Nonlinear Dynamic Response Analysis Research Articles

Nonlinear dynamic response analysis of localized damaged laminated composite structures in the context of component mode synthesis

The aim of this study is the prediction of the dynamic response of damaged laminated composite structures in the context of component mode synthesis. Hence, a method of damage localization of complex structures is proposed. The dynamic behavior of transversely isotropic layers is expressed through elasticity coupled with damage based on an existing macro model for cracked structures. The damage is located only in some regions of the whole structure, which is decomposed on substructures. The incremental linear dynamic governing equations are obtained by using the classical linear Kirchhoff-Love theory of plates. Then, considering the damage-induced nonlinearity, the obtained nonlinear dynamic equations are solved in time domain. However, a detailed finite element modelling of such structure on the scale of localized damage would generate very high computational costs. To reduce this cost, Component Mode Synthesis method (CMS) is used for modelling a nonlinear fine-scale substructure damaged, connected to linear dynamic models of the remaining substructures, which can be condensed and not updated at each iteration. Numerical results show that the mechanical properties of the structure highly change when damage is taken into account. Under an impact load, damage increases and reaches its highest value with the maximum of the applied load and then remains unchanged. Besides, the eigenfrequencies of the damaged structure decrease comparing with those of an undamaged one. This methodology can be used for monitoring strategies and lifetime estimations of hybrid complex structures due to the damage state is known in space and time.

Nonlinear dynamic response and damage analysis for functionally graded metal shallow spherical shell under low-velocity impact

The nonlinear dynamic response and damage evolution of functionally graded shallow spherical shell under low-velocity impact are investigated in this work. Basing on continuum damage theory, a damage constitutive relation is established for functionally graded material and the Kachanov damage evolution law is adopted to predict the damage propagation in the structure. A modified contact model suitable for non-homogenous material (functionally graded material) is applied to model the contact force in impacting process. The laminated modeling method is adopted to model the functionally graded shell with varying material constants along the thickness by dividing the shell to N plies with the constant material properties for each ply. With the established damage constitutive relations and nonlinear geometric relations of FGM shallow spherical shell with elastic modulus varying as a power-law function, the nonlinear motion equations of FGM shallow spherical under low-velocity impact have been obtained in the term of displacement functions. The problems are solved by using the orthogonal collocation point method, the Newmark method and the iterative method synthetically. Some numerical examples are carried out to validate present impacting model and the calculating methods, and parametrical analysis are presented to discuss the effects of the material properties, the geometrical size and impacting velocity on damage state and dynamic response of the structure when under low-velocity impact.

A case study on the application of passive control and seismic isolation techniques to cable-stayed bridges: A comparative investigation through non-linear dynamic analyses

This paper investigates the seismic performance of an existing steel cable-stayed bridge located in a high seismic zone. In 1988 the structure experienced the failure of one of its anchorage plates needing closure and structural repair as a consequence of seismic activity. In this study, the possibility of retrofitting the original bridge with different passive supplemental damping and seismic isolation systems is proposed and assessed, in order to improve the response of the structure in its longitudinal direction. To this end a Finite Element model of the bridge is developed and the structural response is evaluated through non-linear dynamic response analyses under a set of historical ground motions of different intensities, including a near field record. Strength degradation capabilities are introduced in the model, allowing the occurrence of brittle failure in all the members. Seismic performance indices referred to the dynamic response of the unretrofitted structure and to the results of a pushover analysis are defined and used to compare the proposed innovative solutions. The major improvement on the overall response of the bridge is shown and conclusions regarding the most appropriate retrofit alternative for the particular case study are determined.

Point selection strategy based on minimizing <italic>GL</italic><sub>2</sub>-discrepancy and its application to multi-dimensional numerical integration

An optimal point selection strategy based on minimizing GL 2 -discrepancy, where the effects of assigned probabilities are involved, is proposed in the present paper for multi-dimensional numerical integration and stochastic dynamical response analysis. By doing so the optimal point selection is converted to a nonlinear optimization problem. In the case the coordinates of the points are prescribed, a two-step approach is suggested. The existence and uniqueness of the solution is proved. Through typical numerical examples, the GL 2 -discrepancy of different point sets and the accuracy of the numerical integration are compared, and the effectiveness and advantages of the proposed method is verified. Based on the investigation, the probability density evolution method is employed to implement the nonlinear stochastic dynamic response analysis of a concrete frame structure.

Assessment of Seismic Performance of High-Rise Thin RC Wall Buildings in Lima, Peru Using Fragility Functions

The actual behavior of thin RC wall high-rise buildings during an earthquake in Lima, Peru, and the associated seismic loss is unknown. This type of building was assessed done using analytical fragility functions. The numerical model was based on full-scale tests done in Lima, Peru. Nonlinear dynamic response analysis was performed using records simulated for Lima. The damage ratio was estimated for four damage states and fragility functions were obtained assuming that the damage ratio followed log-normal distributions. Seismic performance was evaluated by considering the probability of different damage states for three seismic hazard levels. It was found that highrise buildings present a low probability of collapse in severe earthquakes.

Analysis of Nonlinear Dynamic Response of Wind Turbine Blade Under Fluid–Structure Interaction and Turbulence Effect

In this paper, the entity model of a 1.5 MW offshore wind turbine blade was built by Pro/Engineer software. Fluid flow control equations described by arbitrary Lagrange–Euler (ALE) were established, and the theoretical model of geometrically nonlinear vibration characteristics under fluid–structure interaction (FSI) was given. The simulation of offshore turbulent wind speed was achieved by programming in Matlab. The brandish displacement, the Mises stress distribution and nonlinear dynamic response curves were obtained. Furthermore, the influence of turbulence and FSI on blade dynamic characteristics was studied. The results show that the response curves of maximum brandish displacement and maximum Mises stress present the attenuation trends. The region of the maximum displacement and maximum stress and their variations at different blade positions are revealed. It was shown that the contribution of turbulence effect (TE) on displacement and stress is smaller than that of the FSI effect, and its extent of contribution is related to the relative span length. In addition, it was concluded that the simulation considering bidirectional FSI (BFSI) can reflect the vibration characteristics of wind turbine blades more accurately.

Analysis of nonlinear dynamic response for delaminated fiber–metal laminated beam under unsteady temperature field

The nonlinear dynamic response problems of fiber–metal laminated beams with delamination are studied in this paper. Basing on the Timoshenko beam theory, and considering geometric nonlinearity, transverse shear deformation, temperature effect and contact effect, the nonlinear governing equations of motion for fiber–metal laminated beams under unsteady temperature field are established, which are solved by the differential quadrature method, Nermark-β method and iterative method. In numerical examples, the effects of delamination length, delamination depth, temperature field, geometric nonlinearity and transverse shear deformation on the nonlinear dynamic response of the glass reinforced aluminum laminated beam with delamination are discussed in details.

A Simplified Model for Hysteretic Nonlinear Dynamic Response Analysis of Concrete Covering Grouting

A Simplified Model for Hysteretic Nonlinear Dynamic Response Analysis of Concrete Covering Grouting

Assessment of expected damage on buildings subjected to Lorca earthquake through an energy-based seismic index method and nonlinear dynamic response analyses

The city of Lorca (Spain) was hit on May 11th, 2011, by two consecutive earthquakes of magnitudes 4.6 and 5.2 M $$_\mathrm{w}$$ , causing casualties and important damage in buildings. Many of the damaged structures were reinforced concrete frames with wide beams. This study quantifies the expected level of damage on this structural type in the case of the Lorca earthquake by means of a seismic index $$I_{v}$$ that compares the energy input by the earthquake with the energy absorption/dissipation capacity of the structure. The prototype frames investigated represent structures designed in two time periods (1994–2002 and 2003–2008), in which the applicable codes were different. The influence of the masonry infill walls and the proneness of the frames to concentrate damage in a given story were further investigated through nonlinear dynamic response analyses. It is found that (1) the seismic index method predicts levels of damage that range from moderate/severe to complete collapse; this prediction is consistent with the observed damage; (2) the presence of masonry infill walls makes the structure very prone to damage concentration and reduces the overall seismic capacity of the building; and (3) a proper hierarchy of strength between beams and columns that guarantees the formation of a strong column-weak beam mechanism (as prescribed by seismic codes), as well as the adoption of counter-measures to avoid the negative interaction between non-structural infill walls and the main frame, would have reduced the level of damage from $$I_{v}$$ $$\,=\,$$ 1 (collapse) to about $$I_{v}$$ $$\,=\,$$ 0.5 (moderate/severe damage).

Effects of near-fault and far-fault ground motions on nonlinear dynamic response and seismic damage of concrete gravity dams

As the forward directivity and fling effect characteristics of the near-fault ground motions, seismic response of structures in the near field of a rupturing fault can be significantly different from those observed in the far field. The unique characteristics of the near-fault ground motions can cause considerable damage during an earthquake. This paper presents results of a study aimed at evaluating the near-fault and far-fault ground motion effects on nonlinear dynamic response and seismic damage of concrete gravity dams including dam-reservoir-foundation interaction. For this purpose, 10 as-recorded earthquake records which display ground motions with an apparent velocity pulse are selected to represent the near-fault ground motion characteristics. The earthquake ground motions recorded at the same site from other events that the epicenter far away from the site are employed as the far-fault ground motions. The Koyna gravity dam, which is selected as a numerical application, is subjected to a set of as-recorded near-fault and far-fault strong ground motion records. The Concrete Damaged Plasticity (CDP) model including the strain hardening or softening behavior is employed in nonlinear analysis. Nonlinear dynamic response and seismic damage analyses of the selected concrete dam subjected to both near-fault and far-fault ground motions are performed. Both local and global damage indices are established as the response parameters. The results obtained from the analyses of the dam subjected to each fault effect are compared with each other. It is seen from the analysis results that the near-fault ground motions, which have significant influence on the dynamic response of dam–reservoir–foundation systems, have the potential to cause more severe damage to the dam body than far-fault ground motions.

Seismic Damage Estimation of an Actual Reinforced Concrete Structure Using Subset MCMC

To estimate seismic damage of structures under strong motions is very important to know true safety of structures. However, we have to deal with very small failure probability issue to investigate quantitatively. If we use standard MCS (Monte Calro Simulation) to discuss failure probability, e.g., 1 × 10-6 order, since we have to execute nonlinear dynamic response analyses of approximate 107 times, it is not realistic. Recently, a subset simulation, which reduces the computation time by replacing small failure probability into the product of conditional failure probabilities, was proposed. In this study, the subset simulation is applied to estimate failure probability of an actual reinforced concrete building with 11 stories, and discuss the safety of the structure by checking with design criteria.

Energy conserving and decaying algorithms for corotational finite element nonlinear dynamic responses of thin shells

On the basis of the finite element corotational formulation for geometric nonlinear static analysis of thin shells with large rotation and small strain established before and from the generalized-α time integration algorithm, the energy conserving and decaying algorithms for corotational formulation nonlinear dynamic response analysis of thin shells are established in this paper. Responses are solved by means of a predictor-corrector procedure. In the case of ignoring the structural damping, the conserving or decaying total energy of structure and the controllable numerical damping for high frequency responses can ensure the numerical stability of the algorithm. The inertial parts are linearly interpolated directly in the fixed global coordinate system by using the element nodal displacement in the global coordinate system for obtaining the constant mass matrix, while the elastic parts adopt the corotational formulation. Hence, the whole formulation obtained in this paper is element independent. Through three typical numerical examples, the performances of the algorithm in this paper were compared with those of the classical Newmak and HHT-α algorithms to indicate that the algorithm in this paper could accurately solve nonlinear dynamic responses of thin shells with large displacements and large rotations.

Nonlinear dynamic response analysis of supercavitating vehicles

A finite element model for the supercavitating underwater vehicle was developed by employing 16-node shell elements of relative degrees of freedom. The nonlinear structural dynamic response was performed by introducing the updated Lagrangian formulation. The numerical results indicate that there exists a critical thickness for the supercavitating plain shell for the considered velocity of the vehicle. The structure fails more easily because of instability with the thickness less than the critical value, while the structure maintains dynamic stability with the thickness greater than the critical value. As the velocity of the vehicle increases, the critical thickness for the plain shell increases accordingly. For the considered structural configuration, the critical thicknesses of plain shells are 5 and 7 mm for the velocities of 300 and 400 m/s, respectively. The structural stability is enhanced by using the stiffened configuration. With the shell configuration of nine ring stiffeners, the maximal displacement and von Mises stress of the supercavitating structure decrease by 25% and 17% for the velocity of 300 m/s, respectively. Compared with ring stiffeners, longitudinal stiffeners are more significant to improve structural dynamic performance and decrease the critical value of thickness of the shell for the supercavitating vehicle.

Strength reduction factor demands for building structures under different seismic levels

SUMMARYDamage levels of building structures under a design earthquake are closely related to the assigned values of strength reduction factors. This paper is to investigate the strength reduction factor demands of building structures that were designed considering various earthquake ground intensity levels, soil ground types, and strength reduction factors. In the investigation, a huge number of rigorous nonlinear inelastic dynamic response analyses of various analytical models of five‐story and nine‐story frame structures were conducted under various generated ground motions with variations in phrase angles but identical response spectral acceleration amplitudes. Various scaled earthquake records were also considered for evidence of the investigation. The obtained results showed that when the same values of the strength reduction factors were used for determination of the design lateral seismic forces, the damage and reliability level demands of the structures designed for moderate seismic areas were much less than those for severe seismic ones. As a result, it is proposed that the strength reduction factor demands given in design codes can additionally be expressed in a linear relation of the maximum ground acceleration. Copyright © 2012 John Wiley & Sons, Ltd.

Comparative study of special and ordinary braced frames

SUMMARYThe collapse probability of ductile and non‐ductile concentrically braced frames was investigated using nonlinear dynamic response analysis. Two buildings with three and nine stories located in Boston and Los Angeles, respectively, were designed and subjected to ground motions from the areas. In Boston area, three‐story and nine‐story buildings were designed as ordinary concentrically braced frame with response modification reduction factor R equal to 3 1/4 to be considered as non‐ductile structural systems; comparatively, in Los Angeles area, three‐story and nine‐story buildings were designed as special concentrically braced frame with response modification reduction factor R equal to 6 to be considered as ductile structural systems. In order to evaluate the performance of ductile and non‐ductile concentrically braced frames in moderate and severe seismic regions, ATC‐63 would be used as reference to assess the seismic behaviors. Evaluation approach recommended by ATC‐63 was adopted, and hundreds of nonlinear dynamic analyses were performed. Through alternating the scale factors of designated ground motions, median of structural collapse intensity was presented for each structure. By observing the results of statistical performance assessment, the seismic performance of the systems was evaluated, and some observations are made based on the study. Copyright © 2012 John Wiley & Sons, Ltd.

Nonlinear Dynamic Response Analysis of the Braced Steel Frame with Wedge Devices

In order to research the nonlinear dynamic respond analysis of a new braced steel frame with wedge devices under the action of earthquake, its damping mechanism is analyzed, and the computational model is obtained. Based on the mechanism of multiple resistant lateral system, the explicit nonlinear dynamic analysis and dynamic contact algorithm are adopted to separately analyze the steel frame with no brace, with centric and eccentric brace, and with the new braced wedge block. During the analysis, in order to take the material and geometrical bi-nonlinear into account, the material model is chosen as the bilinear equivalent strength, and the explicit centered difference algorithm is adopted. It can be obtained from structural deformation and energy and so on. The results show that the stiffness of structure decays after plastic deformation in the earthquake effect, and the hysteresis energy consumption and system dumping appear. The nonlinear dynamic response of steel frame is affected by resistant lateral stiffness, plastic deformation, and system damping. The braced steel frame with wedge block regulates the displacement and acceleration response with yield energy dissipation of brace, as it provides resistance lateral stiffness to control the deformation. This kind of structure has strong adaptability to earthquake intensity and good seismic performance.

Nonlinear Dynamic Response and Safety Analysis of Suspended Submarine Pipeline

With the application of ANSYS finite element analysis software and environmental data in ChengDao oil field, a nonlinear finite element model of suspended submarine pipeline coupled with sea-floor soil is developed. Discarding the traditional and imprecise pipeline model with double clamped or simply supported ends, the model is founded on the theory of elastic foundation beam, in which the nonlinear effect between pipeline and sea-floor soil is considered. Base on the model we developed, the influences of span length and shear strength of soil at the ends of span on the span’s natural frequency are discussed. And the effects of span length, shear strength of soil and current velocity on the dynamic response of span are also analyzed in this paper. The model we developed in this paper fits the actual structure better, and the analysis is instructive for preventing and controlling the suspending of submarine pipeline.

A Practical Numerical Method for Earthquake-Induced Horizontal Displacement of Submarine Slope

Earthquake shakes the soil and induces modulus softening and liquefaction of non-cohesive soil, which causes instability of the slope. A practical numerical method is proposed for predicting large deformation and horizontal displacement of submarine gentle slope due to earthquake. The new method take normal wave loads as pseudo-static steady pressure and initial excess pore water pressure. Using 2-D nonlinear effective stress finite element method, dynamic response and liquefaction analysis are conducted with an infinite submarine slope model. Regarding the seismic motion of soil skeleton as process of softening gradually, softened soil modulus is attained during earthquake. Deformation analysis is performed with the modulus of liquefied and softened soil and the process of lateral movement is obtained. Compared with other related researches, the proposed method shows that gives reasonable results for the conditions indicated. The influences of non-liquefied surface layer, liquefied layer thickness and slope angle on horizontal displacement are studied by series of cases.

Analytical fragility curves for typical Algerian reinforced concrete bridge piers

This paper illustrates the results of a seismic vulnerability study aimed to derive the fragility curves for typical Algerian reinforced concrete bridge piers using an analytical approach. Fragility curves express the probability of exceeding a certain damage state for a given ground motion intensity (e.g., PGA). In this respect, a set of 41 worldwide accelerometer records from which, 21 Algerian strong motion records are included, have been used in a non-linear dynamic response analyses to assess the damage indices expressed in terms of the bridge displacement ductility, the ultimate ductility, the cyclic loading factor and the cumulative energy ductility. Combining the damage indices defined for 5 damage rank with the ground motion indices, the fragility curves for the bridge piers were derived assuming a lognormal distribution.

An energy-based method for seismic retrofit of existing frames using hysteretic dampers

This paper proposes a method for the seismic retrofitting of existing frames by adding hysteretic energy dissipating devices (EDDs). The procedure is based on the energy balance of the structure, and it is used to determine the lateral strength, the lateral stiffness and the energy dissipation capacity of the EDDs needed in each story to achieve prescribed target performance levels for a given earthquake hazard. The performance levels are governed by the maximum lateral displacement. The earthquake hazard is characterized in terms of input energy and several seismological parameters, and further takes into account the proximity of the earthquake to the source. The proposed method deals with the effect of the EDDs explicitly in terms of hysteretic energy, bypassing equivalent viscous damping approximations, and directly quantifies the cumulative damage induced in the EDDs. The validity of the method is assessed numerically through nonlinear dynamic response analyses with near-fault and far-field ground motions, as well as experimentally through dynamic shaking table tests.