The dynamic analysis of structures is a computationally intensive procedure that must be considered, in order to make accurate seismic performance assessments in civil and structural engineering applications. To avoid these computationally demanding tasks, simplified methods are often used by engineers in practice, to estimate the behavior of complex structures under dynamic loading. This paper presents an assessment of several machine learning (ML) algorithms, with different characteristics, that aim to predict the dynamic analysis response of multi-story buildings. Large datasets of dynamic response analyses results were generated through standard sampling methods and conventional response spectrum modal analysis procedures. In an effort to obtain the best algorithm performance, an extensive hyper-parameter search was elaborated, followed by the corresponding feature importance. The ML model which exhibited the best performance was deployed in a web application, with the aim of providing predictions of the dynamic responses of multi-story buildings, according to their characteristics.

The extended finite element method (XFEM) has been successfully implemented in solving crack propagation problems by enriching the polynomial basis functions of standard finite elements with specialized non-smooth functions. The resulting approximation space can be used to solve problems with moving discontinuities, such as cracks, without the need of remeshing in the vicinity of the crack. The enrichment of the displacement field in XFEM inflicts a substantial increase in the ellipticity of the discretized problem. As a consequence, the resulting algebraic systems become strongly ill-conditioned, rendering the convergence of iterative solvers very slow. On the other hand, direct solvers may become inefficient in 3D problems, due to the increased bandwidth of the system matrix. In this paper, two of the most efficient domain decomposition solvers, namely the FETI-DP and P-FETI-DP, are proposed for solving the linear systems resulting from XFEM crack propagation analysis in large-scale 3D problems. Both solvers are amenable to parallelization and can be implemented in modern parallel computing environments, with multicore processors and distributed memory systems, following appropriate modifications, to achieve a drastic reduction of memory and computing time in computationally intensive problems.

Although large ground motion databases are widely available today, in many occasions, the selection of ground motion records still hampers the use of nonlinear response history analysis in seismic engineering practice. This paper presents a novel optimization-based tool for creating subsets of ground motion records extracted from large databases. Existing heuristic methods select and/or scale ground motion records so that their mean spectrum fits a target spectrum, while methods that also consider the variability have been proposed. The paper presents a new and simple approach that selects and, if necessary, scales the ground motion records so that both their mean and variability optimally fit a target spectrum. The proposed approach is a multiobjective optimization methodology that can be solved quickly and efficiently with an evolutionary optimization algorithm. Contrary to other approaches, a Monte Carlo step is not required, while the proposed procedure is easy to implement and able to quickly search large databases. Furthermore, among the suite of optimum solutions (Pareto front) obtained, a criterion for choosing the most suitable design is proposed. The efficiency of the proposed tool is demonstrated with two numerical examples. In the first example, the target spectrum is a uniform hazard spectrum, while in the second example, a conditional mean spectrum (CMS) is adopted instead.

Differential evolution (DE) is a population-based metaheuristic search algorithm that optimizes a problem by iteratively improving a candidate solution based on an evolutionary process. Such algorithms make few or no assumptions about the underlying optimization problem and can quickly explore very large design spaces. DE is arguably one of the most versatile and stable population-based search algorithms that exhibits robustness to multi-modal problems. In the field of structural engineering, most practical optimization problems are associated with one or several behavioral constraints. Constrained optimization problems are quite challenging to solve due to their complexity and high nonlinearity. In this work we examine the performance of several DE variants, namely the standard DE, the composite DE (CODE), the adaptive DE with optional external archive (JADE) and the self-adaptive DE (JDE and SADE), for handling constrained structural optimization problems associated with truss structures. The performance of each DE variant is evaluated by using five well-known benchmark structures in 2D and 3D. The evaluation is done on the basis of final optimum result and the rate of convergence. Valuable conclusions are obtained from the statistical analysis which can help a structural engineer in practice to choose the suitable algorithm for such kind of problems.

Constrained optimization is a highly important field of engineering as most real-world optimization problems are associated with one or several constraints. Such problems are often challenging to solve due to their complexity and high nonlinearity. Differential evolution (DE) is arguably one of the most versatile and stable population-based search algorithms that exhibits robustness to multi-modal problems and has shown to be very efficient when solving constrained global optimization problems. In this paper we investigate the performance of several DE variants existing in the literature such as the traditional DE, the composite DE (CoDE), the adaptive DE with optional external archive (JADE) and the self-adaptive DE (jDE and SaDE), for handling constrained structural optimization problems. The performance of each DE variant is quantified by using three well-known benchmark structures in 2D and 3D. It is shown that JADE, which updates control parameters in an adaptive way, truly exhibits superior performance and outperforms the other DE variants in all the cases examined.

We propose a novel spectra-matching framework, which employs a linear combination of raw ground motion records to generate artificial acceleration time histories perfectly matching a target spectrum, taking into account not only the acceleration but also the seismic input energy equivalent velocity. This consideration is leading to optimum acceleration time histories which represent actual ground motions in a much more realistic way. The procedure of selection and scaling of the suite of ground motion records to fit a given target spectrum is formulated by means of an optimization problem. Characteristic ground motion records of different inherent nature are selected as target spectra, to verify the effectiveness of the algorithm. In order to assess the robustness and accuracy of the proposed methodology the seismic performance of single- and multi- degree of freedom structural systems has been also considered. The portion of the seismic input energy that is dissipated due to viscous damping action in the structure is quantified. It is shown that there exists a good agreement between the target and optimized spectra for the different matching scenarios examined, regardless of the nature of target spectra, demonstrating the reliability of the proposed methodology.

Structural damage identification is a scientific field that has attracted a lot of interest in the scientific community during the recent years. There have been many studies intending to find a reliable method to identify damage in structural elements both in location and extent. Most damage identification methods are based on the changes of dynamic characteristics and static responses, but the incompleteness of the test data is a great obstacle for both. In this paper, a structural damage identification method based on the finite element model updating is proposed, in order to provide the location and the extent of structural damage using incomplete modal data of a damaged structure. The structural damage identification problem is treated as an unconstrained optimization problem which is solved using the differential evolution search algorithm. The objective function used in the optimization process is based on a combination of two modal correlation criteria, providing a measure of consistency and correlation between estimations of mode shape vectors. The performance and robustness of the proposed approach are evaluated with two numerical examples: a simply supported concrete beam and a concrete frame under several damage scenarios. The obtained results exhibit high efficiency of the proposed approach for accurately identifying the location and extent of structural damage.

Although large ground motion databases are today widely available, the selection of records still hampers the use of nonlinear response history analysis in engineering practice. We propose a method that is based on a novel optimization algorithm in order to create subset of records chosen from a large database. Existing heuristic methods select and/or scale ground motion records so that their mean spectrum is close to a target/design design spectrum. The records obtained following this practice offer good estimates of the mean response but considerably underestimate the inherent response variability, thus providing no insight regarding the dispersion around the mean. The proposed method selects and scales the ground motion records so that their mean spectrum and the (period-depended) dispersion fit best a target spectrum and its dispersion. The problem is formulated as a two-objective optimization problem, where the record selection considers both the mean spectrum and its dispersion at the range of periods of interest. The problem is solved with the aid of the Differential Evolution algorithm which searches for potential record combinations whose mean and variance match the target spectral values (median and percentiles) obtained either from a code-compatible smooth spectrum or from a ground motion prediction equation (GMPE). The proposed procedure is efficient, easy to implement and able to quickly search a large pool of ground motion records, identifying record subsets that provide estimates of the response quantities of interest with a minimum number of ground motions. A three-storey moment frame building is considered as a benchmark problem in order to demonstrate the efficiency of the proposed optimization scheme.

Many failures of structural components are attributed to fatigue due to repeated loading and unloading conditions. The crack growth due to fatigue, represents a critical issue for the integrity and capacity of structural components. Apart from the loading conditions, the shape of the structural components plays an important role in their service life. In this study, extended finite element and level set methods are integrated into a probabilistic shape design optimization framework aiming to improve the service life of structural components under fatigue. In this context, the relation between the geometry of the structural components and their service life is investigated. The effect of uncertain material properties as well as the crack tip initialization, described by random variables is also examined. Comparisons between optimized shapes obtained for various targeted fatigue life values are addressed, while the location of the initial imperfection along with its orientation are found to have a significant effect on the optimal shapes for the components studied.

This paper investigates the influence of uncertain spatially varying material properties on the fracture behavior of structures with softening materials. Structural failure is modeled using the sequentially linear analysis (SLA) proposed by Rots (2001), which replaces the incremental nonlinear finite element analysis by a series of scaled linear analyses and the nonlinear stress–strain law by a saw-tooth curve. In this paper, SLA is implemented in the framework of a stochastic setting. The proposed approach constitutes an efficient procedure avoiding the convergence problems encountered in regular nonlinear FE analysis. Two benchmark structures are analyzed and comparisons with nonlinear analysis results are provided. The effect of uncertain material properties described by homogeneous stochastic fields (Young’s modulus, tensile strength, fracture energy) on the variability of the load–displacement curves is examined. The response variability is computed by means of direct Monte Carlo simulation. The influence of the variation of each random parameter as well as of the probability distribution, coefficient of variation and correlation length of the stochastic fields is quantified. It is shown that the load–displacement curves and the failure probability of the structures are affected by the statistical characteristics of the stochastic fields.