Response Of Structural Systems Research Articles

Hierarchical Bayesian modeling for calibration and uncertainty quantification of constitutive material models: Application to a uniaxial steel material model

Constitutive material models play an integral role in finite element (FE) modeling of structural components and systems and are governed by a set of parameters. The values of the material model parameters are important for the FE model to be able to predict the real structural behavior as closely as possible. Realistic cyclic material constitutive models well calibrated to experimental data are critical when predicting the nonlinear dynamic response of structural systems to extreme loads (e.g., earthquakes, high winds, blast). Hence, this study focuses on the inference and uncertainty quantification of material model parameters from an experimental dataset consisting of data from experiments on multiple specimens of the same kind, which is a topic of great interest to the structural modeling and simulation community. Traditionally, Bayesian inference is performed by pooling the data from all the specimens, or by considering the data from a single specimen, disregarding the inherent variability (aleatory uncertainty) among specimens of the same kind. Consequently, traditional approaches fail to capture the population distribution of material model parameters, which represents the aleatory specimen-to-specimen variability that is essential for conducting reliability analysis and uncertainty propagation studies. Moreover, these approaches cannot accurately simulate the response of new specimens. To overcome these limitations, this study introduces a novel application of hierarchical Bayesian inference for calibrating material model parameters. By simultaneously considering experimental data from multiple specimens of the same kind, hierarchical Bayesian modeling quantifies both epistemic uncertainty and aleatory specimen-to-specimen variability. In this study, the parameters of the well-known Giuffré-Menegotto-Pinto (GMP) uniaxial material model for reinforcing steel are calibrated and validated based on a dataset of experimental cyclic tests conducted on thirty-six steel specimens, or coupons, originating from three different manufacturing mills, complying to two different manufacturing standards, and subjected to different strain histories. These strain histories are similar to those experienced during seismic events by reinforcing steel bars within reinforced concrete structures. The material model parameters are calibrated using both the traditional and the hierarchical Bayesian approach and the results are compared. Based on the experimental dataset employed in this study, a joint probability distribution of the GMP material model parameters that quantifies both epistemic (due to finite sample size) and aleatory (coupon-to-coupon) variability or uncertainty is provided which can be used for uncertainty propagation in reliability and risk analyses of nonlinear dynamic systems.

Breach diameter prediction of reinforced concrete wall under contact/near-contact explosives using deep neural network

In recent years, the use of Machine Learning (ML) has been expanded to several engineering fields with applications in structural engineering. Deep Neural Network (DNN) models have been widely implemented to predict the response of structural systems under conventional loading. The accuracy of these DNN models relies on the size of the dataset used, which can vary from hundreds to thousands of data points, typically formed by images, test data, and/or finite element models built for a specific environment. Such dependency becomes a limitation when DNN models are intended to be used in blast analysis and/or design, as data are typically scarce or restricted. This paper introduces the implementation of an ML/DNN model for the prediction of breach diameter of a reinforced concrete target subjected to contact and near-contact explosions. The DNN model predicts the breach diameter using experimentally collected concrete breach data. The DNN model considers several parameters related to the charge (e.g., type, geometry, orientation, casement properties) and wall target (e.g., material properties, geometry, reinforcement, fiber content), as well as proximity between the target and explosive. It was found that charge geometry, charge placement type, target thickness, scaled distance, and fiber content in the mix were important features affecting the breach diameter prediction.

Improved implementation of concentrated plasticity models in real-time hybrid simulation

Real-time hybrid simulation (RTHS) is a cost-effective experimental testing technique for evaluating the dynamic response of structural systems. In RTHS, a portion of the structure is modeled numerically (i.e., numerical substructure), while the remaining part is tested physically (i.e., experimental substructure). These substructures are coupled in real time. A significant challenge in RTHS is accurately computing the dynamic response of the numerical substructure in real time during testing. Constrained by this challenge, numerical substructures in RTHS are often oversimplified (e.g., spring-mass-dashpot models), failing to capture more complex dynamic behaviors and limiting the applicability of RTHS. However, with the increasing use of innovative structural systems, new materials, and advanced design guidelines to ensure resilient and sustainable civil infrastructure against natural hazards, the demand for real-time executable higher-fidelity numerical substructures in RTHS is growing. Consequently, concentrated plasticity model (CPM) has gained attention as the numerical substructure in RTHS for its good balance between numerical accuracy and computational efficiency, as well as its popularity in structural engineering applications. Currently, static condensation is utilized to prevent an increase in computational degrees of freedom (DOFs) induced by the hinges in CPM, aiming to save computational cost. However, this method proves counterproductive for nonlinear analyses. While reducing the number of computational DOFs, it complicates the stiffness representation, thereby necessitating more demanding arithmetic operations for stiffness updating. In this study, multi-point constraints are applied to enhance the computational efficiency, specifically for nonlinear analyses involving stiffness updating, and the versatility of CPM. Moreover, direct stiffness updating method and sparse matrix-vector multiplication are introduced for further enhancement in computation. An open-source MATLAB/Simulink-based computational tool, namely the Hybrid2D, is developed to promote the use of the improved CPMs in RTHS as numerical substructures. Numerical simulations are first conducted to verify the accuracy and the computational efficiency of the improved CPMs in Hybrid2D. Subsequently, two RTHS examples are experimentally conducted to demonstrate the effectiveness of the Hybrid2D in enabling RTHS with a higher-fidelity numerical substructure for more complex structural systems.

Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using random vibration analysis is possible, when the input is properly modeled as a stochastic process, to derive pieces of information about the structural response with a high quality (if compared with other tools), especially in terms of reliability prevision. Moreover, the random vibration approach is quite complex in cases of non-linearity cases, as well as for non-stationary inputs, as in cases of seismic events. For non-stationary inputs, the assessment of second-order spectral moments requires resolving the Lyapunov matrix differential equation. In this research, a numerical procedure is proposed, providing an expression of response in the state-space that, to our best knowledge, has not yet been presented in the literature, by using a formal justification in accordance with earthquake input modeled as a modulated white noise with evolutive parameters. The computational efforts are reduced by considering the symmetry feature of the covariance matrix. The adopted approach is applied to analyze a multi-story building, aiming to determine the reliability related to the maximum inter-story displacement surpassing a specified acceptable threshold. The building is presumed to experience seismic input characterized by a non-stationary process in both amplitude and frequency, utilizing a general Kanai–Tajimi earthquake input stationary model. The adopted case study is modeled in the form of a multi-degree-of-freedom plane shear frame system.

Uncertainty quantification in the strain response of prestressed reinforced concrete structures using fractile based sampling

The probabilistic evaluation of the capacity and response of structural systems is often done by probabilistic simulation. This approach relies on a considerable number of deterministic analyses to obtain an accurate estimation of the desired statistical characteristics. However, the need of performing a large number of analyses hinders the application of probabilistic simulation in practice, especially when the deterministic calculation of the structural response is computationally expensive in itself (e.g. nonlinear finite element analysis). To increase the appeal of probabilistic simulation, the number of analyses should be very small (i.e. ten or less). This study shows how different sampling techniques can be adopted to select a very small sample subset of analyses to be run, and how they can yield accurate results in estimating the shear capacity of prestressed reinforced concrete beams. Based on the results of the study, the Fractile Based Sampling (FBS) method emerges as a more promising sampling strategy than other sampling techniques, like Latin Hypercube Sampling (LHS). For the same small number of samples, the results show that FBS is preferable over LHS and other sampling techniques for capturing both the general distribution of the response and the tails of the distribution, which shows its usefulness in assessing probability of failure and reliability.

Memeplex-based memetic algorithm for the multi-objective optimal design of composite structures

Hybrid construction is proposed to decrease costs in lightweight structures using fiber-reinforced plastics (FRP) composite materials. Minimum weight, minimum strain energy (stiffness), and minimum energy variability of the structural system response are the objectives of the robust design optimization approach applied to composite shell structures with stiffeners. The trade-off depends on given stress, displacement, and buckling constraints imposed on composite structures considering non-linear geometric behavior. The design variables are ply angles and ply thicknesses of shell laminates, the cross-section dimensions of stiffeners, and the variables related to the selection of materials and their distribution at the laminate level and subsequently of the laminates along the structure. A Multi-Objective Memetic Algorithm (MOMA) applies multiple learning procedures exploring the synergy of different cultural transmission rules. An enlarged virtual population with a dual age-dominance nature captures and updates the Pareto curve. The concept of memeplex controls the meme selection and their propagation along the hybrid genetic and cultural evolution path. The success of memetic learning procedures is analyzed by measuring each meme's relative and absolute success events according to different approaches, depending on the reference time used in evolutionary history. Results show that MOMA is promising in multi-objective optimization of composite hybrid structures.

Numerical Studies on Seismic Response of Structural Systems Using a Response-Spectra Based Intensity Measure

This paper proposes a novel intensity measure (IM) based on the geometric mean of acceleration response spectral ordinates to assess the probabilistic performance of structures subjected to seismic loading. Instead of relying solely on the fundamental period, the proposed IM is evaluated across a fixed period range for all structural systems, which allows consideration of higher mode effects and period changes due to nonlinearity. The proposed seismic IM is evaluated using two established indices sufficiency and efficiency. Sufficiency quantifies the independence of an engineering demand parameter at a specific intensity level with ground motion characteristics such as seismic magnitude [Formula: see text] and distance from site to fault plane [Formula: see text]. It is calculated by linear regression analysis, or using gradient-based relative sufficiency measures. On the other hand, efficiency is measured as dispersion across ground motions at a given intensity level for any physical response quantity. It helps to reduce computational demand for failure probability assessment by considering a smaller number of records compared to an inefficient IM for similar confidence levels. The effectiveness of the proposed IM along with 10 other IMs is demonstrated on single degree of freedom systems with various fundamental periods by performing nonlinear time history analysis using a far-field ground motion record set. The study is also extended to five degree of freedom lumped mass stick models, 2D models (4-, 8-, and 12-story archetype steel frames), and 3D reinforced concrete shear wall building model. The results indicate that the proposed IM limits dispersion to within 10% for long-time period structures, and demonstrates improved sufficiency across different structural systems. For example, gradient of the proposed IM with respect to magnitude [Formula: see text] and site-to-source distance [Formula: see text] for a 12-story steel frame is reduced by 42.9% and 94%, respectively, compared to spectral acceleration at fundamental time period. Potential application of this research lies in efficiently conducting seismic reliability assessment and design for structural systems.

Effective sensor location for detection of change in structural dynamic response

This paper investigates the sensitivity of structural system response to the sensor location by investigating consequences of small changes in the location to the structural system response. The paper discusses how maximum observability (based on mode shape and the participation of that mode in the input provided) drives optimal location. The structural responses were investigated in terms of the g-rms response for various low-frequency inputs (pure sinusoids and real-life inputs such as an earthquake and trains). Results were then analyzed in the context of Modal Contributions Factors (MCF) and changes to the Force-to-response Transfer Functions (TRFs). A modal-matching process is first presented using a MatlabTM-based Finite Element Method (FEM) model of a cantilever beam and instrumentation to determine the location of a small mass based on three different criteria. Subsequently, the structural response is investigated using experiments and the FEM model. The accelerometer of small mass (at 1/3 height) was moved up or down to obtain changes in the structural response (TRF) to various realistic low-frequency inputs. Modal Contribution Factor (MCF) and derivative (slope) of the associated mode-shapes were correlated to the observed changes in TRFs. Results show how optimal sensor locations for detecting change in structural response can be based on the MCFs and the associated mode-shapes.

The Integration Between the Structural System and the Envelope System in Earthquake Resistance Design

Earthquakes are one of the most serious natural disasters affecting the stability and the durability of buildings, threatening the life of its occupants. These buildings should be withstanding earthquakes by both architectural and structural engineers. The Integration between structural and envelope system is negatively affected due to; the lack of architectural knowledge in earthquake resistance, and the absence of cooperation between architectural and structural engineers in earthquake resistant design. In this research the lack in the nature of the integrative relationship between the structural and envelope system of earthquake-resistant buildings design is presented. Also, he relationship between these systems, their patterns, and levels in the building to resist earthquakes are highlighted. Where the concept of integration, patterns and levels are verified, using inductive methodology (descriptive, and analytical) through election, analyzing of two different case studies. major result show that the performance pattern is the most common type of three other integration patterns. Also the envelope ,structural system response achieves an equal degree of response as both of them are integrated with each other without revoking one the role of other or affecting the optimal seismic resistance of buildings, and conclusion are presented further.

Vision-Based Dynamic Response Measurements of Structures by Using Smartphone Videos and Alternative Techniques

This study aimed to measure dynamic responses of structural systems using smartphone videos and vision-based sensing processes. Two algorithms, based on template matching and feature extraction, are employed for this purpose. They were verified on the shake table experiments with single and multi-degree freedom steel specimens where their videos were captured by an ordinary smartphone during excitation. Dynamic responses such as strains at discrete sections as well as displacements, velocities, and accelerations at the floor levels of the specimens were obtained by following the signs of physical or virtual markers during the video recording. Through comprehensive experiments and one available full-scale multi-story shake table experiment in the literature, the developed vision-based algorithms were validated to be used with smartphone videos. It was also shown that regardless of the quality of the video record, substantial characteristics of a specimen or a structure could be determined reasonably by smartphone videos since the absolute mean relative differences varied between 10% to 20%.

A digital twin-based framework for multi-element seismic hybrid simulation of structures

This paper proposes a digital twin-based multi-element hybrid simulation (DMHS) framework to predict the nonlinear cyclic response of structural components (digital twin), e.g., seismic fuses, that are not physically tested due to laboratory limitations by leveraging the experimental test data collected from the physical test specimen (physical twin) during hybrid simulation. This data-based simulation approach can address biased results of hybrid simulation of structures that contain multiple critical components while improving the efficiency of the seismic hybrid simulation. The digital twin is trained in two phases: (1) passive (initial) training phase using past experimental test data before the hybrid simulation starts, and (2) recursive model updating phase using the active (real-time) data produced by the physical specimen during hybrid simulation. The passive training is achieved using the Prandtl–Ishlinskii (PI) hysteresis model combined with the sparse identification technique, while the recursive least-squares algorithm is used in the second phase as the model updating scheme. In particular, the sparse identification technique facilitates the selection of the optimal number of hysteretic model parameters in the passive training phase, which are then tuned in the model updating phase. The architecture of the proposed DMHS framework is first presented, followed by digital twin training steps. The application of the proposed DMHS is then demonstrated, and its simulation accuracy is assessed through virtual hybrid simulation of a two-storey steel buckling-restrained braced frame, which consists of a digital twin (second-storey brace) and a virtual experimental specimen (first-storey brace) integrated into the numerical model of the structure that is subjected to a set of earthquake ground motion accelerations. The results obtained from the verification study serve to validate the proposed architecture of the DMHS framework and evaluate the accuracy and efficiency of this technique in simulating the nonlinear seismic response of structural systems.

A novel approach for multi‐output structural system reliability problem with small failure probability

AbstractThe multi‐output structural system with implicit function widely exists in actual engineering, which refers that the multiple output responses of structural system can be obtained by one experiment or finite element simulation. Considering the correlation of multiple output responses and the small failure probability involved in multi‐output structural system, this article proposes a novel active learning Kriging (ALK) based reliability method for multi‐output structural system by combining multiple response Gaussian process (MRGP) and importance sampling (IS). First, due to the Kriging model can only construct the surrogate model under the single‐output variable, the MRGP model is introduced to substitute the Kriging model and thus the correlation in multiple output responses can be efficiently described by a correlation matrix in MRGP model. Second, for the case that the distance information of new iterated sample point is not considered by the commonly used learning functions (U‐function, EFF‐function and H‐function) in ALK, three improved learning functions are correspondingly proposed. Finally, aiming at the problem that the small failure probability leads to the increasing of candidate sample pool and further results in low computational efficiency, the IS method is combined with the MRGP model to efficiently accomplish the reliability analysis for multi‐output structural system. Several examples are also provided to demonstrate the effectiveness of the proposed method.

Data Completion, Model Correction and Enrichment Based on Sparse Identification and Data Assimilation

Many models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor’s location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology.

Generative Design of Structured Materials for Controlled Frequency Responses.

Spatially varying material properties allow the dynamic response of structural systems to be almost arbitrarily tailored, far beyond the first or fundamental natural frequency. Continuing advances in manufacturing technology are making it possible to achieve the necessary range of stiffness and density variations, but the design of these property distributions is a challenging task because of the complex multidimensional nature of the problem. Generative design methods based on evolutionary optimization algorithms have been successfully used to obtain solutions based on multi-material distributions. However, the applicability of these solutions is limited by their reliance on multi-material additive manufacturing (AM), which currently only offers digitally mixed acrylic polymer options that are generally unsuitable to produce functional parts. A novel structured material solution is proposed here, in which the problem domain is divided into several volume elements (voxels), each of which contains a structure whose geometrical form is altered to adjust its effective properties to desired values. The single material structural solution will be amenable for ready fabrication by the powder-based selective laser sintering and melting processes with real engineering polymer and metal systems, thereby allowing for the realization of the benefits in real-world applications. The resulting continuous design spaces are searched using a modern evolutionary algorithm, the covariance matrix adaptation evolution strategy (CMA-ES). A MATLAB implementation of this evolutionary design method, in conjunction with finite element simulations for fitness evaluation, showed good convergence for several different cantilever beam test cases when tested against several different sets of target natural frequencies. Correlations with the multi-material solutions show that the single structured material approach is on par or even better in some cases, even though the test domain was discretized into 80% fewer voxels than for the multi-material case. Furthermore, the voxel structures can be realized using current AM technologies.

Probabilistic Structural System Response to Differential Settlement Resulting from Spatially Variable Soil

The role of spatially variable soil stiffness and strength on structural performance has been increasingly recognized with the rapid development of geotechnical reliability-based design tools. Performance criteria linked to the angular distortion between foundations and the probability of exceeding certain limit states as a function of linear-elastic soil property autocorrelation have shed light on the link between foundation soils and potential structural damage. However, the role of soil-structure interaction (SSI), especially considering nonlinearity in soil and structural elements, to redistribute shear and flexure within structures that result from differential foundation movements, has been largely neglected. This study presents a critical examination of the effect of nonlinear SSI to redistribute flexural demands within a steel structure founded in soils exhibiting spatial variability and the corresponding differential settlements through a comparison of uncoupled and coupled Monte Carlo simulations (MCS). This study shows that the differential settlement, Δs, computed using coupled (i.e., SSI) analyses are significantly smaller than those derived from the uncoupled analyses for the random field models (RFMs) used to simulate soil spatial variability. The effect of SSI is to substantially reduce the probability of exceeding selected limit state criteria due to differential movements that vary in magnitude with the level of stringency of the limit state criteria; the most significant reduction corresponds to the structural ultimate limit state (ULS). Furthermore, the effect of SSI on structural performance and the critical scale of fluctuation, δcrit, becomes more apparent and beneficial as the severity of differential movement increases. Smaller and/or “allowable” angular distortions are governed by the local footing-to-footing distance, whereas the probability of exceeding the ULS (i.e., yielding of beams) is controlled by the entire structure working to redistribute the flexural demands. Limit state severity appears to control the critical soil autocorrelation length for angular distortion, indicating that the role of SSI in the performance of structures in spatially varying soils cannot be ignored.

Structural Health Monitoring of a Foot Bridge in Virtual Reality Environment

Aging civil infrastructure systems require imminent attention before any failure mechanism becomes critical. Structural Health Monitoring (SHM) is employed to track inputs and/or responses of structural systems for decision support. Inspections and structural health monitoring require field visits, and subsequently expert assessment of critical elements at site, which may be both time-consuming and costly. Also, fieldwork including visits and inspections may pose danger, require personal protective equipment and structure closures during the fieldwork. To address some of these issues, a Virtual Reality (VR) collaborative application is developed to bring the structure and SHM data from the field to the office such that many experts from different places can simultaneously “virtually visit” the bridge structure for final assessment. In this work, we present a SHM system in a VR environment that includes the technical and visual information necessary for the engineers to make decisions for a footbridge on the campus of the University of Central Florida. In this VR application, for the visualization stage, UAV (Unmanned Air Vehicle) photogrammetry and LiDAR (Light Detection and Ranging) methods are used to capture the bridge. For the technical assessment stage, Finite Element Analysis (FEA) and Operational Modal Analysis (OMA) from vibration data as part of SHM are analyzed. To better visualize the dynamic response of the structure, the operational behavior from the FEA is reflected on the LiDAR point cloud model for immersive. The multi-user feature allowing teams to collaborate simultaneously is essential for decision-making activities. In conclusion, the proposed VR environment offers the potential to provide beneficial features with further automated and real-time improvements along with the SHM and FEA models.

Optimal design of tuned liquid column damper inerter for vibration control

In this paper, the use of a novel passive control device defined as Tuned Liquid Column Damper Inerter (TLCDI) is studied to control the seismic response of structural systems. The TLCDI, recently introduced as an enhanced version of the conventional Tuned Liquid Column Damper, may achieve improved seismic performances by exploiting the mass amplification effect of the so-called inerter device. For this purpose, an optimization procedure for the design of the TLCDI based on a statistical linearization technique and the minimization of the structural displacement variance is proposed. Notably, by assuming a white noise base excitation and considering some additional approximations, pertinent closed-form expressions for the optimal TLCDI parameters are provided. The reliability of the proposed analytical solutions is proved by a comparison with numerical results obtained by a more computationally demanding iterative optimization technique on the original damped system. Finally, the efficiency of the control performance of TLCDI-controlled structures is examined using real recorded seismic signals as external excitation.

Investigation of one dimensional multi-layer periodic unit cell for structural base isolation

Conventional base isolators like lead rubber bearing, high damping rubber bearing and friction pendulum bearing are not suitable for structures containing crucial pipelines and other sensitive structural components, since these structures with conventional isolators are usually subjected to large relative displacements between the superstructure and the base. Concepts from solid state physics have led to the evolution of a new technique of base isolation for civil engineering structures through the use of a foundation system consisting of periodic materials, namely periodic foundation. Periodic structures have the ability to block the passage of elastic waves within a certain frequency range through them. This frequency range is called the band gap or the attenuation zone of the periodic structure. Periodic foundations can be one dimensional (1D) or two dimensional (2D) or three dimensional (3D) periodic foundations depending of the arrangement of the periodic materials in the foundation. The band gap characteristics of 1D periodic foundations can be computed through the Plane Wave Expansion (PWE) method by expressing material properties in the form of Fourier series expansion in the reciprocal lattice space and obtaining the band gap through an eigenvalue problem using Bloch’s theorem. In the present study the PWE method has been formulated to analyse a generic multi-layer periodic unit cell. The generalized formulation has then been applied to the case of a 1D periodic foundation with three material layers. The results obtained from the analysis have shown wider attenuation zones with lower starting frequencies in the 1D three-layer periodic foundation as compared to a 1D two-layer periodic foundation. The effect of material and geometric parameters on the first attenuation zone of 1D three-layer foundation has also been investigated in the present study. Additionally, experimental studies on a single storey frame and numerical studies on a ten storey frame conducted with chosen configurations of periodic foundations showed that both 1D two-layer and 1D three-layer periodic foundations are effective in attenuating the vibration responses of structural systems.

Closed-form solutions for the piezoresistivity properties of short-fiber reinforced composites with percolation-type behavior

A new analytical formulation for the modeling of piezoresistive fiber-reinforced composites with percolation-type behavior is presented in this work. Firstly, we develop a closed-form solution of the electrical conductivity of oriented short-fiber reinforced composites by using generalized spherical harmonics series expansions of a Mori-Tanaka (MT) model. Piezoresistive effects are accounted for by means of three distinct mechanisms, namely filler reorientation, volume expansion, and breakage/formation of conductive paths. Then, this solution is used to derive simple analytical formulas to estimate the linear piezoresistivity coefficients. To illustrate the potentials of the proposed formulation, numerical results and discussion are presented on its application to the modeling of the piezoresistive composites doped with carbon nanotubes (CNTs). The presented formulation is also inlaid in a standard 3D finite element code to simulate the electromechanical response of full-scale CNT-based structural elements. The reported results demonstrate the capabilities of the proposed formulation to link the microstructural properties of short-fiber composites with the macroscopic response of structural systems with extraordinarily fast computation times and accuracy.

A review of methods for determining structural fire severity—Part I: A historical perspective

Summary There is a risk of a building suffering unsustainable structural damage in the event of a large fire. Therefore, it is necessary to design buildings to withstand expected fires. A widely used simplified calculation method is the so‐called ‘time‐equivalence’ method. There are significant concerns about the suitability of this method. This paper is Part I of a twofold study examining the state of the art of time‐equivalence methods. The purpose of this paper is to provide a detailed background of the development of time‐equivalence methods since its first introduction in 1928 and to provide an initial high‐level assessment of the accuracy of these methods. A simple scoring system is used to assess the methods based on the accuracy of the analysis techniques used in their derivation. The study revealed that most methods do not account well for structural system response to fire exposure. While some time‐equivalence methods do yield accurate results, further analysis is required to fully assess their suitability.