Nonlinear Structural Analysis Research Articles

Dynamic response analysis of nonlinear structures with hybrid uncertainties

The physical systems of nonlinear structural dynamics are usually expressed mathematically as ordinary differential equations. When hybrid uncertainties are in the system, it is necessary to understand the effects of uncertainties in the system response to accurately predict its behavior using mathematical models. To address the hybrid uncertainty of random and interval parameters often encountered in engineering applications, we propose the nonlinear structural dynamics analysis with hybrid uncertainty (NSDAHU) method. The expressions for calculating the statistical characteristics (i.e., mean and variance) of nonlinear structural dynamic responses with hybrid uncertainties are derived using random interval moment and random interval perturbation methods. The applicability, accuracy, and efficiency of the NSDAHU method are verified using Monte Carlo simulation method (MCSM). The NSDAHU method can not only solve hybrid random interval problems but also solve single interval, single random, and linear structural dynamics problems.

A Mathematical Model for Non-Linear Structural Analysis Reinforced Beams of Composite Materials

The beams are frequently utilized in construction as well as in the fabrication of vehicles like as trains, ships, and airplanes. Depending on the necessary working circumstances, several materials may have been utilized in the production of these beams, from high fatigue resistance, high corrosion resistance, strong earthquake resistance, and other aspects. As a result, composite beams made of glass or carbon fibers are increasingly commonly employed. This is a result of its strong collapse resistance, light weight, and strong fatigue stress resistance. In order to compare the models' resistance to deformations, stresses, and strains that they are exposed to during loading, this article focuses on constructing a variety of models using a variety of composite materials and shapes. The outcomes demonstrate a rise in the rate of deformation. against beams with linear shapes in those with non-linear shapes. Additionally, the findings demonstrate an increase in stresses and strains in regions with curves (i.e., areas that are nonlinear).

A Cartesian spatial discretization method for nonlinear dynamic modeling and vibration analysis of tensegrity structures

For vibration analysis of a tensegrity structure, the development of a dynamic model is a key step. A common issue in the traditional dynamic modeling methods for vibration analysis of tensegrity structures is that structural members are oversimplified. Member internal displacements, including those in longitudinal directions for bar and cable members and those in transverse directions for cable members, were neglected. This oversimplification would inevitably prevent the dynamic model of a tensegrity structure so developed from revealing accurate responses, especially for those in the high-frequency domain. To resolve this issue, a new method called the Cartesian spatial discretization method is developed for nonlinear dynamic modeling and vibration analysis of tensegrity structures. This method can successfully incorporate member internal displacements in dynamic modeling of a tensegrity structure by defining positions of structural members as a summation of internal terms and boundary-induced terms in a global Cartesian coordinate system. The proposed method is applied to vibration analysis of a planar Snelson’s X tensegrity structure, a three-dimensional tensegrity tower, and an irregular tensegrity grid in simulation, and compared with the Lagrangian method based on generalized coordinates, the commercial finite element analysis software ANSYS and the finite element analysis method in literatures, respectively. Results show that the proposed method is accurate in predicting dynamic responses of tensegrity structures, especially for vibration analysis in the high-frequency domain. It is also demonstrated that the proposed method is applicable to both simple and complex tensegrity structures, and computationally efficient as it converges in a super-linear rate by using only a small number of internal terms of member displacements.

SHAKER: A selector of consistent and energetically equalized natural ground motions using the Italian earthquake database

Input motion set selection for nonlinear dynamic structural analysis is commonly based on spectral compatibility, obtained through the uniform scaling of natural signals. Due to the aleatory nature of the expected time history, alone spectral compatibility requirement appears very weak to guarantee scaled ground motions that suit local seismic hazard. Magnitude-Distance interval pairs to control selection and scaling factor thresholds do not always provide input motions with adequate energy levels. In order to tackle these critical issues, a novel computer-aided selection method based on consistency analysis to provide conservative energy levels has been developed. The method equalizes the ground motions subject to the spectral compatibility process to the modified Housner Intensity of the hazard spectra. A multi-parametric consistency analysis based on statistic confidence is performed on the equalized (by uniform scaling) ground motion set by comparing it with the larger regional natural dataset on the same Magnitude-Distance pairs. The consistency analysis involves multiple ground motion parameters taken into relation with the focal mechanism too. Sensitivity tests show the capability of the method to reach high spectral compatibility joined with high consistency degrees by multi-parametric calibration. Compared with the traditional ones, this method also shows greater performance in composing ground motion sets close to real occurrences with a more assorted spectral frequency distribution.

3D printing concrete with recycled sand: The influence mechanism of extruded pore defects on constitutive relationship

Recycled sand (RS) as an environmental-friendly building material, has shown great prospects for the digital construction of buildings. In this study, 3D printed recycled sand concrete (3DPRSC) mixed with RS was prepared, and the related compressive strength and constitutive relationships were investigated on different RS replacement ratios and construction methods. The geometric characteristics and spatial distribution of pore defects were analyzed by the combined X-CT and MIP, and the microscopic morphology of RS and natural sand was analyzed by SEM. The results showed that the compressive strength and constitutive curves have apparent anisotropic characteristics. With the increase in the RS replacement rate, the compressive strength tended to decrease. The ellipsoidal pore geometry's arrangement of 3DPRSC extruded pore defects differs in different printing directions, and the pore defect distribution characteristics vary with the accumulated height of the filaments and the printing direction. The mechanism of the formation and distribution of extruded pore defects on the compressive strength and constitutive relationship was analyzed, and a model of the constitutive curve based on extruded pore defects and anisotropy was established, which provided a theoretical basis for the nonlinear analysis of the engineering structure of 3DPRSC.

Nonlinear dynamic thermal-mechanical behaviors of framed structures under temperature variations

An abnormal change in dynamic characteristics is considered an indicator of structural damage and can help the optimal design of structures suffering from dynamic loads, but these characteristics are also affected by ambient temperature. Therefore, a novel advanced computational method based on the fiber-based approach is proposed for the first time to predict the nonlinear dynamic behaviors of frames under environmental temperature changes with linear and nonlinear profiles by using Fortran programming language. The cross-section will be divided into a matrix of fibers, and by assigning the different temperatures to each fiber, all linear and nonlinear temperature gradients in both vertical and horizontal directions will be operated. The material nonlinearity is traced by the distributed plasticity model using the same mesh as the fiber-based approach whereas the effects of geometric nonlinearity due to member curvature and member chord rotation are considered by using the stability functions and a geometric matrix, respectively. A sequential nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson algorithm and Newmark-β method is also developed to address the nonlinear dynamic problems due to temperature variations. The accuracy and computational performance of the proposed method are validated by comparing the obtained results with those from experiments and the Abaqus. Results obtained show that the proposed method is exact for the nonlinear inelastic dynamic thermo-mechanical analysis of framed structures. It would offer a tool for thermal-structural design practice instead of using time and cost-consuming commercial software.

Cross-Sectional Shape Optimization of Cylindrical Elastomer Spring for Sensitive Cargo Container

High-value sensitive cargoes are often damaged by low-frequency vibration and shock of containers during land and rail transport processes or mixed transport processes. Therefore, a dedicated cylindrical elastomer spring that absorbs vibration transmitted into the container has been developed. This study developed an optimal shape using a polyurethane material instead of the existing rubber spring. Elastomer spring requires an optimal design that satisfies the design target stiffness and strength by nonlinear finite element analysis. In order to develop an elastomer spring for a cargo container, the material constant was obtained by a hyperelastic behavior test of natural rubber, and based on this, the necessary optimal material constant of the new spring was predicted. In addition, nonlinear structural analysis was performed using ABAQUS to obtain the optimal shape of the spring, and optimal design was performed with I-SIGHT software. As a result of the sum of squared difference minimization with the comparison algorithm, it was found that the polyurethane material constant C10, C20, and C30 with the same characteristics as natural rubber was obtained. In addition, analysis using three optimization algorithms, Hooke–Jeeves algorithm, multi-island genetic algorithm, and optimal Latin hypercube, yielded a maximum principal strain of 0.244 of the spring obtained through the optimal cross-sectional shape design. It was found that this value was about 39% lower than the natural rubber spring in use. As a result of the compression load-displacement test of the actually developed product, it was confirmed that the correlation coefficient between the predicted value and the measured value was 0.928.

An Accurate, Controllably Dissipative, Unconditionally Stable Three-Sub-Step Method for Nonlinear Dynamic Analysis of Structures

An implicit truly self-starting time integration method for nonlinear structural dynamical systems is developed in this paper. The proposed method possesses unconditional stability, second-order accuracy, and controllable dissipation, and it has no overshoots. The well-known BN-stability theory is employed in the design of algorithmic parameters, ensuring that the proposed method can stably solve nonlinear structural dynamical systems without restricting the time step size. The spectral analysis shows that compared to existing second-order accurate time integration methods, the proposed method enjoys a considerable advantage in low-frequency accuracy. For nonlinear problems where the currently popular Generalized-[Formula: see text] method and [Formula: see text]-Bathe method fail, the proposed method shows strong stability and accuracy. Further, for nonlinear problems in which all methods’ results are convergent, the proposed method has greater accuracy, efficiency, and energy-conservation capability.

Determination of the change in the structural performance of an RC building due to a nearby deep excavation

In this study, the structural performance of an existing thirteen-story reinforced concrete building is evaluated and compared to the case caused by the ground motion due to a nearby deep excavation. Accordingly, the effects of this event on structural safety emerge. First of all, the structural system details, geometry, layout, and material properties of the existing building are determined by field surveys and laboratory studies. Secondly, the structure is modelled with finite element software, and nonlinear structural analyses are carried out with pushover analyses, taking into account various loading conditions, which consist of four cases: vertical and seismic loading with and without ground displacements caused by the event. The nonlinear behaviour is defined, and deformation values in the cross-sections of the structural elements are obtained by using fiber hinges in vertical structural elements and lumped hinges on the beams. Finally, the seismic performance levels of the building are found before and after excavation, taking into account the latest Turkish Building Earthquake Code (TBEC 2018). This case study provides a methodology for engineering practice in evaluating the structural performance and modelling of reinforced concrete (RC) buildings affected by a similar deep excavation event.

Nonlinear Analysis of Cable Structures with Geometric Constraints

The purpose of this paper is the modelling in large displacement of systems composed of a rigid platform suspended by flexible cables, as can be observed in lifting systems of a construction crane or in cable-driven parallel robots (CDPRs). A recent approach has been proposed in the literature to model the nonlinear behavior of a cable element based on three dimensional catenary elastic modelling and the general displacement control method (GDCM) as solver. In this paper, two modifications of this method are proposed to take into account the geometric constraints coupling the large displacements of the cable extremities. The first approach is to consider these constraints using penalty functions thus modifying the tangent stiffness matrix and the second method by adding external explicit elastic forces. These two methods are tested and compared by using numerical examples. The first method is numerically safer because it is not dependent on the poor numerical conditioning of the cable’stiffness matrix encountered when internal cable’s tension cannot balance the external forces.

A Response Spectrum Method for Base-Isolated Structures with Equivalent Base Excitations

Base isolation is an effective seismic design strategy that has received considerable attention in recent decades. This research is dedicated to developing a response spectrum method (RSM) for analysis of base-isolated structures under seismic excitation. A novel analytical model consisting of a linear superstructure under equivalent base excitations is proposed in the present study. To determine the response spectra corresponding to the base excitations, termed as the base response spectra, a sufficient number of samples of base excitations comprising base responses need to be obtained through time-history analysis of the nonlinear base-isolated structure in conjunction with the Monte Carlo simulation (MCS). To improve the efficiency for each sample analysis, the recently proposed explicit time-domain method (ETDM) is utilized for fast analysis of the base acceleration and velocity responses with a dimension-reduced iteration scheme. Once the base response spectra are obtained, the mean peak values (MPVs) of structural responses of the linear superstructure can be conveniently evaluated through the complete quadratic combination (CQC) rule. A 4-story nonlinear base-isolated frame structure was analyzed to validate the effectiveness of the proposed analytical model and the feasibility of the present approach for seismic response analysis of nonlinear base-isolated structures.

Thermal structure and hydrodynamic analysis for a new type of flexible temperature-control curtain

Stratified water temperature and low temperature outflow water caused by water storage characteristics in deep reservoirs are common practical problems. The temperature-control curtain (TCC) is a novel low-temperature water treatment technique, characterized by a simple structure and low cost. In the present paper, a new type of flexible TCC scheme is proposed. Moreover, its applicability in engineering is explored by analyzing the thermal structure and hydrodynamic characteristics of the TCC. The general notions and theoretical basis of Boussinesq approximation for thermal flow are first elaborated. Then, the three-dimensional TCC form is obtained through the structural nonlinear analysis method based on Vector Form Intrinsic Finite Element (VFIFE). In addition, using a reservoir which is under TCC construction in southwest China as the research object, the thermal structure change with and without TCC scenario is observed to evaluate the improvement effect of outflow temperature from April to June. Lastly, taking the flood situation from July to August as the most unfavorable condition, the hydrodynamic characteristics are investigated, including the static and the dynamic pressures applied on the curtain. These preliminary modeling works provide important theoretical references for further engineering operation.

Extremum hybrid intelligent-inspired models for accurate predicting mechanical performances of turbine blisk

In complex aeroengine structures, it is necessary to consider multi-physical loads involving vibrational, structural, aerodynamical and heat loads for safe design. Turbine blisk commonly involves multi-failure modes such as stress, strain, deformation, fatigue, and creep under multi-physical loads during operation, so that efficient and accurate simulating approach is one of main issues in structural safety design. Machine learning (ML) approaches using artificial intelligence (AI) are workable to improve the simulation efficiency of mechanical responses under nonlinear dynamic structural analysis. In this work, hybrid artificial neural network (ANN) models are proposed to simulate the failure modes of turbine blisk. The accuracy of AI-based ANN is discussed using six music-inspired optimization algorithms named as harmony search (HS), improved HS (IHS), global-best HS (GHS), improved GHS (IGHS), adaptive GHS (AGHS) and Gaussian GHS (GGHS). Herein, these six music-inspired optimization algorithms are employed to find the undetermined coefficients and hyperparameters for the ANN models, and two adjusting strategy is introduced to explore the optimal values of the undetermined coefficients and hyperparameters in the IGHS, AGHS and GGHS. These hybrid models are used to perform the approximation of dimensional mechanical capacities such as stress, strain and deformation of aeroengine structures. These hybrid models are compared by using tendency, accuracy and agreement for failure modes of turbine system. It was conducted that the music-inspired basis harmony optimization procedures can provide the acceptable nonlinear connection between input and output responses of aeroengine turbine blisk in training phase of ANN models. The GGHS algorithm shows superior performance with the highest accuracy and tendency among other HS optimization algorithms.

Prediction of the Time to Failure of Boiler Tubes Flawed With Localized Erosion

AbstractA failure mechanism prevalent with boiler tubes operating in harsh environmental conditions is localized erosion. The consequence of the erosion mechanism is a substantial reduction of the tube thickness, ultimately leading to plastic collapse and consequently rupturing of the tubes. Locating and repairing all the affected tubes within the boiler are time consuming and expensive. It will be worthwhile to rank all the identified flaws so that critical flaws that cannot survive till the next scheduled shutdown are prioritized for repair. Consequently, nonlinear structural analysis was conducted on various boiler tubes that failed by localized erosion. The tubes had a wide range of localized erosion flaws that required a detailed assessment technique. The failure was evaluated numerically using various stress and strain-based failure criteria as well as performing the American Petroleum Institute and the American Society of Mechanical Engineers (API-ASME) fitness-for-service (FFS) assessment on the tubes. A projected time to failure (Pt) for each tube based on the various criteria used in this study was determined. This enabled the ranking of the flawed tubes based on the priority of their repair. The outcome of this study demonstrates the potential for a tool which will enable industry users to prioritize the replacement or repair of critically flawed tubes and avert replacing tubes that are still safe for future operation.

An optimization-based rigid block modeling approach to seismic assessment of dry-joint masonry structures subjected to settlements

A rigid block modeling approach is presented for rocking dynamics and nonlinear static analysis of dry-joint masonry structures subjected to settlements and earthquake excitations. For the different types of analysis, a unified optimization-based formulation is adopted, which is equivalent to the system governing the static and dynamic structural response. Sequential solution procedures are used for time integration and for pushover analysis which take into account the effects of large displacements under the combined action of support movements and lateral loads. No-tension elastic contacts with finite shear strength are considered at block interfaces for time-history analysis and to obtain the elastic branch of pushover curves in nonlinear static analysis. A unilateral rigid contact behavior is also considered to obtain the descending post-peak branch of pushover curves corresponding to the activation of the rigid-body rocking motion, according to displacement-based assessment methods of failure mechanisms adopted in the standards. Comparisons with numerical models and experimental tests on a rocking block and on a buttressed arch are presented to show the accuracy of the developed approach. Simple tests on dry-joint tuff panels on the tilting table were also carried out to show the effects of imposed movements at support on the response to lateral loads. Finally, an application is presented to a full-scale triumphal arch subjected to the combined action of support movements and earthquake excitation to discuss, on the basis of the developed model, the effects of settlement-induced damage on seismic performance. The numerical analyses showed that the lateral force, the displacement capacity and the rocking response can be significantly affected by support movements, pointing out the relevance of the current building condition in the seismic safety assessment.

A multiaxial inertial macroelement for deep foundations

A hyperplastic macroelement is proposed as an efficient means for simulating nonlinear and multi-directional soil-piles interaction in the nonlinear analysis of structures. The macroelement relates the generalised forces exchanged between the superstructure and the foundation to the corresponding displacements and rotations of the foundation raft. The inertial effects developing under dynamic loading can be reproduced by coupling the macroelement with the participating masses of the soil-foundation system, obtainable with a modal identification of the pile group. Failure conditions of the foundation are described by a hyper-ovoidal ultimate limit state surface in the force space, which is calibrated through standardised procedures. The plastic behaviour, controlled by a series of yield surfaces with kinematic hardening, produces the desired directional coupling and allows to model the cyclic response and the irreversible deformation of the foundation. The macroelement is implemented in the analysis framework OpenSees for a prompt use in earthquake engineering applications. Its predictions under monotonic loads are validated against experimental data and advanced, fully coupled numerical modelling, while its dynamic response is tested on a reference case study.

Reinforced L-Shaped Frame Made of Textile-Reinforced Concrete

Textile-reinforced concrete is becoming more and more popular. The material enables the realization of very thin structures and shells, often with organic shapes. However, a problem with this reinforcement occurs when the structure is bent (contains a corner), and the flexural stiffness around this bent area is required. This article presents the design, solution, and load-bearing capacity of an L-shaped rigid frame made of textile-reinforced concrete. Basic material parameters of concrete matrix and carbon textile reinforcement were supplemented by a four-point bending test to calibrate fracture energy Gf, critical compressive displacement Wd, solver type, and other parameters of a numerical model created by Atena Engineering in specialized non-linear structural analysis software for reinforced concrete structures. The calibrated numerical model was used to evaluate different variants of carbon textile reinforcement of the L-shaped frame. The carbon textile reinforcement was homogenized using epoxy resin to ensure the interaction of all fibers, and its surface was modified with fine-grained silica sand to increase the cohesion with the concrete matrix. Specimens were produced based on the most effective variant of the L-shaped frame reinforcement to be experimentally tested. Thanks to the original shaping and anchoring of the reinforcement in the corner area, the frame with composite textile reinforcement is rigid and can transmit the bending stresses in both positive and negative directions. The results of the mechanical loading test on small experimental specimens correspond well to the results of numerical modeling using Atena Engineering software.

Developed drift damage index-based failure criterion for framed-wall structure system

Recently, significant progress has been observed in high-rise buildings, positively affecting the economy and society. Since the damage and failure of these structures could cause tremendous disasters for society and humanity, investigating the damage performance of the building and assessing this damage is urgently needed. The numerical methods combined with the damage mechanics theory have shown to be a crucial tool to simulate and capture the damage of these structures. Therefore, this study introduces an effective simulation procedure and performs the non-linear dynamic analysis of a framed-wall structure with different heights under various seismic events and intensities using the incremental dynamic analysis technique. The tensile damage is well captured through the adopted damage model, and it is illustrated that the damage initiation and propagation are varied at different seismic events, which significantly affects the structure response. Moreover, an extensive study on the damage assessment has been provided to evaluate the damage degree of the structure using the Park-Ang damage index. The key point of this study is to recognize an efficient criterion to determine the structure’s state under different dynamic loads. Accordingly, a new formula has been proposed to quantify the damage to the framed-wall structures efficiently with low computational efforts, which will be of great importance in the case of assessing the damage for the city-scale model rapidly. This study demonstrated that the proposed formula could accurately assess the damage induced in the framed-wall structures where the results agree with the calculated values through the Park-Ang damage index. Finally, the results of the collapse state have been emphasized through the collapse analysis, which proves the efficiency and reliability of the proposed formula.

An Experimental Study on Energy Absorption Capability of Cast and 3D Printed Architected Cement-based Materials

Previous studies have demonstrated that Architected Cement-based Materials (ACMs), which have architected internal configurations at mm-cm scale, can have desired and/or unusual mechanical characteristics that the brittle base material does not possess. 3D Concrete Printing (3DCP) is promising technology to fabricate the complicated geometry of ACMs, but relevant research and development are still scarce. In this study, we fabricated truss-type ACMs with enhanced specific energy absorption capacity by either casting or 3D-printing. The ACM was designed by a generative design framework that integrates reinforcement learning and nonlinear structural analysis. The performances of the ACMs were evaluated by uniaxial compression tests. The cast series showed same trend in the cracking characteristics as the simulation. However, the printed ACM showed significantly lower strength and energy absorption than the simulation result. Unexpected damage localization was observed in the printed ACM, especially around the corners of the truss members where relatively large voids tend to be formed during 3D-printing. The degree and location of these defects can be partly controlled by the printing path, which was not considered in the simulation. Therefore, to realize high-performance ACMs by 3DCP, base material properties, internal geometry, and printing path should be simultaneously considered in the design process.

Nonlinear oscillations, chaotic dynamics, and stability analysis of bilayer graphene-like structures.

In this work, we have investigated the nonlinear oscillations and chaotic dynamics of perturbed bilayer graphene-like structures. The potential energy surface (PES) of bilayer graphene-like geometries is obtained by considering interactions of a co-aligned and counter-aligned arrangement of atoms. We studied the dynamics using the Poincaré surface of section for co-aligned hydrofluorinated graphene (HFG) and counter-aligned hexagonal boron nitride (h-BN) and generalized it for other systems using various choices of interaction parameters. The nature of the oscillations is understood via power spectra and the Lyapunov exponents. We found that the PES is very sensitive to the perturbation for all bilayer graphene-like systems. It is seen that the bilayer HFG system displays chaotic oscillations for strong perturbation, while for the h-BN system, the signature of chaos is found for weak perturbation. We have also generalized the work for perturbed bilayer graphene-like geometries, considering different interlayer interactions and the strength of perturbation. We found a signature of transition from regular to quasiperiodic and finally chaotic oscillations tuned via the strength of the perturbation for these geometries. The nature of the equilibrium points for bilayer graphene-like systems is analyzed via Jacobian stability conditions. We found three stable nodes for co-aligned HFG and counter-aligned h-BN systems for all interaction strengths. Though all other nodes are unstable saddle nodes, the signature of a local bifurcation is also found for weak perturbation.