Nonlinear Structural Analysis Research Articles

Nonlinear dynamic seismic analysis of a modern concrete core wall building in Los Angeles using the BTM‐shell methodology

AbstractThis paper discusses the nonlinear dynamic seismic response of a 14‐story reinforced concrete core wall building designed with the prescriptive requirements of the 2019 California Building Code for a near‐fault site in Los Angeles, California, simulated with a detailed nonlinear analysis of the complete structure and subjected to an ensemble of three‐component ground motion input. The study follows up on a recently published work by the authors, which examined the response of the specific building to static lateral loads. The nonlinear model of the building was developed in the software FE‐Multiphys using a shell‐element implementation of the beam–truss model (BTM). The BTM has been extensively validated through prior studies for planar, flanged, and coupled walls under static and dynamic loading. The building model was subjected to an ensemble of ground motions scaled at the design and risk‐targeted maximum considered earthquake levels. The vertical ground motion component and the out‐of‐plane shear degradation of wall piers were included in the simulations. The analyses elucidate the profound effect of nonlinear flexure–shear interaction and of the multidirectional behavior of the flanged coupled core wall on the evolution and localization of damage and on residual deformations. The coupling behavior between the core wall, the slabs, and the columns is also analyzed, and the importance of modeling the nonlinear behavior of all slabs for the residual damage evaluation is demonstrated. The aim of this study is to improve the understanding of issues arising from prescriptive design requirements as well as of issues associated with limitations of standard nonlinear seismic analysis.

Nonlinear optical properties, structural and transition state analyses of ionic liquids: DFT and DFT-D2/D3 studies

This paper includes the structural properties, transition state analysis and NLO properties of the ionic liquids in quantum chemical calculations. Hydrogen bond geometries calculated by B3LYP and ωB97XD approaches have been compared with the crystallographic data in the literature. Transition state analysis have been carried out using Synchronous Transit-Guided Quasi-Newton (STQN) method with QST2 option and Density Functional Theory. Forms according to the positions of the proton on hydrogen bond axes and transition states have been evaluated by relative energy scanning. Interactions between anions and cations in ionic liquids optimizations have been studied by CP approach with D2 and D3 versions of Grimme’s dispersion correction. Electric dipole moments, dipole polarizability, first and second dipole hyper polarizability and important components have been calculated, statically and dynamically for ionic liquids. Effective and stable structures in terms of NLO have been evaluated. In addition, B3LYP and ωB97XD functionals approaches have been tested considering Grimme’s D2/D3 dispersion models for lithium interactions with bis(trifluoromethanesulfonyl)amide and methylsulfonate anions.

Use of Continuous Wavelet Transform to Generate Endurance Time Excitation Functions for Nonlinear Seismic Analysis of Structures

This paper presents the use of continuous wavelet transform (CWT) to capture the frequency contents, spectra of dominant frequencies and associated time durations of real earthquakes for generating artificial excitations to perform endurance time analysis (ETA) of structures. Applying CWT to three sets of forty earthquakes, the 90 percentile frequencies that span the ranges 0.08–18.41 Hz, 0.61–12.73 Hz, and 0.56–15.53 Hz; with associated time durations of 20, 15 and 16 s, respectively, for these earthquake sets are extracted. Artificial excitations that contain these ground motion characteristics are generated, progressively scaled up and applied to the target structure until failure. The scaling used is a block-shaped envelope that increases in size by a factor of 3/2 over time. Nonlinear seismic analyses of a steel frame and a concrete bridge bent using these artificial excitations have shown that the method not only successfully predicts the base shear–roof displacement responses of these structures, it also correctly identifies behavior such as weak story, concrete spalling, and core cracking. When compared with the increment dynamic analysis and time history analysis using multiple earthquakes, the proposed method is capable of producing comparable results with a significant reduction in computational time and a much smaller output file size.

Nonlinear dynamic analysis and vibration suppression on the composite laminated plates with general boundary conditions in supersonic airflow

This paper performs the nonlinear dynamic analysis and vibration reduction of the panel structures subjected to supersonic airflow. The negative capacitance piezoelectric shunt damping circuit (PSDC) which contains bonded piezoelectric element and external negative capacitance is adopted. Based on the modified Ritz approach and energy approach, the formulations of the nonlinear panel structure with attached piezoelectric element are derived. A unified mathematical model for the nonlinear dynamic analysis of composite panels subjected to general edge boundaries in supersonic airflow is formulated. Furthermore, the Newmark approach and Newton iteration approach are utilized to calculate time domain responses of panel structures under aerodynamic pressure. Several numerical cases are further performed to verify the present formulations. Finally, impacts of several factors on the flutter characteristics of panel structures are investigated and the comparisons concerning the vibration responses of panels having and without PSDC are performed to verify vibration reduction properties of the present method. The numerical results show that the vibration and flutter of panels in supersonic airflow can be sufficiently suppressed by the present simple vibration reduction strategy.

Nonlinear analysis of GFRP reinforced concrete beams using moment-rotation approach and conjugate beam method

The moment-rotation approach is a promising methodology aimed to predict the rotational capacity of reinforced concrete members. Recently, several authors have applied this method to evaluate the bending behavior of beams, replacing the moment–curvature approach. Considering the partial interaction phenomena, the moment-rotation approach can be used to develop parametric analyses and to assist in the formulation of rational equations for different material combinations. However, the techniques to integrate the moment-rotation approach into a nonlinear structural analysis have not been deeply explored, and the wider use of this methodology requires a rigorous validation. This study proposes and validates a modeling framework that integrates the moment-rotation approach into a reinforced concrete beam analysis based on the conjugate beam method. This model simulates the global stiffness decrease of beams as the cracking progresses. The numerical results were compared with experimental tests from literature performed on fiber-reinforced and plain concrete beams with glass‐fiber reinforced polymer (GFRP) bars. The experimental behavior of deflection, the crack-opening moment, and the moment–curvature were accurately simulated, especially for fiber-reinforced concrete beams. This accuracy indicates that the strategy adopted to integrate the moment-rotation approach into a structural analysis is definitely promising when modeling beams made of new materials.

Collaborative filtering‐based collapse fragility assessment

AbstractThis paper presents a computationally efficient collapse fragility assessment approach that leverages the collaborative filtering (CF) technique. The proposed method randomly selects and runs a subset of the nonlinear response history analyses (NRHAs) required for the incremental dynamic analysis. The structural performance in the omitted cases is then estimated using CF, which requires significantly less time and effort than the nonlinear structural analysis. The NRHA‐based and CF‐generated building performances are then assembled to determine the empirical probability of collapse at each intensity, which is later fitted with a lognormal distribution to obtain the median collapse capacity and associated dispersion. The proposed approach is applied to three steel moment frames, demonstrating that it can reduce the required NRHAs by 50% while providing a reliable collapse fragility estimate for the selected ground motion sets (FEMA P695 44 far‐field records and a site‐specific record‐set). The results from sensitivity analyses reveal that the proposed method is reasonably robust unless the input parameters are assigned extreme values.

Comprehensive evaluation of target spectra for selecting bidirectional ground motions in nonlinear response history analysis of frame buildings at far‐field sites

AbstractAn ensemble of bidirectional ground motions (GMs) is required as input for nonlinear response history analysis (RHA) of complex 3D structures. In building codes, an ensemble of GMs is often developed from a given design spectrum, or target spectrum. In the research literature, several target spectra have been proposed for such intensity‐based assessments. The present study aims to comprehensively evaluate different options for developing target spectra to select bidirectional GMs as inputs to nonlinear RHAs of 3D structural systems. To achieve this goal, we conducted both intensity‐based and risk‐based assessments of 49 multistory buildings with varying dynamic characteristics, heights, and plan shapes. The results from performing 11,074 bidirectional nonlinear RHAs and deriving the seismic demand hazard suggest that the Conditional Mean Spectrum‐Uniform Hazard Spectrum (CMS‐UHS) Composite Spectrum appears to be the most promising alternative. With less computational effort than use of multiple CMS, the Composite Spectrum tends to accurately estimate story drift ratios (average overestimation of 4%) and floor accelerations (average overestimation of 3%). Moreover, the relative ranking between the various target spectra options remains largely independent of the building type, height, and plan shape. However, the precision in estimates of demand tends to decrease for buildings with increasing complexity (e.g., more realistic, or taller, or more asymmetrical in plan).

Random vibration analysis of nonlinear structure with viscoelastic nonlinear energy sink

Most engineering structures serve in complex and harsh dynamic environments and suffer from nonlinear vibrations generated by random excitations such as strong winds and waves, which need to be mitigated. To this end, a novel viscoelastic nonlinear energy sink (VNES) device is proposed for the vibration control of structures, whereby the random vibration of a nonlinear oscillator with a VNES device is analyzed in this paper. Specifically, the mathematical model of the structure-VNES is formulated. An approximate technique for the treatment of viscoelastic damping element modeled by the fractional derivative is developed, whereby an equivalent nonlinear system without fractional derivative is derived. The averaged Itô equations associated with the amplitude envelopes are then obtained by resorting to the stochastic averaging method. The closed-form solution of the stationary response is solved from the Fokker–Planck–Kolmogorov (FPK) equation and verified by the Monte Carlo simulation (MCS) data simultaneously. The effects of system parameters and noise intensity on the stationary response are sequentially examined. By comparing the VNES system to the case without attachment and one equipped with the commonly used tuned mass damper (TMD) device, the performance and robustness of the VNES are highlighted. The conclusions of this work may contribute to the efficacy of the application of the VNES in practice.

Linearly Implicit Algorithm with Embedded Newton Iteration of Velocity and its Application in Nonlinear Dynamic Analysis of Structures

With the application of energy dissipation and damping techniques such as viscous dampers and viscoelastic dampers in seismic engineering, dynamic equilibrium equations of overall structures involve nonlinear damping force. Therefore, numerical integration methods with explicit velocity expressions are more favorable. Based on the average acceleration method, a novel linearly implicit algorithm with explicit expression of velocity is proposed in which once Newton iteration is embedded. The stability of the proposed algorithm in solving equations of motion containing nonlinear restoring force and nonlinear damping force is analyzed using the root locus method. The nonlinear stability of the proposed algorithm is also examined using a single-degree-of-freedom shear-type structure. The dynamic response analysis of a three-storey shear structure model equipped with viscous dampers, a three-storey shear structure equipped with metal dampers, and an eight-storey planar frame structure, are carried to investigate the accuracy and stability of the proposed method with respect to the Chang method and the CR method. The results show that the proposed algorithm exhibits higher accuracy and finer stability for nonlinear dynamic problems.

Modeling and Simulation of the Hysteretic Behavior of Concrete under Cyclic Tension-Compression Using the Smeared Crack Approach.

Concrete structures under wind and earthquake loads will experience tensile and compressive stress reversals. It is very important to accurately reproduce the hysteretic behavior and energy dissipation of concrete materials under cyclic tension-compression for the safety evaluation of concrete structures. A hysteretic model for concrete under cyclic tension-compression is proposed in the framework of smeared crack theory. Based on the crack surface opening-closing mechanism, the relationship between crack surface stress and cracking strain is constructed in a local coordinate system. Linear loading-unloading paths are used and the partial unloading-reloading condition is considered. The hysteretic curves in the model are controlled by two parameters: the initial closing stress and the complete closing stress, which can be determined by the test results. Comparison with several experimental results shows that the model is capable of simulating the cracking process and hysteretic behavior of concrete. In addition, the model is proven to be able to reproduce the damage evolution, energy dissipation, and stiffness recovery caused by crack closure during the cyclic tension-compression. The proposed model can be applied to the nonlinear analysis of real concrete structures under complex cyclic loads.

Seismic fragility analysis of nuclear containment structure under chloride-induced reinforcing steel corrosion conditions

Chloride-induced corrosion of reinforcing steel is one of the critical degradation factors influence the life cycle performance of the containment structure. Therefore, it is of great significance to study the safety performance of containment structure under chloride-induced reinforcing steel corrosion condition. This study presents fragility evaluation of the containment structure under chloride-induced reinforcing steel corrosion condition. Nonlinear time history analysis of the containment structure under different reinforcing steel corrosion conditions is carried out considering various uncertainties including uncertainty in material strength, record to record uncertainty and uncertainty in corrosion parameters. Roof drift under different ground motion intensity levels and seismic fragility of the containment structure corresponding to different performance level with typical service life are analyzed. Results reveal that with the increase of the service life of the containment structure, the increasing rate for roof drift of the containment structure decreases, while the variability of roof drift of the containment structure changes slightly. Service life of the containment structure has different impacts on the fragility of the containment structure corresponding to different performance levels. With the increase of service life, the increasing rate for failure probability of containment structure increases.

Instability-Induced Origami Design by Topology Optimization

Instability-induced wrinkle patterns of thin sheets are ubiquitous in nature, which often result in origami-like patterns that provide inspiration for the engineering of origami designs. Inspired by instability-induced origami patterns, we propose a computational origami design method based on the nonlinear analysis of loaded thin sheets and topology optimization. The bar-and-hinge model is employed for the nonlinear structural analysis, added with a displacement perturbation strategy to initiate out-of-plane buckling. Borrowing ideas from topology optimization, a continuous crease indicator is introduced as the design variable to indicate the state of a crease, which is penalized by power functions to establish the mapping relationships between the crease indicator and hinge properties. Minimizing the structural strain energy with a crease length constraint, we are able to evolve a thin sheet into an origami structure with an optimized crease pattern. Two examples with different initial setups are illustrated, demonstrating the effectiveness and feasibility of the method.

Optimal Acceleration and Energy-Based Record Selection Using Artificial Intelligence Approaches and NP

ABSTRACT The new trend toward modern earthquake-resistant design of buildings based on nonlinear dynamic analysis accounting for peak and energy demands requires efficient ground motion record selection procedures. For this reason, in the present work, two record selection strategies based on acceleration and input energy spectrum considering the spectral shape via Np are presented. Furthermore, both record selection strategies are optimized by means of four artificial intelligence (AI) techniques: Genetic Algorithms (GA), Harmony Search (HS), Particle Swarm Optimization (PSO) and Vibrating Particle System (VPS). In particular, the effectiveness of each AI approach toward the best set of ground motion records for nonlinear dynamic analysis is compared. For this aim, spectral acceleration and input energy design spectra were considered, as well as 1024 seismic records obtained from the Pacific Earthquake Engineering Research Center. For all the AI or meta-heuristic approaches, the fitness function used is focused on minimizing the difference between the average spectrum of eleven ground motion records and the design spectrum using the well-known parameter Np, which represents the spectral shape in a range of periods. In addition, a penalization is included for those spectra with very large or low demands. Thus, 24 sets of eleven seismic records that can be used for nonlinear dynamic analysis of structures with a fundamental period of vibration of 0.6, 1.2 and 1.8 seconds were obtained and purposes. The results demonstrate the ability of the two records selection strategies analyzed and the four meta-heuristic procedures, achieving results quickly and simply regardless of the type of demands, intensities and periods considered. Finally, it is concluded that the VPS algorithm is better in comparison with GA, HS, and PSO since it obtains superior results in almost all the selected cases.

Efficient optimal seismic design method of passive energy dissipation systems based on the inelasticity‐separated finite element method

AbstractInstalling passive energy dissipation dampers in the main structure is an effective way to reduce structural seismic response. The traditional optimal design of passive energy dissipation systems requires a massive nonlinear time history analysis, which is an extremely inefficient process and, as a result, limits its application in practice. In this paper, an efficient optimal design method for dampers is proposed based on the inelasticity‐separated finite element method (IS‐FEM) and genetic algorithm. The IS‐FEM is a novel efficient structural nonlinear analysis method that can avoid the real‐time updating and decomposition of the structural global stiffness matrix in a traditional structure analysis and only requires a small‐scale Schur complementary matrix representing local nonlinear behavior being decomposed per iteration. To make the IS‐FEM available for the analysis of structures equipped with an energy dissipation system, the inelasticity‐separated governing equations of displacement‐based dampers are derived first. Then, an improved constrained optimal genetic algorithm based on population feasibility is presented to enhance the searching ability near the feasible domain boundary. Finally, an efficient damper optimization design method is proposed by combining the developed genetic algorithm with the proposed IS‐FEM‐based analysis procedure for passive energy dissipation structures. The accuracy and efficiency of the proposed method are verified by designing a set of metallic yield dampers to retrofit a steel structure.

Investigation on nonlinear buckling performance of the optimized wing structure under the realistic flight cases

The nonlinear finite element simulation is a standard technique for structural stability analysis, whereas it still has disadvantages of highly computational cost and poor convergence, especially for the large and complex wing structure. In this paper, nonlinear buckling analysis of a wing structure is performed and focused on the local region that is prone to instability, the boundary conditions of which are determined using the sub-modeling technique and realistic flight conditions of an aircraft. Firstly, the flight envelope is calculated based on the preliminary parameters of a large aircraft. Three typically flight cases of the aircraft are selected and the corresponding aerodynamic loads are achieved. Then, an optimization problem with strength and deformation constraints is defined to minimize the weight of the wing structure under the design limit load. A significant reduction in structural weight is achieved by considering three typically flight cases in the optimization process. Next, linear structural analyses come to a conclusion that the upper skin of the wing butt box located between the inner and outer wings is easy to lose stability. The sub-modeling technique is used to extract the local model of the wing butt box from the global model of the wing structure. A nonlinear buckling analysis is performed on the local model by applying the realistic boundary conditions solved from the global model. The skin depressions produced by buckling are carefully studied. Finally, the wing upper skin is reinforced by assigning the stringers to increase the buckling resistance of the structure. The appearance of the skin depressions is significantly postponed, meanwhile the depth is largely reduced.

Seismic fragility analysis of containment structure subjected to near fault ground motions

This study presents seismic fragility analysis of the containment structure subjected to near fault ground motion. Prior to perform seismic fragility analysis, 20 near fault ground motion records with pulse characteristics are selected PEER database. Nonlinear dynamic analysis of the containment structure is performed automatically using Matlab scripts and Batch files. To quantify the global damage behavior of the containment structure subjected to near fault ground motion, energy-based global damage index is proposed. The evolution of global damage behavior and tensile damage of the containment structure are analyzed in depth. Goodness of fit for two widely used fragility fitting methods is compared. To quantify the uncertainty in fragility function parameters, Bootstrap resampling procedure and analytical statistical inference method are adopted to estimate the confidence interval of the fragility function parameters. Results indicated that the bottom of containment structure suffered from severe tensile damage and it is most vulnerable location of the containment structure. With the increase of peak ground motion intensity level, tensile damage increases rapidly and extends to higher elevations of the containment structure. The relative error for fragility function parameter x˜m is not more than 4%, and the error of fragility function parameter β˜R is more than 12%. In general, analytical statistical method provides good estimation for the confidence interval of fragility function parameter x˜m, while overestimate the confidence interval of fragility function parameter β˜R.

Field testing for structural behavior of a stratified monumental complex over time: Palazzo Colonna-Barberini and Templum Fortunae Praeneste

The use of recent technology in heritage conservation incremented the knowledge on structures and materials, reducing the number of uncertainties. There are different activities required for an accurate structural assessment, the interconnection and coordination of the tasks and their results are the main challenges for the optimal exploitation of information. This research presents a holistic methodology to assess the seismic behavior of a complex and stratified historical construction. The assessment methodology includes historical survey, onsite testing for mechanical characterization, geometrical survey, visual inspection and recording to define a three-dimensional model and perform nonlinear structural analysis. The specific contribution of the paper is in the mechanical characterization through the integration of field local testing, as well as sonic tomography, double flat jacks, endoscopy, with virtual inspection assisted by photogrammetry. In this work, the methodology was applied to the Palazzo Colonna-Barberini in the Templum Fortunae Praeneste in Palestrina, Italy. The geometrical model of the actual complex was defined in the Building Information Model environment based on available survey and visual recordings. The structural model was derived from the geometry and integrated with the in-situ testing results, finally it was analyzed considering the nonlinear response of the materials.

A constrained solid-shell model for the geometric nonlinear finite-element analysis of laminates with alternating stiff/soft layers. Applications to laminated glass

Solid-shell models are developed for the geometrically nonlinear analysis of multi-layered composite structures made of alternating layers with large difference in material properties. Exemplificative applications are presented for laminated glass, in which a number of stiff plies of glass are permanently shear-coupled by soft interlayers. The sectional warping due to significant transverse shear strains in the soft layers makes theories of laminated plates based on the plane-section hypothesis unreliable. The proposed approach is based on a geometrically exact solid-shell finite element model with one element per layer in the thickness direction, as alternative to solid discretization. The element approximation is based on the displacement nodal values at the top and bottom surfaces of the layers, with a natural C0 continuity. An alternative solid-shell model with fewer parameters is derived imposing the equal finite rotation of the stiff layers at each surface point by a local rotation-free re-parametrization of the nodal displacements and enforcing the plane stress condition. The approach permits an easy coupling with a fully solid discretization, e.g. to model connections, and is based on a simple strain measure quadratic in the displacement unknowns and suitable for finite strains. Extensive numerical examples for laminated glass plates and curved shells susceptible to large deflections and buckling are provided, comparing the results with those from a fully solid approach.

Geometric Nonlinear Analysis of Self-Supporting Structures for Overhead Transmission Lines

Geometric Nonlinear Analysis of Self-Supporting Structures for Overhead Transmission Lines

Seismic Performance of Reinforced Concrete Buildings with Joist and Wide-Beam Floors during the 26 November 2019 Albania Earthquake

Beams with width greater than their depth and depth equal to the depth of the slab (concealed wide beams) are widespread in Reinforced Concrete (RC) buildings in Albania. A large number of RC buildings with wide beams were hit by a strong Mw6.4 earthquake on 26 November 2019. The earthquake hit two of the most densely populated areas in Albania and caused widespread damage to these buildings. This paper aims to provide an updated view on the seismic performance of buildings with wide beams in light of the new field data following the 26 November 2019 Albania earthquake. To this end, a thorough literature review including experimental and field observations from past earthquakes is presented and data from field visits in Albania are described. It was found that damage to the joists and wide beams themselves was limited, even when the buildings suffered significant non-structural or structural damage in other elements as a result of the earthquake. A discussion on the behavior of wide beam–column frames based on nonlinear structural analyses and tests from the literature is presented. Furthermore, the implications of the results of the analysis for the seismic performance of RC buildings are discussed and confronted with observations from the 2019 Albania earthquake. Based on the literature review, further experimental research on wide beams with longer and more realistic span lengths is recommended.