigensolutions and eigensensitivities of the global structure. A modal transformation matrix, relating the higher modes to the lower modes, is derived to transform the original frequency-dependent matrices of each substructure into frequency-independent ones. A simplified reduced-order eigenequation is then obtained through a few iterations performed on the modal transformation matrix and mass matrix. The eigensolutions and eigensensitivities of the global structure are calculated accurately with a small number of substructural eigenmodes retained, avoiding the inclusion of numerous substructural eigenmodes. Applications of the proposed method to a numerical frame and a practical large-scale structure demonstrate that the eigensolutions and eigensensitivities of the global structure can be calculated accurately with only a small number of substructural eigenmodes and a few iterations.

Comparing the performance of substructure and direct methods to estimate the effect of SSI on seismic response of mid-rise structures

ABSTRACT The effects of soil–structure interaction on seismic responses of structures have always been a challenging topic for earthquake and structural engineers. Over the years, different ways have been introduced by researchers to consider the effect of this phenomenon during design procedure of structures. In this study, the performance of three different modelling methods including one direct and two substructure approaches has been compared to reveal the ability of each method to estimate the seismic responses of mid-rise structures. For this purpose, the seismic behaviour of two steel moment-resisting frames under different modelling conditions has been investigated and the results have been reported in terms of interstorey drift ratio.

Seismic Response Characteristics of a Piled Raft in Clay

This paper presents a study on three-dimensional seismic soil–structure interaction analysis of a piled-raft (PR) foundation in clay by the substructure approach. Two different pile modeling techniques were adopted and compared with centrifuge shaking table test results reported in the literature. The effect of pile spacing on dynamic impedances, kinematic response parameters, axial pile forces and bending moments of PRs is studied. It is found that the presence of a rigid raft on a pile group results in significant variation in vertical and horizontal dynamic stiffness after a dimensionless frequency ([Formula: see text] value of around 0.22. The influence of raft on kinematic response parameters at the top of raft is found to be significantly influenced by pile spacing beyond a dimensionless frequency ([Formula: see text] value of 0.4. The axial forces generated at the pile heads of a PR–structure system during seismic shaking are quantified using a new dimensionless factor, and are found to be significantly influenced by the pile spacing. Pile layout in the PR system is found to play an influential role in seismic response as well as pile bending moment for a structure–PR–soil system studied.

Analysis of seismic damage mitigation for a pile-supported wharf structure

This paper evaluates earthquake-induced permanent ground deformations and the structural response of a typical pile-supported wharf structure built over loose granular fill. Using numerical simulations for a suite of 55 reference seismic ground motions, we investigate the effectiveness of an array of PV drains installed behind the pile-supported deck in mitigating structural damage associated with deformations of the fill. Numerical analyses use a sub-structuring approach in which the ‘free-field’ 2D coupled deformations, and seepage within the soil fill are simulated using the u-p formulation in the OpenSees finite element framework. The complex non-linear and inelastic stress-strain properties of the sand under cyclic loading are represented using the Dafalias-Manzari (DM2004) bounding surface plasticity model, while customized 1-D finite elements are used to describe flow in the PV drains. The resulting ground deformations and excess pore water pressures are treated as boundary conditions in modeling the response of the wharf structure, through macro-elements that represent local pile-soil interactions (after Varun and Assimaki, 2012 [1]). We discuss the associated soil behavior and show how lateral spreading is mitigated by the proposed PV drain array. This mitigation system limits the potential damage to the pile-deck connections enabling much simpler structural retrofit for the wharf.

Using a Dynamic Substructuring Approach to Model the Effects of Acoustic Damping in Coupled Acoustic–Structure Systems

Acoustic–structure coupling can substantially alter the frequency response of air-filled structures. Coupling effects typically manifest as two resonance peaks at frequencies above and below the resonant frequency of the uncoupled structural system. Here, a dynamic substructuring approach is applied to a simple acoustic–structure system to expose how the system response depends on the damping in the acoustic subsystem. Parametric studies show that as acoustic damping is increased, the frequencies and amplitudes of the coupled resonances in the structural response undergo a sequence of changes. For low levels of acoustic damping, the two coupled resonances have amplitudes approximating the corresponding in vacuo resonance. As acoustic damping is increased, resonant amplitudes decrease dramatically while the frequency separation between the resonances tends to increase slightly. When acoustic damping is increased even further, the separation of the resonant frequencies decreases below their initial separation. Finally, at some critical value of acoustic damping, one of the resonances abruptly disappears, leaving just a single resonance. Counterintuitively, increasing acoustic damping beyond this point tends to increase the amplitude of the remaining resonance peak. These results have implications for analysts and experimentalists attempting to understand, mitigate, or otherwise compensate for the confounding effects of acoustic–structure coupling in fluid-filled test structures.

Analysis of the Effects of Soil on the Seismic Energy Responses of an Equipment‐Structure System via Substructure Shaking Table Testing

This study investigated the real‐time substructure shaking table testing (RTSSTT) of an equipment‐structure‐soil (ESS) system and the effects of soil on the seismic energy responses of the equipment‐structure (ES) subsystem. First, the branch modal substructure approach was employed to derive the formulas needed for the RTSSTT of the ESS system. Then, individual equations for calculating the energy responses of the equipment and the structure were provided. The ES subsystem was adopted as the experimental substructure, whereas the reduced soil model was treated as the numerical substructure when the RTSSTT was performed on the ESS system. The effectiveness of the proposed testing method was demonstrated by comparing the test results with those of the integrated finite element analysis. The energy responses of the ES subsystem in the case of rigid ground (i.e., the ES system) were compared with those considering the effects of soil (i.e., the ESS system). The input energy responses of the ES subsystem were found to decrease significantly after taking the effects of soil into account. Differences due to the soil effects should be considered in the seismic design for the ES system.

Overview of Craig‐Bampton Substructuring Approaches for Model Order Reduction of Nonclassically Damped Systems

AbstractThe classical Craig‐Bampton method (1968) does not take any damping effects into account for the model order reduction of damped systems. One procedure to handle nonclassically damped systems is to transform the second‐order differential equations into state‐space representation. Solving the corresponding eigenvalue problem allows the damped equations to be decoupled, but complex eigenmodes and eigenvalues occur. A comparison between different formulations for nonclassically damped systems is given and demonstrated by an example.

Seismic analysis method of equipment–high rise structure–nonlinear soil system

Based on the principle of real-time substructure shaking table test, an interactive numerical computation method which built the calculation model of each substructure in different software programs was proposed for seismic analysis of equipment–high rise structure–soil systems in order to account the effect of nonlinear soil. Considering that the response of soil under strong earthquakes does not totally enter the nonlinear stage, a locally nonlinear soil model was introduced as the numerical substructure, and the equipment–high rise structure subsystem was treated as an experimental substructure in this method. The equation of motion for the equipment–high rise structure–soil system was derived through a combination of the branch modal substructure and linear–nonlinear hybrid constraint modal substructure approaches. A 13-layer steel framework system model is used as an analytical example that the equipment–high rise structure system and local nonlinear soil computing model are built by MATLAB and ANSYS, respectively. The time histories of the system dynamic responses were obtained by interactive numerical computation, to investigate the effects of equipment–high rise structure–soil interaction on the seismic performance of the equipment and structure.

PARADOXES AND STRUCTURAL RULES FROM A DIALOGICAL PERSPECTIVE

AbstractIn recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations do we have (if any) for restrictions on structural rules, and what to make of the plurality of new logics emerging from these restrictions, i.e. how to ‘choose’ among the different options. In this paper, we address these two questions from the perspective of a dialogical conception of logic that we've been advocating in recent years. We will argue that dialogical interpretations of structural rules, that is, as rules determining specific properties of the dialogues in question, provide a conveniently neutral framework to adjudicate between the different substructural proposals that have been made in the literature on paradoxes.

A three-stage damage detection method for large-scale space structures using forward substructuring approach and enhanced bat optimization algorithm

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.

Interaction analysis of three storeyed building frame supported on pile foundation

The study deals with physical modeling of a typical three storeyed building frame supported by a pile group of four piles (2x2) embedded in cohesive soil mass using three dimensional finite element analysis. For the purpose of modeling, the elements such as beams, slabs and columns, of the superstructure frame; and that of the pile foundation such as pile and pile cap are descretized using twenty noded isoparametric continuum elements. The interface between the pile and the soil is idealized using sixteen node isoparametric surface element. The soil elements are modeled using eight nodes, nine nodes and twelve node continuum elements. The present study considers the linear elastic behaviour of the elements of superstructure and substructure (i.e., foundation). The soil is assumed to behave non-linear. The parametric study is carried out for studying the effect of soil- structure interaction on response of the frame on the premise of sub-structure approach. The frame is analyzed initially without considering the effect of the foundation (non-interaction analysis) and then, the pile foundation is evaluated independently to obtain the equivalent stiffness; and these values are used in the interaction analysis. The spacing between the piles in a group is varied to evaluate its effect on the interactive behaviour of frame in the context of two embedment depth ratios. The response of the frame included the horizontal displacement at the level of each storey, shear force in beams, axial force in columns along with the bending moments in beams and columns. The effect of the soil- structure interaction is observed to be significant for the configuration of the pile groups and in the context of non-linear behaviour of soil.