Nonlinear Structural Analysis Research Articles

Nonlinear vibration analysis of FGM sandwich structure under thermal loadings

The geometrically nonlinear thermal frequencies of the functionally graded (FG) sandwich structures are predicted numerically in the current work considering the variable temperature distributions (linear and nonlinear). For numerical analysis of the FG sandwich structure, an in-house finite element code has been developed in MATLAB using the higher-order shear deformation theory (HSDT) and Green–Lagrange nonlinear strain kinematics. The governing equation of motion for the graded sandwich structure is obtained using Hamilton’s principles, and the direct iterative method is used to predict the nonlinear vibration response of the sandwich structure. The temperature distributions along the thickness of the sandwich structure are considered. Temperature dependent material properties are considered in the present work for computation of frequency responses under thermal environment. The material properties are described in accordance with the power-law distribution. The current models are initially validated with the published results. The influence of various input parameters, i.e. the curvature ratio (CRO), thickness ratio (TRO), aspect ratio (ARO), boundary conditions, and power-law indices on the nonlinear vibration behaviours of FG sandwich structure have been studied.

Locking-free isogeometric Timoshenko–Ehrenfest beam formulations for geometrically nonlinear analysis of planar beam structures

In linear isogeometric analysis of beams, the success of selective reduced integration and B ¯ projection methods in mitigating the locking phenomenon has been proved. This study further extends these methods to the geometrically nonlinear analysis with two isogeometric Timoshenko–Ehrenfest beam formulations, that is, C 0 -continuous NURBS selective reduced integration and B ¯ formulations. Three numerical examples are presented examining overall structural responses, strain energy, recovery of cross-sectional stress resultants, and convergence properties. Although the two proposed formulations exhibit the locking-free behavior for highly flexible beam structures, the B ¯ formulation offers higher accuracy, and the proper recovery of strain measures and cross-sectional stress resultants.

Artificial intelligence - finite element method - hybrids for efficient nonlinear analysis of concrete structures

Realistic structural analyses and optimisations using the non-linear finite element method are possible today yet suffer from being very time-consuming, particularly in case of reinforced concrete plates and shells. Hence such investigations are currently dismissed in the vast majority of cases in practice. The "Artificial Intelligence - Finite Element - Hybrids" project addresses the current unsatisfactory situation with an approach that combines non-linear finite element models for reinforced concrete shells with scientific machine learning algorithms to create hybrid AI-FEM models. The AI-based surrogate material model provides the material stiffness as well as the stress tensor for given concrete design parameters and the strain tensor. This paper reports on the current status of the project and findings of the calibration of the AI-based reinforced concrete material model. We successfully calibrated and evaluated k-nearest-neighbour, LGBM and ResNet algorithms and report their predictive capabilities. Finally, some light is shed on the future work of integrating the AI surrogate material models back into the finite element method in the course of the numerical analysis of reinforced concrete structures.

Numerical implementation for isogeometric analysis of thin-walled structures based on a Bézier extraction framework: nligaStruct

We present an open Octave/Matlab package nligaStruct, for linear and nonlinear isogeometric analysis of thin-walled structures. nligaStruct is an extension of NLIGA in aspect of isogeometric structural analysis. A framework for Bézier extraction of T-spline and NURBS is embedded in the simulation pipeline. Both Reissner–Mindlin and Kirchhoff–Love assumptions are considered in the case of static bending and free vibration analysis of thin-walled structures (plates and shells). The convergence behaviors of these two assumptions for both plate and shell are thoroughly studied and compared. The discrete formulations for large deformation of Kirchhoff–Love shells considering geometrical and material nonlinearity are detailedly derived and carefully implemented. Three types of hyperelastic materials, including St. Venant–Kirchhoff, incompressible neo-Hookean and compressible neo-Hookean, are employed in the large deformation of Kirchhoff–Love shells. A series of popular benchmark examples and their geometrical models are demonstrated in the package. The numerical results are validated by comparing with analytical solutions and that obtained from commercial software. The postprocessing is self-contained and implemented by tessellation of Bézier elements. Finally, complete source codes and the data obtained from numerical examples are fully provided and free to access.

Determination and application of path duration of seismic ground motions based on the K-NET data in Sagami Bay, Japan

Duration models are one of the important parameters in ground-motion simulations. This model varies in different study areas, and plays a critical role in nonlinear structural response analysis. Currently, available empirical models are being globally used in ground-motion simulations, with limited research focusing on path duration in specific regions. In this study, we collected 6,486 sets of three-component strong-motion records from 29 K-NET stations in the Sagami Bay, Japan, and its surrounding areas between January 2000 to October 2018. We extracted the effective duration of 386 pieces of ground-motion records by manually picking up the S-wave arrival time and calculating the significant duration. We then obtained the path duration model of the study area based on the empirical equation of dynamic corner frequency and source duration of [7]. Compared with the results of the available empirical models, the Fourier spectrum of the simulated ground motion from our effective duration model showed higher accuracy in the long-term range, with less fitting residuals. This path duration model was then applied to simulate two earthquakes of MW5.4 and MW6.2, respectively, in the region using the stochastic finite-fault method with a set of reliable source, path, and site parameters determined for the study area. The simulation results of most stations fit well with observation records in the 0–30 Hz frequency band. For the MW5.4 earthquake, the simulated ground motions at KNG005/KNG010/SZO008 stations were relatively weak in the mid to high frequency band (1–30 Hz) because the quality factor and geometric diffusion model used in the simulation were the averages of the entire Sagami Bay region, causing a bias in the results of a few stations owing to local crustal velocity anomalies and topographic effects. For the MW6.2 earthquake, the simulated ground motions were relatively weak at all SZO and TKY stations, mainly because of the close distance from these stations to the epicenter and the complex seismic-wave propagation paths. The analysis suggests that the differences between the simulation results of the two earthquakes were mainly related to complex geological conditions and seismic-wave propagation paths.

Experimental and numerical study on the mechanical properties of honeycomb plate box-type hollow roof structure

In this paper, a new honeycomb plate box-type hollow roof structure is prepared. The failure mode and mechanical properties of the box-type hollow roof structure were analyzed by bearing capacity test and numerical analysis. The validity of the numerical analysis model is verified by comparing the results of bearing capacity test with the results of the complete coordinated model and the coupled model analysis. The results show that the failure mode of the specimen is tensile failure of the surface plate of the honeycomb plate with strengthened frame and buckling instability of the plate near the joint. The box-type hollow roof structure has good ductility. The results of static analysis and nonlinear buckling analysis of the honeycomb plate box-type hollow roof structure are carried out by coupling model are more consistent with the results of bearing capacity test.

A solution to the problem of pile settlement caused by vertical static loading with consideration to plastic properties of the foundation soil

Introduction. The article addresses the problem of nonlinear analyses of structures having pile foundations. The purpose of the study is to develop a method for determining the nonlinear behaviour of a single pile. The tasks of the study are to use the analytical method to define and solve the settlement problem of a single pile, taking into account the plastic properties of soils along the lateral surface and under the tip, as well as to verify the obtained solutions using the field data obtained by testing the pile subjected to static loading.
 Materials and methods. The analytical model of the telescopic motion of coaxial cylindrical soil layers around the pile was applied to obtain the solution. Pile settlement due to the punching of the bottom layer was calculated using the available formula dealing with a circular rigid stamp located at a given depth from the surface. To verify the solution, the authors used the materials of static loading tests conducted in respect of three reinforced concrete prismatic piles of the base of a hospital building located in the city of Tver. A static method was used to drive the piles.
 Results. A comparison between the results of the analysis obtained using the proposed solution and the field test data is presented. The analysis of this comparison shows that the solution allows describing the load-settlement curve for the static loading of a single pile. A reasonable mismatch between the calculated and field data is identified; it is associated with the inability of the derived formula to take account of soil consolidation.
 Conclusions.The solution, obtained for single pile settlement, takes into account plastic properties of soil on the lateral surface and under the pile tip. This solution describes the regularity of single pile deformation under static loading. Further research will take soil consolidation into account. The assumed values of the ultimate resistance of a pile along a lateral surface and under the pile tip have a considerable influence on the results of the calculation according to the solution obtained by the authors. A relevant task, to be solved in the course of further research, is to find alternative methods of their determination.

Adaptive Local Maximum-Entropy Surrogate Model and Its Application to Turbine Disk Reliability Analysis

The emerging Local Maximum-Entropy (LME) approximation, which combines the advantages of global and local approximations, has an unsolved issue wherein it cannot adaptively change the morphology of the basis function according to the local characteristics of the sample, which greatly limits its highly nonlinear approximation ability. In this research, a novel Adaptive Local Maximum-Entropy Surrogate Model (ALMESM) is proposed by constructing an algorithm that adaptively changes the LME basis function and introduces Particle Swarm Optimization to ensure the optimality of the adaptively changed basis function. The performance of the ALMESM is systematically investigated by comparison with the LME approximation, a Radial basis function, and the Kriging model in two explicit highly nonlinear mathematical functions. The results show that the ALMESM has the highest accuracy and stability of all the compared models. The ALMESM is further validated by a highly nonlinear engineering case, consisting of a turbine disk reliability analysis under geometrical uncertainty, and achieves a desirable result. Compared with the direct Monte Carlo method, the relative error of the ALMESM is less than 1%, which indicates that the ALMESM has considerable potential for highly nonlinear problems and structural reliability analysis.

A Novel Nonlinear Elasticity Approach for Analysis of Nonlinear and Hyperelastic Structures

There are many materials that the linear elasticity theory cannot predict their mechanical behavior against applied loads. This research proposes a comprehensive theoretical method to obtain the mechanical response of hyperelastic models (with nonlinear elastic deformations) such as polymers and rubbers. They are vital in the design phase of complicated engineering structures like engine mounts and structural bearings in aerospace and automotive industries. The presented theory is implemented in detail and has no limitations in analyzing geometrically and physically nonlinear materials. As a test case, the governing equations of a sheet made of nonlinear elastic material are derived within the framework of this new approach. The derived governing equations are completely nonlinear in all major directions. Consequently, results can be one of the most accurate mathematical simulation results for nonlinear elastic material structures. Then, the obtained equations are solved using a meshless solution method named the semi-analytical polynomial method. The stress and deformation results of the structure under uniform and non-uniform transverse external loadings are obtained for different types of boundary conditions, loading, and material properties. Consequently, this research can be widely used as a suitable essential reference for researchers studying the mechanical behavior of nonlinear elastic structures.

Data-driven models for crashworthiness optimisation: intrusive and non-intrusive model order reduction techniques

To enable multi-query analyses, such as optimisations of large-scale crashworthiness problems, a numerically efficient model is crucial for the development process. Therefore, data-driven Model Order Reduction (MOR) aims at generating low-fidelity models that approximate the solution while strongly reducing the computational cost. MOR methods for crashworthiness became only available in recent years; a detailed and comparative assessment of their potential is still lacking. Hence, this work evaluates the advantages and drawbacks of intrusive and non-intrusive projection based MOR methods in the framework of non-linear structural transient analysis. Both schemes rely on the collection of full-order training simulations and a subsequent subspace construction via Singular Value Decomposition. The intrusive MOR is based on a Galerkin projection and a consecutive hyper-reduction step. In this work, its inter-and extrapolation abilities are compared to the non-intrusive technique, which combines the subspace approach with machine learning methods. Moreover, an optimisation analysis incorporating the MOR methods is proposed and discussed for a crashworthiness example.

Assessment of structural health of an existing prestressed concrete bridge by finite element analysis

ABSTRACT This study investigates the feasibility of an alternative structural health monitoring (SHM) technique for an existing, post-tensioned, prestressed concrete bridge in Niigata, Japan. Currently, a static SHM system is in place to detect the progress of damages within the bridge. However, the existing system cannot properly monitor the structural health of the bridge including the periodic vibration, which is one of the damage-sensitive features of interest. Therefore, to effectively detect the real-time performances of the bridge, a three-dimensional (3D) Finite Element (FE) model was developed as a reference and verified using on-site load-deflection test results. After validating the reference FE model, different damage scenarios, such as degradation of concrete, corrosion & rupture of steel tendons and missing tendons, were incorporated in the FE models. Based on non-linear structural and Eigenvalue analyses, natural frequencies and mode shapes of the bridge remain constant even after careful consideration of all types of damages in the FE model. However, vertical displacements are observed to increase for the damage scenarios. Although the effect of tendon rupture and corrosion showed negligible influences on the vertical displacement, the deterioration of the concrete largely influenced the vertical displacement. Additionally, crack widths were found to vary with damage types. Brifely, this study recommends some effective indicators to monitor the structural conditions of the bridge using FE analysis (FEA).

Non-linear Hygrothermal Structural Analysis of the Elliptical Dome of the Church in the Universidad Laboral, Gijon, Spain

ABSTRACT The Church of the Laboral University of Gijón has the world’s largest elliptical masonry roof with a 40.8 m major axis. This large structure is vertically self-supported with 20 pairs of masonry ribs crossing each other and horizontally supported by means of two elliptical ring beams at the top of the dome. In order to study this historic building, this paper presents the overall three-dimensional structural numerical analysis of the roof. It includes nonlinearities due to materials, geometry, and contacts between structural elements of the building. Temperature, moisture content, and dead loads are included in the hygrothermal structural analysis of the dome. In this nonlinear numerical analysis displacements, stress, cracking, and crushing are evaluated. The influence of moisture content on the structure performance and other relevant conclusions are presented.

Special Issue of Mathematics: Analytical and Numerical Methods for Linear and Nonlinear Analysis of Structures at Macro, Micro and Nano Scale

The mathematical models of physical phenomena are based on the fundamental scientific laws of physics [...]

Development of a CPU-GPU heterogeneous platform based on a nonlinear parallel algorithm

Abstract In order to seek a refined model analysis software platform that can balance both the computational accuracy and computational efficiency, a CPU-GPU heterogeneous platform based on a nonlinear parallel algorithm is developed. The modular design method is adopted to complete the architecture construction of structural nonlinear analysis software, clarify the basic analysis steps of nonlinear finite element problems, so as to determine the structure of the software system, conduct module division, and clarify the function, interface, and call relationship of each module. The results show that when the number of model layers is 10, the GPU is 210.5/s and the CPU is 1073.2/s, and the computational time of the GPU is significantly better, with an acceleration ratio of 5.1. For all the models, the GPU calculation time is much less than that of the CPU, and when the number of model degrees of freedom increases, the acceleration effect of the GPU becomes more obvious. Therefore, the CPU-GPU heterogeneous platform can more accurately describe the nonlinear behavior in the complex stress states of the shear walls, and is computationally efficient.

Component-based model of semi-rigid connections for nonlinear analysis of composite structures

In order to achieve better mechanical performance and construction efficiency, the outrigger bracket with a “through type” interior diaphragm (OBTID) connection is proposed for application in semi-rigidly connected composite structures. The mechanical behaviour of OBTID connections in two frame tests under lateral cyclic loads is investigated to reveal the failure mechanism. Based on the test observations, a component-based model is proposed to analyse the nonlinear behaviour of semi-rigid connections by decomposing the connection components and putting forward the constitutive law of each component. Furthermore, the proposed model is implemented in a general commercial finite element package and a program for nonlinear analysis of semi-rigidly connected composite structures is developed by combining the component-based model with the previous fiber beam-column model. Then, a comparison between the numerical results and experimental results in both connection level and frame level indicates that the proposed component-based model can predict the complex nonlinear behaviour of semi-rigid connections with good accuracy. Additionally, the contribution of bolt slip to connection rotation is analysed to clarify the pinching effect, and the semi-rigidity of OBTID connections are compared with provisions of Eurocode 3 and that of other similar semi-rigid connections.

Study of dynamic debris impact load on flexible debris-resisting barriers and the dynamic pressure coefficient

The use of steel flexible barriers to mitigate landslide risk on natural hillsides is becoming common in the past decade in Hong Kong. The current design approach for this kind of barrier structure involves the adoption of the hydrodynamic load model to predict dynamic impact forces, followed by non-linear structural analyses of flexible barriers using numerical programs based on the pseudo-static force method. From local design guidelines, the dynamic pressure coefficient, a critical input parameter in the hydrodynamic load model, is taken as 2.0. This empirically considers the effect of impacts from boulders up to 2.0 m in diameter. With a view to rationalising the design approach, a series of physical impact tests and numerical analyses was conducted to investigate the dynamic debris impact on flexible barriers and the resulting barrier response. The physical impact tests involved up to 9 m3 of debris resisted by a 1.5 m high steel ring-net barrier. The tests were conducted in the 28 m long large-scale flume facility at the Kadoorie Centre in Hong Kong. Numerical modelling using computer programs LS-DYNA and NIDA-MNN was conducted to analyse the dynamic response of flexible barriers with different structural forms. The study aims to evaluate the dynamic pressure coefficient and to verify the current design approach based on the suggested dynamic pressure coefficient from this study. Results indicate that a dynamic pressure coefficient of 1.0 is, in general, appropriate for design purposes if the debris comprises primarily water and fine-grained particles.

Synthesis, molecular structural, optical, thermal and third harmonic nonlinear optical analysis of Piperazine-1,4-diium bis(2-carboxy-6-nitrobenzoate) tetrahydrate single crystal

Structure and molecular interactions of the title molecular salt (NPP) were established by X-ray diffraction. The elucidated structure model assigns centrosymmetric triclinic arrangement for the molecules. Molecular packing was established through robust O–H⋯O, N–H⋯O and C–H⋯O hydrogen bond network revealing infinite chains, sheets and spiral ladder patterns. The molecular patterns were abridged through C–H … π and π – π linkages expressing several S and R graph set motifs. Single crystals of NPP with defined morphology were grown by the method of slow evaporation from solution from 1: 1 mixed solvent of methanol and water. FT- IR, FT - Raman spectra reinforced the functional groups and with NMR spectra, the protonated-deprotonated nature of the title molecule. UV–visible, Urbach plot, photoluminescence and fluorescence spectral profiles endorsed the electronic transitions and photophysical properties of NPP. Z-scan profile in the closed and open aperture modes was deployed to estimate the magnitude of the third-order nonlinear optical constants. Thermogravimetry coupled with Differential Scanning Calorimetry (DSC) declare the optimal thermal stability of the material till 71.8 °C.

Lumped spring model parameters of RC frame elements for seismic performance assessment

AbstractThis study presents lumped spring model parameters for nonlinear seismic analysis of reinforced concrete (RC) frame structures. The modified Ibarra‐Medina‐Krawinkler (M‐IMK) hysteresis model is used as a lumped spring to simulate the inelastic behaviour of a RC frame element. The influence of loading protocols on the calibration of model parameters is investigated and compared with other hysteresis models, such as the original IMK and Bouc‐Wen‐Baber‐Noori (BWBN) models. Less dependent on the loading protocol used for model identification, the parameters of the modified IMK hysteresis model are calibrated to model a database of 383 rectangular RC columns. To simplify the calibration process, the model parameters that define the monotonic response are determined based on code and empirical equations, while the parameters that control the hysteretic degradations are calibrated against the experimental results. The calibrated model parameters are used to develop regression equations for the model parameters based on physical variables, such as loading, dimensions, and material properties. It is found that the model parameters obtained from the experimental calibration and regression equations generate similar hysteresis curves. The performance of the lumped spring model to nonlinear time history analysis of RC structures subjected to earthquakes is also evaluated through a series of pseudo‐dynamic hybrid simulations.

Deep convolutional generative adversarial networks for the generation of numerous artificial spectrum‐compatible earthquake accelerograms using a limited number of ground motion records

AbstractDeep learning (DL) methodologies have been recently employed to solve various civil and earthquake engineering problems. Nevertheless, due to the limited number of reliable data in the field of earthquake engineering, it is not convenient to obtain accurate results using DL. To tackle this challenge, the generative adversarial network (GAN) approach may be considered a reliable possible candidate. GANs have been introduced as an efficient way to train generative models. GANs exhibited their capabilities as well as versatility in the field of image production. For nonlinear dynamic analyses of structures, artificial ground accelerograms that are compatible with a target response spectrum are usually generated. In this paper, an efficient algorithm is proposed by which numerous artificial spectrum‐compatible earthquake accelerograms are generated using a few ground motion records. For this purpose, a specific well‐established generative model, namely, the deep convolutional GAN (DCGAN), is adopted for the first time and used. It is shown that DCGAN can easily generate desirable artificial ground accelerograms by having a limited number of seismic records as input to train the network. To quantitatively demonstrate the quality of the artificial ground accelerograms generated by the DCGAN, several computer experiments are presented, among which the robustness and feasibility of the proposed method are examined by using only four earthquake accelerograms as the worst scenario. Moreover, the efficiency of the DCGAN is illustrated by comparing various seismic parameters and the spectral response of the generated accelerograms with those of the actual accelerograms. The outcomes illustrate the efficiency and robustness of the presented DCGAN.

A damage-driven integration scheme in physically non-linear transient analysis for quasi-brittle materials

The standard Newton–Raphson scheme suffers from divergence problems due to softening, negative tangent stiffness, bifurcations or snap-back when modelling fracture of quasi-brittle materials, such as masonry and concrete. Convergence can be achieved by applying sequentially linear analysis (SLA) in some cases. However, it has difficulties in dealing with cases in which the displacement history matters such as dynamic damage modelling due to its total approach. Recently, incremental sequentially linear analysis (ISLA) which combines the merits of the N–R method and SLA, has been proposed. The solution search path follows damage cycles sequentially with secant stiffness corresponding to local damage increments, which traces both damage history (explicit) and displacement history (implicit). This work focuses on dynamic damage modelling of quasi-brittle materials accounting for physical non-linearity as well to address the transient effects in the fracture process. The standard ISLA, similar to the large time increment (LATIN) method, the extended finite element method (X-FEM) and strong discontinuity approaches (SDA) which are proposed to capture the crack propagations for quasi-brittle materials, is not suitable for dynamic damage modelling. The objective of this work is therefore to propose a damage integration scheme (damage-driven instead of time integration scheme) based on ISLA for non-linear transient analysis of structures under dynamic loading while retaining the merits of the previous ISLA. The proposed damage integration scheme has been compared with the standard time integration scheme in a dynamically loaded bar example, showing good agreements and sufficient accuracy. The proposed method has been validated further for a notched beam under tension and four-point bending. Since all physical non-linearity is linearized in damage cycles with the explicit secant stiffness of the reduced elastic material model, the algorithm possesses high robustness.