Response Of Linear Structures Research Articles

Fluid Structure Interaction Using Modal Superposition and Lagrangian CFD

This study investigates the impact of fluid loads on the elastic deformation and dynamic response of linear structures. A weakly coupled modal solver is presented, which involves the solution of a dynamic equation of motion with external loads. The mode superposition method is used to find the dynamic response, utilizing predetermined mode shapes and natural frequencies associated with the structure. These essential parameters are pre-calculated and provided as input for the simulation. Integration of the weakly coupled modal solver is accomplished with the Lagrangian Differencing Dynamics (LDD) method. This method can directly use surface mesh as boundary conditions, so it is much more convenient than other meshless CFD methods. It employs Lagrangian finite differences, utilizing a strong formulation of the Navier–Stokes equations to model an incompressible free-surface flow. The elastic deformation of the structure, induced by fluid forces obtained from the flow solver, is computed within the modal coupling algorithm through direct numerical integration. Subsequently, this deformation is introduced into the flow solver to account for changes in geometry, resulting in updated flow pressure and velocity fields. The flow particles and vertices of the structure are advected in Lagrangian coordinates, resulting in Lagrangian–Lagrangian coupling in spaces with weak or explicit coupling in time. The two-way coupling between fluid and structure is successfully validated through various FSI benchmark cases. The efficiency of the LDD method is highlighted as it operates directly on surface meshes, streamlining the simulation setup. Direct coupling of structural deformation eliminates the conventional step of mapping fluid results onto the structural mesh and vice versa.

Analysis of Wave-Induced Forces on a Floating Rectangular Box with Analytical and Numerical Approaches

A three-dimensional mathematical hydrodynamic model associated with surface wave radiation by a floating rectangular box-type structure due to heave, sway, and roll motions in finite water depth is investigated based on small amplitude water wave theory and linear structural response. The analytical expressions for the radiation potentials, wave forces, and hydrodynamic coefficients are presented based on matched eigenfunction expansion method (MEFEM). The correctness of the analytical results of wave forces is compared with the construction of a numerical model using the open-source boundary element method code NEMOH. In addition, the present result is compared with the existing published experimental results available in the literature. The effects of the different design parameters on the floating box-type rectangular structure are studied by analyzing the vertical wave force, horizontal wave force, torque, added mass, and damping coefficients due to the heave, sway, and roll motions, and the comparison analysis between the forces is also analyzed in detail. Further, the effect of reflection and transmission coefficients by varying the structural width and drafts are analyzed.

Design‐oriented nonlinear‐elastic buckling analysis of reinforced concrete wall structures using convex optimization

AbstractThe structural response of slender reinforced concrete (RC) structures may be highly nonlinear due to cracking, reinforcement yielding, and geometrically nonlinear effects. While advanced models can simulate the detailed response of such structures, they are generally ill‐suited for limit state verification in practical design scenarios due to a high computational and modeling effort. A design‐oriented method for evaluating the geometrically linear response of cracked RC wall structures was recently presented and demonstrated to allow the analysis of large‐scale models with more than 2400 finite shell elements within minutes on a standard personal computer. This paper proposes a design‐oriented numerical method for efficient instability analysis of slender RC wall structures, also enabling the inclusion of thermal effects. Based on a two‐step linearized buckling analysis, the method first determines the geometrically linear structural response by solving the complementary energy minimization problem, including, if relevant, thermal strains and reduced material stiffness. This solution is used to derive the sectional stiffness upon which a linearized buckling problem is formulated and subsequently solved as a linear eigenvalue problem. The model is validated using examples with exact solutions, and its applicability to large‐scale models is demonstrated through an example with a four‐story stairwell modeled using more than 3200 finite elements.

Multiscale thermal and thermo-structural optimization of three-dimensional lattice structures

This paper develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored thermal and thermo-structural characteristics. A multiscale approach is implemented where the discrete evaluations of small-scale lattice unit cell characteristics are converted to response surface models so that the properties exist as continuous functions of the lattice micro-parameters. The derived framework constitutes free material optimization in the space of manufacturable lattice micro-architecture. The optimization of individual lattice member dimensions is enabled by the adjoint method and the explicit expressions of the response surface material property sensitivities. The approach is demonstrated by solving thermal and thermo-structural optimization problems, significantly extending previous work which focused on linear structural response. The thermal optimization solution shows a design with improved optimality compared to the SIMP methodology. The thermo-structural optimization solution demonstrates the method’s capability for attaining a prescribed displacement in response to temperature gradients.

Structural dynamic responses of linear structures subjected to Kanai-Tajimi excitation

Aseismic design of building structures is desired to protect them from the disasters associated with earthquakes, which has caused serious casualties and huge economic loss to human society. In this study, an analytic method based on complex modal method (CMM) and pseudo excitation method (PEM), named as CM-PEM, is proposed to solve the spectral moments and variance of structural responses subjected to Kanai-Tajimi excitation. Kanai-Tajimi excitation is firstly represented by white noise excitation through the application of filtering equation, and the basic dynamic equation is decoupled into first-order differential equations with independent complex modal variables by using CMM. Then the unified explicit expressions of the both dynamic response and its power spectral density function (PSDF) are obtained by PEM and introducing generalized variables. Because the PSDF of structural response only contains variable term 1/(pi2 + ω2), which can be integrated to obtain closed-form expression of (0–2)-order spectral moments, when the variable term multiplies with ωi (i = 0, 1). Finally, in order to verify the accuracy and efficiency of the proposed method, a 6-storey structure is investigated by comparing with traditional PEM, with respect to PSDF of ground excitation, PSDF and spectral moments of dynamic responses.

Response Spectrum with Uncertain Damping Using Artificial Neural Networks

It is evident that the response of linear structures under dynamic loads depends to two important dynamics parameters of structures, namely, the natural periods and structural damping. These parameters always characterize the oscillation and the energy dissipation of buildings. In fact, the values of these parameters differ significantly, before, during and after an earthquake from values selected during the design phase. This phenomenon, among other, introduces uncertainty into the building simulation process, which remarkably influences the structural response and associated performance of the structure under dynamic loads. This paper develops a new methodology to estimate the maximum absolute response for linear structures with uncertain damping using the Artificial Neural Networks (ANN) and the Monte Carlo method. The proposed method is illustrated using the target design response spectra corresponding to the EC8 for linear structures exposed to seismic loads. The numerical results revealed the practical applicability of the proposed methodology and the crucial influence of accounting the damping uncertainty in structural dynamics. Additionally, the method can be used in practice, mainly for important and special structures where uncertainty could lead to significant changes in structural response.

Approximation Procedure for Determining Oscillation Period of Frame Structure

Dynamic analysis can be used to find dynamic displacements, time history, and the frequency content of the load. One analysis technique for calculating the linear response of structures to dynamic loading is a modal analysis. In modal analysis, we decompose the response of the structure into several vibration modes. A mode is defined by its frequency and shape. Structural engineers call the mode with the shortest frequency (the longest period) the fundamental mode. Holzer and Stodola's approximate methods for determining the forms and periods of oscillation for frame structures are presented in the paper. An approximation method, based on approximate relative stiffnesses of the storeys and the ground floor, is analyzed and proposed. The results obtained by the proposed approximate procedure do not greatly deviate from those obtained by more accurate calculations. It is therefore emphasized that the method can be used both in practice and for checking computer-based analysis of complex systems. At the end of the paper was given a comparison of the results obtained by approximate methods and some engineering software.

Global/Local Non-Intrusive Crack Analysis Using Element Free Galerkin and Linear Galerkin Finite Volume Methods

Although various numerical methods are proposed to solve a wide range of problems so far, each has its own advantages and disadvantages. Therefore, it would be highly desirable to develop a computationally efficient combined approach, which makes use of their advantages and reduces their drawbacks. In this regard, a non-intrusive iterative global/local (IGL) algorithm is proposed to evaluate the structures with local discontinuity. Firstly, in each iteration, the entire continuum domain is solved using the Galerkin Finite Volume (GFV) method, which consumes light computational workload for predicting accurate results of linear structural response. Then, the Element Free Galerkin (EFG) meshless method is locally employed as an accurate but computationally expensive solver to cover the shortcomings of the GFV solver in the crack analysis. The specific form of Quasi-Newtonian and dynamic accelerators are adopted to increase the convergence rate in each computational increment. Finally, the proposed method's accuracy and speed are examined by computing stress intensity factors (SIFs) for several distinct 2D cracked models.

Interaction of ocean waves with floating and submerged horizontal flexible structures in three-dimensions

A three-dimensional general mathematical hydroelastic model dealing with the problem of wave interaction with a floating and a submerged flexible structure is developed based on small amplitude wave theory and linear structural response. The horizontal floating and submerged flexible structures are modelled with a thin plate theory. The linearized long wave equations based on shallow water approximations are derived and results are compared. Three-dimensional Green’s functions are derived using fundamental source potentials in water of finite and infinite depths. The expansion formulae associated with orthogonal mode-coupling relations are derived based on the application of Fourier transform in finite and infinite depths in case of finite width in three-dimensions. The usefulness of the expansion formula is demonstrated by analysing a physical problem of surface gravity wave interaction with a moored finite floating elastic plate in the presence of a finite submerged flexible membrane in three-dimensions. The numerical accuracy of the method is demonstrated by computing the complex values of reflected wave amplitudes for different modes of oscillation and mooring stiffness. Further, the effect of compressive force and modes of oscillations on a free oscillation hydroelastic waves in a closed channel of finite width and length for floating and submerged elastic plate system is analysed.

Optimum Tuned Mass Dampers under seismic Soil-Structure Interaction

Tuned Mass Damper (TMD) devices are widely adopted as a valid mechanical solution for the vibration mitigation of structural systems and buildings under dynamic excitation. In the specific challenging context of seismic engineering, TMDs may represent a convenient option for both aseismic structural design and seismic retrofitting. However, the expectable efficiency rate of TMDs in that context is still debated. Besides, potential Soil-Structure Interaction (SSI) effects may become crucial in the mechanical system, and should properly be taken into account for the optimum TMD design, in order to avoid possible de-tuning. This work contributes to this framework, by investigating the effectiveness of an optimum TMD in reducing the linear structural response to strong-motion earthquakes of a given set of Multi-Degree-Of-Freedom (MDOF) low- and high-rise shear-type frame structures, by embedding SSI within the dynamic and TMD optimisation model. The TMD is seismically tuned through a dedicated two-variable optimisation procedure, for each specific case (primary structure, seismic event and soil type), therefore providing the optimum device setting for each given context. Average primary structure response indices are specifically targeted to that purpose, while maximum ones are monitored. A quite considerable range of optimisation cases is considered (eighty instances), to outline rather general considerations and average trends on TMD optimisation and effectiveness within the seismic SSI framework, for both low- and high-rise buildings. Such an investigation shall provide useful guidelines for a comprehensive tuning of TMDs in mechanical systems and specifically in the presence of seismic SSI, to be consulted in view of real-case applications.

A comparative study of refined and simplified thermo-viscoplastic modeling of a thrust chamber with regenerative cooling

The thermostructural response of the cooling channel of a regeneratively cooled thrust chamber employed for rocket applications can be evaluated by means of analytical and numerical methods. The heat fluxes produced by the combustion inside the thrust chamber cause elevated temperatures in the copper structure composed of ligaments separating the coolant flow from the combustion gases. Those thermal loads together with the mechanical loads due to the flowing coolant and hot gases, lead to a non linear structural response. In the present work a comprehensive study of the viscoplastic phenomena is carried out and a simplified finite element model, which does not take into account strain rate-dependent effects, is adopted.The aim of the work is twofold: understanding and detail modeling of the thermo-viscoplastic phenomena occurring in the copper inner liner of a rocket thrust chamber and evaluating the degree of importance of strain-hardening rate-dependent phenomena. The present paper demonstrates that the simplified viscoplastic model adopted in this work is suitable in the preliminary design phase since the percentage difference detected with respect to rate dependent models, such as Perzyna's and Robinson's ones, is slightly larger than 10%. Furthermore, this model is particularly useful when the results of strain hardening tests, aimed at evaluating strain rate dependent properties, are not available for the chosen material.

Interval Fractile Levels for Stationary Stochastic Response of Linear Structures With Uncertainties

Abstract In the framework of stochastic analysis, the extreme response value of a structural system is completely described by its CDF. However, the CDF does not represent a direct design provision. A more meaningful parameter is the response level which has a specified probability, p, of not being exceeded during a specified time interval. This quantity, which is basically the inverse of the CDF, is referred to as a fractile of order p of the structural response. This study presents an analytical procedure for evaluating the lower bound and upper bound of the fractile of order p of the response of linear structures, with uncertain stiffness properties modeled as interval variables subjected to stationary stochastic excitations. The accuracy of the proposed approach is demonstrated by numerical results concerning a wind-excited truss structure with uncertain Young’s moduli.

Comparison of Reduced-Order Models to Analyze the Dynamics of a Tall Building under the Effects of Along-Wind Loading Variability

Aeroelastic vibration, influenced by wind load effects, is relevant to the structural design of tall buildings. In the framework of performance-based design of wind load–sensitive structures, the effects induced by variability in the loading estimation, often relying on the results of a wind tunnel test, must be evaluated. This research is a continuation of a recent study by the author on the stochastic dynamics of tall buildings, contaminated by experimental errors, wind load uncertainty, and modeling simplifications. A number of reduced-order models are described and discussed. Among these models, a recently developed one that couples the along-wind dynamic response with intervention costs due to nonstructural damage on the external façade is considered. Even though the models assume a linear structural response dominated by the primary vibration modes and vortex shedding effects are not directly considered, they are sufficiently accurate for the purpose of evaluating, in a semianalytical form, the probability density function of the generalized dynamic response. The study examines the use of the reduced Fokker–Planck equation in high dimensions to derive the probability function of stationary wind response, depending on the mean wind speed and standard deviation of a parametric along-wind loading error term.

Damage detection of moment frames using ensemble Empirical Mode Decomposition and clustering techniques

Most of the damage detection methods implement dynamic response of linear structures for indication of damage. Time-frequency methods employ signal processing techniques to detect temporal changes in frequency characteristics of vibration response of the system. However, most of these techniques fail facing with nonlinear systems due to consecutive changes in stiffness that lead to fake damage indications. This study is divided into two parts. First, the Empirical Mode Decomposition method (EMD) is compared to Ensemble EMD (EEMD) to clarify the capability of these methods as signal processing tools. For this reason, the acceleration responses of a nonlinear steel moment frame are extracted by EMD and EEMD. Second, Hilbert transform based on EEMD is employed in conjunction with a density-based clustering technique to classify the changes in frequency and amplitude patterns to identify and estimate the extent of damage. Simulation results demonstrate that frequency is not an appropriate parameter to determine the extent of damage for nonlinear systems.

Effect of the Seismic Input on Non-Linear Response of R/C Building Structures

The effects of the variability of seismic input on system structural response are investigated. Non linear time history analyses are performed using as input sets of accelerograms satisfying the compatibility criteria with an elastic design spectrum according to the Eurocode 8. The response of elastic SDOF systems, in terms of spectral acceleration, is analyzed; the same parameter, for corresponding non linear SDOF systems as well as ductility demand and strength reduction factors, is also discussed. The analyses are extended to a r/c multi-storey space frame, which is designed according to Eurocode provisions. The main conclusion of the paper is that, when the input is selected according to the Eurocode 8 provisions as recorded accelerograms, a “natural” mean CoV of spectra ordinates is expected; it proportionally conditions the CoV of the parameters characterising the non linear response of structures.

Response Spectral Characteristics and Reliabilities of Linear Structures to Both Intensity and Frequency Content Time-Varying Earthquake Loads

AbstractA numerical method for estimating the useful spectral characteristics of responses of classically damped linear elastic structures to the Yeh-Wen model of fully nonstationary random earthquake loads is developed. The derivation of the method is carried out in three steps. First, the stationary Gaussian white noise process in the space of a frequency modulation function is transformed to the uniformly modulated Gaussian white noise process in the time space. Second, the numerical computation procedure for the unit impulse response functions in the time domain of the Clough-Penzien filters modified in the space of a frequency modulation function is proposed. Finally, the numerical solutions for the useful spectral characteristics of responses of linear structures to the Yeh-Wen model are given, from which the first-passage reliability problem can be solved by using Vanmarcke’s approximation. Numerical investigation of a simple oscillator shows the effect of the frequency modulation functions on the ...

An evolutionary stochastic ground-motion model defined by a seismological scenario and local site conditions

This paper is concerned with modeling earthquake-induced ground accelerations and the simulation of the dynamic response of linear structures through the principles of stochastic dynamics. A fully evolutionary approach, with nonstationarity both in amplitude and in frequency content, is proposed in order to define the seismic action, based on seismological information in the form of a small number of input parameters commonly available in deterministic or probabilistic seismic design situations. The signal is obtained by filtering a Gaussian white-noise. The finite duration and time-varying amplitude properties are obtained by using a suitable envelope function. By utilizing a subset of the records from the PEER-NGA strong-motion database, and time-series analysis tools extended to nonstationary processes, the key transfer-function properties, in terms of circular frequency, damping ratio and spectral intensity factor, are identified. A regression analysis is conducted for practical and flexible application of this model, in order to empirically relate the identified time-varying parameters of the filter to the characteristics defining earthquake scenarios such as magnitude, rupture distance and soil type. A validation study and a parametric investigation using elastic response spectra is also included. Results show that the final seismic model can reproduce, with satisfactory accuracy, the characteristics of acceleration records in a region, over a broad range of response periods.

Mechanism and Tafel Lines of Electro-Oxidation of Water to Oxygen on RuO2(110)

How to efficiently oxidize H(2)O to O(2) (H(2)O → 1/2O(2) + 2H(+) + 2e(-)) is a great challenge for electrochemical/photo water splitting owing to the high overpotential and catalyst corrosion. Here extensive periodic first-principles calculations integrated with modified-Poisson-Boltzmann electrostatics are utilized to reveal the physical origin of the high overpotential of the electrocatalytic oxygen evolution reaction (OER) on RuO(2)(110). By determining the surface phase diagram, exploring the possible reaction channels, and computing the Tafel lines, we are able to elucidate some long-standing puzzles on the OER kinetics from the atomic level. We show that OER occurs directly on an O-terminated surface phase above 1.58 V vs NHE, but indirectly on a OH/O mixed phase below 1.58 V by converting first the OH/O mixed phase to the O-terminated phase locally. The rate-determining step of OER involves an unusual water oxidation reaction following a Eley-Rideal-like mechanism, where a water molecule from solution breaks its OH bond over surface Os with concurrent new O-OH bond formation. The free energy barrier is 0.74 eV at 1.58 V, and it decreases linearly with the increase of potential above 1.58 V (a slope of 0.56). In contrast, the traditionally regarded surface oxygen coupling reaction with a Langmuir-Hinshelwood mechanism is energetically less favored and its barrier is weakly affected by the potential. Fundamentally, we show that the empirical linear barrier~potential relation is caused by the linear structural response of the solvated transition state to the change of potential. Finally, the general strategy for finding better OER anode is also presented.

Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)

Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted showing that for a very wide range of parameters the SLT gives satisfactory results in terms of variance of displacement and velocity but not in terms of joint Probability Density Function (PDF). It has also been shown that at steady state the two processes, displacement and velocity, may be considered as independent ones.

Instantaneous damage detection of bridge structures and experimental verification

An extended Kalman filtering (EKF) method was developed and applied to instantaneously identify elemental stiffness values of a structure during damaging seismic events based on vibration measurement. This method is capable of dealing with nonlinear as well as linear structural responses. Identification of the structural elemental stiffness enables location as well as quantification of structural damage. The instantaneous stiffness values during an event can provide highly useful information for post-event capacity estimation. In this study, a large-scale shaking table test of a three-bent concrete bridge model was performed in order to verify the proposed damage detection method. The bridge model was shaken to different damage levels by a sequence of earthquake motions with increasing intensities. The elemental stiffness values of the structure were instantaneously identified in real time during the damaging earthquake excitations using the EKF method. The identified stiffness degradations and their locations agreed well with the structural damage observed by visual inspection and strain measurements. More importantly, the seismic response accelerations analytically simulated using the instantaneous stiffness values thus identified agreed well with the measured accelerations, demonstrating the accuracy of the identified stiffness. This study presents an experimental verification of a structural damage detection method using a realistic bridge model subjected to realistic seismic damage. Copyright © 2007 John Wiley & Sons, Ltd.