Nonlinear Dynamic Analysis Of Structures Research Articles

Influence of Elastomeric Bearings in Tension on the Seismic Performance of Base-Isolated r.c. Buildings

Elastomeric bearings are commonly used in base-isolation systems to protect the structures from earthquake damages. Their design is usually developed by using nonlinear models where only the effects of shear and compressive loads are considered, but uncertainties still remain about consequences of the tensile loads produced by severe earthquakes like the near-fault ones. The present work aims to highlight the relapses of tension on the response of bearings and superstructure. To this end, three-, seven- and ten-storey r.c. framed buildings are designed in line with the current Italian seismic code, with a base-isolation system constituted of High-Damping-Rubber Bearings (HDRBs) designed for three values of the ratio between the vertical and horizontal stiffnesses. Experimental and analytical results available in literature are used to propose a unified nonlinear model of the HDRBs, including cavitation and post-cavitation of the elastomer. Nonlinear incremental dynamic analyses of the test structures are carried out using a homemade computer code, where other models of HDRBs considering only some nonlinear phenomena are implemented. Near-fault earthquakes with comparable horizontal and vertical components, prevailing horizontal component and prevailing vertical component are considered as seismic input. Numerical results highlight that a precautionary estimation of response parameters of the HDRBs is attained referring to the proposed model, while its effects on the nonlinear response of the superstructure are less conservative.

Three-dimensional nonlinear dynamic analysis of slack cable structures using node Relaxation method

This study proposes a robust technique for large displacement analysis of slack cable structures subjected to dynamic loadings using a novel method, entitled Node Relaxation. Ordinary numerical methods are usually unable to analyze cable structures due to singularities arising from large displacements and rotations following any alteration of the applied loads. When dynamic loads are considered, handling these singularities in numerical analyses becomes even more challenging. In this paper, an effective iterative method is proposed for three-dimensional large-displacement dynamic analysis of structures consisting slack cables as the primary load-bearing system. The cable structure is modeled using a set of nonlinear springs with properties that are constantly updated as the structural form gradually responds to the applied loads. The large changes in the cable forms are captured by considering an impedance relation that is used to determine the displacement magnitude in the directions where the structure does not have an appreciable stiffness. The method is verified against closed-form solution of wave transfer phenomenon. The effectiveness of the method is also demonstrated by solving several numerical examples.

Generation of seismic excitations compatible with target spectrum: application to Eurocode 8

PurposeThis paper aims to artificially generate seismic accelerograms compatible with the response spectrum imposed as a function of the given environmental parameters such as magnitude, epicentral distance and type of soil. This study is necessary for the non-linear dynamic analysis of structures in regions where real seismic records are not available.Design/methodology/approachFirst, a stochastic iterative method is used to estimate the spectral densities of acceleration power from the respective target response spectra. Thereafter, based on the superposition of seismic waves, a subsequent iterative procedure, which implicitly takes into account the non-stationary character of temporal intensity content of strong ground motions, is developed to synthesize, from these power spectral density, the corresponding acceleration time histories. The phase contents of the ground acceleration samples, thus obtained, are generated using a probability density function of phase derivatives with characteristic parameters estimated from seismological considerations. When based on seismic codes spectrum compatible criteria, this procedure can be used to generate strong ground motions for structural design.FindingsThe results found show that the forms of acceleration of the target and the simulated signals have similar characteristics in terms of strong motion durations, the peak ground acceleration values, corresponding time of occurrence and also, the corresponding cumulative energy functions follow practically the same pattern of variations.Originality/valueThe aim of this study is to generate seismic accelerograms compatible with regulatory spectra by the composition of the three acceleration duration segments based on environmental parameters (magnitude, epicentral distance and type of soil) and which subsequently serves to control the time envelope of the generated signals, and therefore the random generation of phase derivatives, which has not been previously treated.

Indirect reduced-order modelling: using nonlinear manifolds to conserve kinetic energy.

Nonlinear dynamic analysis of complex engineering structures modelled using commercial finite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost by constructing low-dimensional models using a static solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and in-plane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with fixed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, we exploit the concept of nonlinear manifolds to show how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. This new insight enables indirect reduction methods to be applied to a far wider range of structures while maintaining accuracy to higher deflection amplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.

Experimental Study of Masonry Structure under Impact Loading and Comparing it with Numerical Modeling Results via Finite Element Model Updating

Given the sophisticated nature of the blast phenomenon in relation to structures, it is of significance to accurately investigate the structure behavior under blast loads. Due to its rapid and transient nature, blast loading is one of the most important dynamic loadings on the structures. Since masonry materials are widely used as the partition and bearing walls in the existing and newly-built structures, the current research aims to investigate the buried blast effects on unreinforced masonry structures. In order to apply the blast load on a crater as time history, it is required to determine the maximum free field pressure caused by the blast. Accordingly, Finite Element Model Updating (FEMU) was used to calculate the maximum free-field pressure. Thus, for a non-linear dynamic analysis of a blast-loaded structure, a code written in FORTRAN was used. Mohr-Coulomb yield surface with tensile and compression cap and classic Mohr-Coulomb yield surface were used for the structure and the soil modeling, respectively. The comparison of the numerical analysis results in FEMU to field data shows a good consistency between the numerical results and the field data.

Portfolio Seismic Loss Estimation and Risk-based Critical Scenarios for Residential Wooden Houses in Victoria, British Columbia, and Canada.

This study presents a city-wide seismic risk assessment of single-family wooden houses in Victoria, British Columbia, and Canada. The novelty and uniqueness of this study include considerations of detailed building-by-building exposure model for residential houses, current national seismic hazard model for Canada, and rigorous seismic fragility modeling of wooden houses based on nonlinear dynamic analysis of structures subjected to mainshock-aftershock sequences. A full consideration of stochastic event scenarios in probabilistic seismic risk analysis allows the identification of critical scenarios from overall regional seismic risk perspectives and provides valuable insights in informing earthquake disaster risk management actions. Outputs from the developed catastrophe model for Victoria are compared with the empirical model that was developed based on insurance claim data from the 1994 Northridge earthquake. Results of the seismic loss calculations highlight the importance of seismic resistance of the existing houses and of aftershock effects. The integrated use of the outputs from the advanced catastrophe model facilitates risk-based identification of critical earthquake scenarios, which are useful for different stakeholders for earthquake risk management purposes.

Knowledge-Enhanced Deep Learning for Wind-Induced Nonlinear Structural Dynamic Analysis

AbstractRecent advancements of performance-based wind design of tall buildings have placed increasing importance on effectively modeling of the nonlinear structural dynamic response under extreme s...

On the non-linear dynamics of torus-shaped and cylindrical shell structures

In this study, the non-linear dynamic analysis of torus-shaped and cylindrical shell-like structures has been studied. The applied material is assumed as the functionally graded material (FGM). The structures are considered to be used for important machines such as wind turbines. The effects of some environmental factors on the analysis like temperature and humidity have been considered. The strain field has been calculated in general form and in continue the dynamic governing equations of torus structure have been derived based on the first-order shear deformation theory. The rotation around two independent axes in the torus coordinate system is considered and time-dependent equations are solved using SAPM semi-analytical method. The stresses and deformations generated in the torus and cylindrical shaped structures are plotted. The rotation of structures has been attended due to some transportation purposes. The effect of internal pressures as well as rotational speed at torus and cylindrical structures has been investigated in several numerical diagrams. The results are presented in the form of graphs that consider the rotational effects, loading, thermal and humid (hygro-thermal) environments, and size of the structures. This research can provide scientific perspectives to researchers who will examine the dynamic analysis of torus and cylindrical shaped structures.

3D nonlinear dynamic analysis of cable-moored offshore structures

The nonlinear oscillations of the floating structures anchored by cables are studied in three dimensions. The floating structure is anchored by four symmetric mooring lines and the mooring lines are fixed on the seafloor at the other ends. The stiffness matrix of 3D cable element has been established and applied to analyze the dynamics of the 3D floating structures anchored by cables. The complex compatibility conditions which relate the responses of the floating body and cables have been proposed. The equations of motion for the mooring lines and floating body are individually formulated. Then they are combined as an entire system by utilizing the compatibility conditions. At last, the entire system is analyzed numerically with horizontal harmonic excitations applied on the floating body. The amplitudes for both the responses of the platform and the maximum mooring force are studied as the excitation frequency changes. The responses of the platform and the maximum mooring force are also investigated for varieties of cable parameters.

Evaluation of Supplementary Constraints on Dispersion of EDPs Using Real Ground Motion Record Sets

Nonlinear dynamic analysis is the most advanced structural analysis method, and it has become very widespread method to determine structural responses for seismic design or assessment. On the other hand, structural responses strongly rely on the selection of earthquake records for nonlinear dynamic analysis. In this study, several earthquake record selection strategies which impose different compatibility levels between the spectral shape of earthquake records and target spectrum are introduced. Eurocode-8 procedure is considered as reference record selection strategy. Four main engineering demand parameters (EDPs): maximum floor acceleration, global drift ratio, inter-story drift ratio and residual global drift ratio, are used to investigate the superiority of presented strategies. Nonlinear dynamic analyses of three representative low- and mid-rise RC frames are carried out to obtain the EDPs. The central tendency and dispersion of the EDPs are utilized to investigate efficiency of the strategies. Results indicated that the EDPs are correlated with dispersion of spectral accelerations. Numerical evaluations have also highlighted that the presented strategies are capable of providing consistent mean structural responses. It is thought that the presented strategies can be used to select real earthquake records for nonlinear dynamic analysis of structures.

Combination reduction dynamic analysis for complex jointed structures with local hysteresis nonlinearity

A combination nonlinear dynamic reduction method is developed to obtain the steady-state dynamic responses of the complex jointed structures having local hysteresis nonlinearity. The harmonic balance method is used to reformulate the nonlinear dynamical governing equations as a set of nonlinear algebraic equations. The local nonlinearity transformation reduction strategy is used to decrease the dimensions of the nonlinear algebraic equations to improve the computational efficiency by defining the local nonlinear contact forces as iteration vector. The transfer functions only related to nonlinear joints are extracted to connect the local nonlinear dynamic responses with the local nonlinear contact forces and external excitations. The Newton’s iteration with the arc-length continuation is then used to obtain the nonlinear solutions. Comparison with the nonlinear dynamic analysis methods in the literature is performed to validate the proposed method by using a lap-type bolted joint beam system and a complex jointed structure. The good agreement of the comparison results of two examples validates the proposed method, and indicates a higher computational efficiency with much less computational costs. Combined with the finite element analysis, the proposed method indicates a potential performance of the nonlinear dynamic analysis of the large-scale complex engineering structures.

Surrogate SDOF models for probabilistic performance assessment of multistory buildings: Methodology and application for steel special moment frames

This paper proposes a methodology for generating surrogate single-degree-of-freedom (SDOF) models that can be utilized to estimate the probability distribution of the roof drift ratio of multistory buildings at various ground motion intensity measures. The use of an SDOF model as a surrogate for multistory buildings can significantly alleviate the high computational cost for probabilistic seismic demand assessment considering both model uncertainty and record-to-record variability. The surrogate SDOF model generated herein explicitly accounts for model uncertainties and can be used as an alternative to the nonlinear dynamic analysis of detailed building structures. Applications for such surrogate models include regional risk and resilience analyses and comprehensive parametric studies. To showcase the proposed methodology, an SDOF surrogate model for steel special moment frame (SMF) buildings is developed using the suggested surrogate SDOF model generating methodology. The properties of the surrogate model representing a multi-degree-of-freedom (MDOF) structure are computed using a probabilistic function of the fundamental period of the structure developed using Bayesian linear regression. To validate the surrogate model for SMFs, the response statistics produced using detailed multistory SMF models are compared with those of the corresponding surrogate SDOF models. The results show that the proposed surrogate SDOF model captures the probability distribution of the roof drift ratio of SMFs up to collapse with acceptable accuracy while reducing the runtime by at least one order of magnitude.

Fragility analysis of an ageing monopile offshore wind turbine subjected to simultaneous wind and seismic load

The loads induced as a result of seismic activities may jeopardize the serviceability of offshore wind turbines or may even lead the structure to reach the ultimate strength. The maximum load-carrying capacity of a support structure can be estimated by performing a structural assessment which accounts for the nonlinear effects arising from the material and geometry. The present work aims to analyze the fragility of a 5 MW monopile offshore wind turbine structure subjected to seismic activities accounting for soil interactions and time-variant structural degradation. The offshore wind turbine structure is subjected to different ground motions with different intensity. The nonlinear full transient dynamic structural analysis is carried out based on the finite element method, and the nonlinear monopile structural response during the different seismic activities is discussed. Finally, the fragility curves associated with the serviceability limit state design and the ultimate strength limit state are developed.

A new algorithm in generating spectrum-compatible ground accelerograms

ABSTRACTArtificial ground accelerograms are usually generated to match a target response spectrum for the purpose of nonlinear dynamic analyses of structures. A simple spectral matching algorithm is proposed in this paper for engineering application. This approach directly adjusts the response deformation oneperiod at a time in order to find the modified ground accelerogram. Such a direct single-period spectral matching scheme ensures numerical stability, as compared with a multi-period spectral matching process, and has numerical efficiency, as compared with a traditional single-period spectral matching process, in generating artificial ground accelerograms. Several examples are presented to demonstrate the efficiency of this new method.

An Adaptive Model Order Reduction Method Based on the Damage Evolution for Nonlinear Seismic Analysis

Nonlinear seismic analysis, an approach to evaluate the seismic performance of a structure, is facing the challenge of computational efficiency for large‐scale and high‐fidelity simulation. This paper proposes an adaptive model order reduction (MOR) method based on the damage evolution among the overall structure to alleviate the computational burden. The damage state of each component during seismic loadings is distinguished as the initial‐elastic phase, the plastic‐damage phase, and the residual‐elastic phase. In order to exploit the potential of model order reduction based on the damage evolution, a duration spectrum analysis is utilized to evaluate the characteristics of the residual‐elastic phase for SDOF systems with bilinear hysteretic behaviour. Thus, an adaptive MOR method has been proposed to handle the nonlinear dynamic analysis of structures during different damage evolution phases. The overall structure is adaptively partitioned into linear substructures and nonlinear substructures on the basis of the time‐varying damage distribution. The model order of linear substructures is reduced using the initial stiffness‐based vibration modes, while nonlinear substructures that keep in the residual‐elastic phase are reduced using the tangent‐stiffness‐based vibration modes. The residual displacements of nonlinear substructures are treated as the initial deformation during the residual‐elastic phase. Compared with the traditional time step integration method, the proposed adaptive MOR method is able to increase the computational efficiency as yielding comparative results.

Second-order inelastic analysis of shallow and non-shallow steel arches

This work presents a second-order inelastic analysis of steel arches. The analysis of shallow and non-shallow arches with several cross sections and boundary and loads conditions are discussed. The computational platform used is the homemade CS-ASA, which performs advanced nonlinear static and dynamic analysis of structures. The nonlinear geometric effects are considered using a co-rotational finite element formulation; the material inelasticity is simulated by coupling the Refined Plastic Hinge Method (RPHM) with the Strain Compatibility Method (SCM), and the static nonlinear solution is based on an incremental-iterative strategy including continuation techniques. In the simulated nonlinear steel arch models, special attention is given to the equilibrium paths, the influence of rise-to-span ratio, support and loading conditions and full yield curves among other factors. The numerical results obtained show good agreement with those from literature and highlight that the arch rise-to-span ratio has great influence on the structure resistance and that the shallow arches can lose stability through the snap-through phenomenon.

Nonlinear dynamic analysis of piezoelectric-bonded FG-CNTR composite structures using an improved FSDT theory

In the present work, a geometrically nonlinear finite shell element is first presented to predict nonlinear dynamic behavior of piezolaminated functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shell, to enrich the existing research results on FG-CNTRC structures. The governing equations are developed via an improved first-order shear deformation theory (FSDT), in which a parabolic distribution of the transverse shear strains across the shell thickness is assumed and a zero condition of the transverse shear stresses on the top and bottom surfaces is imposed. Using a micro-mechanical model on the foundation of the developed rule of mixture, the effective material properties of the FG-CNTRC structures, which are strengthened by single-walled carbon nanotubes (SWCNTs), are scrutinized. The effectiveness of the present method is demonstrated by validating the obtained results against those of other studies from literature considering shell structures. Furthermore, some novel numerical results, including the nonlinear transient deflection of smart FG-CNTRC spherical and cylindrical shells, will be presented and can be considered for future structure design.

Simulation of Structural Applications and Sheet Metal Forming Processes Based on Quadratic Solid–Shell Elements with Explicit Dynamic Formulation

In this work, nonlinear dynamic analysis of thin structures is investigated using quadratic solid–shell (SHB-EXP) elements. The proposed SHB-EXP elements are based on a fully three-dimensional formulation using an in-plane reduced-integration scheme along with the assumed-strain method in order to alleviate most locking phenomena. These developments consist of a 20-node hexahedral element, denoted SHB20-EXP, and its 15-node prismatic counterpart, denoted SHB15-EXP. The formulation of these elements is combined with fully three-dimensional behavior models, including elastic behavior as well as anisotropic plastic behavior for metallic materials. The resulting formulations are implemented into the ABAQUS explicit/dynamic software package in the framework of large displacements and rotations. First, to assess the performance of the SHB-EXP elements, four representative nonlinear dynamic benchmark tests have been conducted. Then, impact/crash problem and deep drawing of cylindrical cup have been performed to demonstrate the capabilities of the SHB-EXP elements in handling various types of nonlinearities (large strains, anisotropic plasticity, and double-sided contact). Comparisons with results obtained by ABAQUS elements as well as with reference solutions taken from the literature show the good capabilities of the developed quadratic SHB-EXP elements for the explicit dynamic simulation of thin structures.

Seismic demand assessment of self-centering steel plate shear walls

In previous studies, a post-tensioned rocking system has been introduced to steel plate shear wall (SPSW) system as a means for reducing its residual drifts. The success of this method and the performance of self-centering SPSWs (SC-SPSWs) is evaluated, in this study, by nonlinear dynamic analysis of previously-designed structures. For this purpose, a numerical model is developed and validated against experimental results. This model is, then, used for representing five 3- and 9-story SC-SPSWs that reflect various design assumptions. The median and dispersion of various response parameters are then extracted using a set of 20 ground motion records scaled to three different intensity levels. A comparative assessment is next performed between response of the studied structures in presence and absence of the rocking system. This assessment reveals that the rocking system is not effective in reducing the residual deformations of SPSW system. Nevertheless, the rocking behavior is shown to effectively mitigate the ductility demand at the beams' end portion and provide a more uniform distribution of plasticity along beams and within web plates of different stories.

Nonlinear dynamic analysis of shell structures by the formulation based on a discrete shear gap

In this work, a shear locking-free three-node shell element based on Mindlin–Reissner theory is presented for a nonlinear dynamic analysis including sheet metal forming. In the present formulation, only displacement and rotational degrees of freedom are utilized, and the discrete shear gap of each field node is deduced using rotations of all three field nodes in a local coordinate system by the integral from the fictitious central point to the corresponding field node, which makes it alleviate the shear locking phenomenon. In order to validate the availability in solving nonlinear dynamic problems, several benchmark problems and sheet metal forming applications are employed. The results show potentiality in application to practical problems because of the simple implementation.