Static Structural Response Research Articles

Finite element modeling to explore static bending responses of four-layer FG beam structures considering sliding motions

Finite element modeling to explore static bending responses of four-layer FG beam structures considering sliding motions

A convex combination based approach for uncertain static responses of structures subjected to fuzzy external loadings

A convex combination based approach for uncertain static responses of structures subjected to fuzzy external loadings

Approximate Bayesian Computation for structural identification of ancient tie-rods using noisy modal data

Masonry arches and vaults are common historic structural elements that frequently experience asymmetric loading due to seismic action or abutment settlements. Over the past few decades, numerous studies have sought to enhance our understanding of the structural behavior of these elements for the purpose of preventive conservation. The assessment of the structural performance of existing constructions typically relies on effective numerical models guided by a set of unknown input parameters, including geometry, mechanical characteristics, physical properties, and boundary conditions. These parameters can be estimated through deterministic optimization functions aimed at minimizing the discrepancy between the output of a numerical model and the measured dynamic and/or static structural response. However, deterministic approaches overlook uncertainties associated with both input parameters and measurements. In this context, the Bayesian approach proves valuable for estimating unknown numerical model parameters and their associated uncertainties (posterior distributions). This involves updating prior knowledge of model parameters (prior distributions) based on current measurements and explicitly considering all sources of uncertainties affecting observed quantities through likelihood functions. However, two significant challenges arise: the likelihood function may be unknown or too complex to evaluate, and the computational costs for approximating the posterior distribution can be prohibitive. This study addresses these challenges by employing Approximate Bayesian Computation (ABC) to handle the intractable likelihood function. Additionally, the computational burden is mitigated through the use of accurate surrogate models such as Polynomial Chaos Expansions (PCE) and Artificial Neural Networks (ANN). The research focuses on setting up numerical models for simple structural systems (tie-rods) and inferring unknown input parameters, such as mechanical properties and boundary conditions, through Bayesian updating based on observed structural responses (modal data, strains, displacements). The main novelties of this research regard, on the one hand, the proposal of a methodology for obtaining a reliable estimate of the axial force in ancient tie-rods accounting for different sources of uncertainty and, on the other hand, the application of ABC to obtain the structural identification inverse problem solution.

Nonstationary response statistics of structures with hysteretic damping to evolutionary stochastic excitation

The damping of a structure has often been modeled as linear hysteretic damping (LHD), so its corresponding equation of motion (EOM) is an integro-differential equation that involves the Hilbert transform of response displacement. As a result, the system is non-causal in nature, and it is challenging to compute its nonstationary response statistics under evolutionary stochastic excitation. This article develops an efficient solution method to obtain closed-form solutions for various nonstationary response statistics, including the evolutionary power spectrum (EPS), correlation function and mean square values. The novel solution method utilizes the concept of causalization time to introduce a “causalized” impulse response function (IRF), by which causal response statistics are computed based on a pole-residue approach. This approach requires obtaining a pole-residue form of the transfer function (TF) from the frequency response function (FRF) of the system, which is readily obtained from the EOM. Subsequently, the desired response statistics are obtained by shifting the causal response statistics back to the original time. To obtain the pole-residue form of the TF, two steps are necessary: (1) taking the inverse Fourier transform of the FRF of the oscillator to obtain a discrete IRF and (2) using the Prony-SS method to decompose this discrete IRF to obtain the pole residues associated with the TF. The correctness of the proposed method is numerically verified by Monte Carlo simulations through examples of hysteretic damping and mixed viscous-hysteretic damping oscillators that are subjected to white noise, modulated white noise and modulated Kanai–Tajimi model random excitations.

A finite difference method on crack resistance of reinforced glass beam with non-linear adhesive

Reinforced glass beam (RG beam) is a type of structural glass member that has been developed in recent years. This RG beam consists of a glass beam to which reinforcement material, such as steel, is adhesively attached in the tensile side to improve crack resistance. The adhesive plays a critical role in the structural performance of RG beam. However, the effect of non-linear shear-slip behavior of the adhesive layer remains unclear and has been neglected in most previous studies, which can result in inaccurate estimations. To address this issue, this paper presents a finite difference model (FDM) that utilizes an explicit step-by-step method and trial-and-error iterative method for interfacial stress analysis. The model predicts the static structural response of a simply-supported RG beam that simulates the adhesive with non-linear stress-slip behavior. Furthermore, the model describes the adherend’s shear deformation in elastic. The FDM results are then compared with the finite element method (FEM), adopting discrete nonlinear connectors (springs) to simulate the adhesion, and available analytical methods. Detailed parametric studies are further conducted to investigate the influences of glass strength, load pattern, reinforcement ratio and height-to-span ratio for proposing design recommendations.

On the use of aluminium alloys in sustainable design, construction, and rehabilitation of bridges: emerging applications and future opportunities

Over the last few decades, aluminium alloys have been widely used as primary structural material in building construction. This is due to their advantageous properties such as low density, high strength-to-weight ratio, durability and excellent corrosion resistance, and high recyclability. The scope of this review paper is to explore the potential use of aluminium alloys in bridge design and construction. To this end, a thorough discussion of the material properties is presented to identify if the aluminium alloys can meet the bridge design and construction requirements. Particular emphasis is also given on total life-cycle cost of aluminum alloys and their potential role towards sustainability and decarbonisation of bridge structures. Moreover, the possibility of using aluminium alloys as an alternative for bridge rehabilitation and strengthening is investigated herein. A review of the existing research on the static, dynamic and fatigue structural response of aluminium bridge decks is also conducted. The main findings are highlighted, and research gaps are identified. Finally, corresponding future research to fill these gaps is recommended.

StructGNN: An efficient graph neural network framework for static structural analysis

In the field of structural analysis prediction via supervised learning, neural networks are widely employed. Recent advances in graph neural networks (GNNs) have expanded their capabilities, enabling the prediction of structures with diverse geometries by utilizing graph representations and GNNs' message-passing mechanism. However, conventional message-passing in GNNs doesn't align with structural properties, resulting in inefficient computation and limited generalization to extrapolated datasets. To address this, a novel structural graph representation, incorporating pseudo nodes as rigid diaphragms in each story, alongside an efficient GNN framework called StructGNN is proposed. StructGNN employs an adaptive message-passing mechanism tailored to the structure's story count, enabling seamless transmission of input loading features across the structural graph. Extensive experiments validate the effectiveness of this approach, achieving over 99% accuracy in predicting displacements, bending moments, and shear forces. StructGNN also exhibits strong generalization over non-GNN models, with an average accuracy of 96% on taller, unseen structures. These results highlight StructGNN's potential as a reliable, computationally efficient tool for static structural response prediction, offering promise for addressing challenges associated with dynamic seismic loads in structural analysis.

State-Space Approaches to Complex Structures in Aerospace

The state-space approach (SSA), traditionally utilized in modern control theory, has been successfully adopted over the last three decades to investigate the mechanical behaviors of complex structures composed of composite or smart materials. This is largely due to their increasing application across various fields, including aerospace, civil and marine engineering, and transportation vehicles. This paper provides a comprehensive review of the establishment of state-space formulations for structures of typical configurations, such as beams, plates, shells, and trusses, with a particular focus on their applications in the mechanical analyses of various complex aerospace or smart structures using the transfer matrix method. The paper first summarizes the three-dimensional SSAs applied to laminated structures without any assumptions on physical fields. By employing structural theories such as various beam, plate, and shell theories, simplified one-dimensional and two-dimensional SSAs for laminated structures are developed. The paper then outlines the advances in generating analytical solutions for the mechanical behaviors of laminated structures. For the sake of completeness, the paper also provides an account of SSAs applied to complex periodic structures, particularly in beam and truss forms. To overcome the limitations of conventional SSAs related to structures with specialized geometric configuration or under arbitrary boundary conditions, state-space based numerical methods have been proposed, for example, the state-space based differential quadrature method and state-space based finite-element method. The applications of these methods in the analyses of static and dynamic responses of complex structures are extensively reviewed. It is observed that there are still intriguing and potential research topics for the development of advanced SSAs with enhanced versatility and the studies on practical complex structures used in modern engineering, particularly in aerospace industry. Therefore, this review is expected to be beneficial for researchers in the fields of analytical and numerical methods, composite structures, aerospace, structural engineering, and more.

On the nonlinear dynamics of a multi-scale flexoelectric cylindrical shell

The flexoelectric property shows the relationship between the strain gradient and the electric polarization and has a significant effect on static and dynamic responses of structures at small scales such as micro and nano. Nowadays, experimental studies for intelligent/composite ultra-small mechanical systems are complex, challenging, and in most cases still impossible, especially for nonlinear dynamic behavior analysis. For the first time, this study presents an advanced and complex generalized model for the nonlinear vibrations of a piezo-flexoelectric mechanical system based on a cylindrical shell. It should be noted, that the formulated boundary value problem is generalized, well-posed, and can be applied to the system at micro and nano scales. Hamilton's variational principle as well as assumptions of the first-order shear deformation theory (FSDT) and reformulated flexoelectric theory were used to derive equations of motion of the multi-scale intelligent shell system. To introduce nonlinear effects, von-Kármán strains are applied. Appropriate classical and non-classical mechanical/electric boundary conditions as well as higher-order forces and moments are determined to fully close the formulated problem. The Galerkin method combined with the GDQM, supported by the displacement control strategy and the weighted residual method, have been used to discretize and solve the nonlinear governing equations of the shell with different boundary conditions. Good convergence between the current results and the results from previous studies for simpler cases of the shell was proved. Furthermore, the results showed that geometric ratios of the structure, gradation of material properties, thickness of the flexoelectric layers, and the size effect parameter significantly influence the nonlinear frequency of the structure under the direct flexoelectric effect.

A dual-horizon peridynamic model for Reissner–Mindlin plates with arbitrary horizon sizes and shapes

A dual-horizon peridynamic (DHPD) model with arbitrary horizon sizes and shapes is proposed for predicting structural responses of thin-walled structures subjected to out-of-plane loadings. The proposed DHPD method can diminish the influence arising from ghost forces in irregular particle distributions and lessen the computational consumption with optimal refinement discretizations. Meanwhile, the variable PD parameters of each discrete particle that derive based on its own current horizon domain are adopted to mitigate the PD surface effect. Several static and dynamic structural responses with different geometric and boundary conditions are compared between the reference and DHPD approaches. It is concluded that the proposed DHPD method can effectively reproduce structural behaviors in fracture mechanics problems with less computational effort.

Static and dynamic analysis of couple-stress elastic structures by using peridynamic differential operator

In this paper, a peridynamic differential operator (PDDO) method is developed to analyze the static and dynamic responses of size-dependent elastic structures in the frame of a consistent couple stress theory (CCST). The displacement governing equations together with the boundary conditions of the couple-stress static problems are transformed from the local differential form to the nonlocal integral form through a fourth-order PDDO and then solved by a meshfree scheme. For dynamic cases, the time-domain problems are first transformed into frequency domain by Fourier transform, then solved by the PDDO meshless method in the frequency domain. The time-domain results are finally obtained by using an exponential window method (EWM). The size effects on the static and dynamic responses of some typical elastic problems are investigated by the developed PDDO method. A very high level of computational accuracy is achieved by comparing with the analytical solutions and the existing numerical results.

General boundary conditions implementation for the static analysis of anisotropic doubly-curved shells resting on a Winkler foundation

In the present work an Equivalent Single Layer (ESL) formulation is proposed for the static analysis of doubly-curved anisotropic structures of arbitrary geometry and variable stiffness resting on a Winkler elastic foundation. In-plane and out-of-plane general distributions of linear elastic springs are provided for the implementation of general external constraints along the edges of the structure. The structure is geometrically described accounting for the principal curvatures of the shell object of analysis. A generalized set of blending functions based on Non-Uniform Rational Basis Spline (NURBS) curves is adopted so that arbitrary shaped structures can be modelled with the same approach. The fundamental governing equations are obtained in terms of displacement field unknowns, which has been effectively described accounting for a unified formulation based on the minimum potential energy principle. General anisotropic lamination schemes are considered, setting a general orientation of each lamina, as well as all possible material symmetries. The numerical implementation is performed by means of the Generalized Differential Quadrature (GDQ) method, thus allowing a strong formulation of the structural problem. A series of validation examples is performed on shells with zero, single and double curvatures in which the static structural response provided with the proposed formulation has been compared to that obtained from a refined three-dimensional finite element model, showing a great accordance between these different approaches. The research shows that the employment of higher order theories, together with the GDQ method, allows to obtain very accurate results with a reduced computational cost, compared to finite element simulations.

Mechanical-electro-magnetic coupling enriched finite element method for static analysis of magneto-electro-elastic composites

Magneto-electro-elastic (MEE) composites have promising application prospects due to the rapid response to the excitation of external electric or magnetic fields. Finite element simulation of the multi-physics coupling problems in MEE-based structures is significant. The enriched finite element method (EFEM) is derived from the standard finite element method (FEM), with finite element shape functions improved by interpolation covers. Considering the complex mechanical-electro-magnetic multi-physics coupling mechanism of MEE-based structures, the mechanical-electro-magnetic coupling enriched finite element method (MEM-EFEM) was proposed. The method is well worked for investigating the mechanical-electro-magnetic multi-physics coupling issues to calculate the generalized displacement (displacement components, electric and magnetic potential) with 3-node triangular elements. In a set of numerical experiments involving the static analysis of MEE-based structures, MEM-EFEM outperforms the regular FEM. When it comes to the same solution accuracy level, the number of elements used by MEM-EFEM is lower than that of the standard FEM, suggesting that MEM-EFEM has better convergence and accuracy on this subject. Besides, the MEM-EFEM solution accuracy can be enhanced by mesh refinement. Overall, the MEM-EFEM has the potential to be used in engineering practice to solve the static responses of MEE-based structures on mechanical-electro-magnetic multi-physics coupling issues.

Numerical convergence and error analysis for the truncated iterative generalized stochastic perturbation-based finite element method

The main aim of this work is to present a numerical analysis of convergence and accuracy of the selected generalized perturbation-based schemes in linear and nonlinear problems of solid mechanics. An algorithm for determining the basic probabilistic characteristics has been developed using the iterative generalized stochastic higher-order perturbation method adjacent to symmetrically truncated Gaussian random variables. It has been confirmed that usage of a sufficiently high order of the Truncated Iterative Stochastic Perturbation Technique (TISPT) allows for achieving any desired accuracy in determining up to the fourth-order probabilistic characteristics of static structural response. The semi-analytical probabilistic approach is the reference solution in this study, which is based upon the same composite response functions determined with the use of the Least Squares Method created using specific series of FEM experiments. The entire methodology has been provided for the given extreme value of the coefficient of variation αmax of the input uncertainty source. On the other hand, a selection procedure of the stochastic perturbation method order to achieve 1% numerical accuracy in all up to the fourth-order probabilistic moments has been proposed. Computational experiments include simply supported elastic Euler–Bernoulli beam, a set of steel diagrid structures, nonlinear tension of steel round bar as well as homogenization procedure of some particulate composite.

Quantifying the effect of amplitude scaling of real ground motions based on structural responses of vertically irregular and regular RC frames

Increasing number of real ground motion (GM) record databases raised nonlinear dynamic analysis (NDA) as an attractive option to determine structural response statistics. Structural responses are sensitive to input motions and the appropriate selection and scaling of real GMs is one of the crucial topics in earthquake engineering. In this paper, the influence of amplitude scaling on important earthquake demand parameters (EDPs), namely, global drift ratio, inter-story drift ratio and maximum floor acceleration, were studied using different scaling approaches and scaling limits. Eurocode-8 was used as a reference seismic code and amplitude scaling effects on structural responses of vertically irregular and regular structures were quantified. Efficiency and sufficiency of amplitude scaling were assessed in terms of mean, dispersion and non-exceedance probability curves of the EDPs. Statistical distribution of GM characteristics and their dependence on GM amplitude scaling were also discussed. Evaluations have shown that similar mean responses can be obtained regardless of scaling limits, approaches, and building topology if spectral shape compatibility is ensured. Furthermore, results demonstrated that neither building regularity nor scaling of GMs influenced the statistical distribution of ground motion parameters and non-exceedance probability curves of the EDPs. In fact, it was revealed that record selection scenario including spectral compatibility of individual GMs had a dramatic impact on dispersion and exceedance probability of structural responses.

Model Updating for a Continuous Concrete Girder Bridge Using Data from Construction Monitoring

Finite element (FE) model updating can guarantee the accuracy of the numerical analyses for civil structures. However, two deficiencies currently exist with the traditional FE model updating technique based on the measurements of modal parameters and/or the static structural responses of the built structure with respect to its reference information insufficiency and its non-unique solution generally obtained, hampering its extensive use. It becomes the goal of the whole engineering community to introduce new effective methods for the civil structural FE model update. To this end, an innovative FE model updating method using data from construction monitoring is proposed in this article. With regard to its theoretical novelty, the new method transforms the complicated multi-variable optimization mathematical problem with the traditional FE model updating technique into many simple single-variable parameter identification problems. Under the engineering background of Huangsha Harbor Bridge, a three-span concrete continuous box girder bridge constructed utilizing the symmetric cantilever casting method, the effectiveness and the efficiency of the new model updating practice were validated. It is demonstrated using quantitative data that the abundant data measured on Huangsha Harbor Bridge in construction stages can enhance the reference information for the more accurate FE model updating of the structure, and the uncertain parameters with the initial FE model of Huangsha Harbor Bridge can be progressively and easily identified for the proposed model updating method using many single-variable linear regression models, instead of one complicated multi-variable mathematical or numerical model employed by the traditional model updating approaches, which generally leads to non-unique solutions rendered by normal optimization algorithms.

A new interval perturbation method for static structural response bounds using radial basis neural network differentiation

A new interval perturbation method for static structural response bounds using radial basis neural network differentiation

Computation‐with‐confidence for static elasticity: Data‐driven approach with order statistics

AbstractThis paper presents a data‐driven method to identify a bound for the structural response of interest when a data set of elastic material responses is available. The obtained bound is probable in the sense that, at least with a certain confidence level, the probability that the structural response is within the bound is no smaller than a certain target value of reliability. The confidence level is ensured by considering the order statistics of the given data points. In this manner, this paper introduces the concept of reliability to the framework of data‐driven computational elasticity to address uncertainty in the data set. The method does not require any statistical information of the data points. Two numerical examples demonstrate the use of the proposed method to analyze static responses of structures by using only given material data sets.

Abnormal Data Recovery of Structural Health Monitoring for Ancient City Wall Using Deep Learning Neural Network

ABSTRACT Continuous structural health monitoring is of great importance to preventive conservation for ancient architectural heritages. However, abnormal monitoring data may trigger false alarming of structural damages. SHM of ancient buildings also needs abnormal data recovering. Most of the existing studies used the neural network with single input dimension and forward prediction to recover abnormal data, which is difficult to accurately predict long data sequences. This study developed a novel abnormal data recovery framework. The main novelty of the proposed framework is that the input and output configurations of the GRU model are optimized. Meanwhile, to make full use of the forward and backward information of the abnormal data sequence, bidirectional prediction is used to improve the prediction accuracy. The framework is implemented in the abnormal monitoring data recovering for an ancient city wall built 600 years ago in Beijing. Three types of abnormal data, including outlier, drift, and missing, are considered in this study. The results reveal that the proposed framework has high accuracy in abnormal data recovering of strain and crack width. The recovered data has the same regular diurnal variation as the normal monitoring data. The linear correlation between the structural responses and wall temperature gets obviously improved after data recovering. The proposed framework shows great capacity of abnormal data recovery for structural static responses of ancient buildings, which are usually influenced by environmental temperature variation.

The damage effect on the dynamic characteristics of FRP-strengthened reinforced concrete structures

The present work aims to assess the modal properties of reinforced concrete structures strengthened with FRP-based systems subjected to progressive damage. In particular, an integrated numerical fracture model, based on a cohesive crack approach and an embedded truss model, has been used to simulate the damage phenomena of such kinds of structures under quasi-static loading conditions. Subsequently, at predefined damage levels, the dynamic response, in terms of natural vibration frequencies, has been obtained by solving the problem of small amplitude free oscillations and then compared with the numerical and experimental results. The comparisons show the beneficial strengthening effect of the FRP system on both static and dynamic structural response, in terms of load-carrying capacity and natural vibration frequency degradation, highlighting the applicability of the proposed numerical model in the framework of model-based damage identification methods for FRP-strengthened concrete structures.