Inelastic interactions in the dynamic response of structures

The dynamic responses of a 20-story nonlinear structural frame representative of a modern high rise building are analyzed with the aid of a digital computer. Related analytical studies of continuous systems are carried out. Quantitative information is provided on the importance of a wide range of modes to the various responses of a multi-story structure during an earthquake. The effect of yielding on the response is observed. The magnitude of the structural responses are compared with common measurements of earthquake strength. At the ends of each girder and column of the structural frame are yield hinges which have bilinear bending moment- rotation hysteretic characteristics. Two beam models having such characteristics are studied; one of these models can treat curvilinear hysteretic behavior. Three definitions of ductility factor are discussed, one of which is applicable to both bilinear and curvilinear hysteresis loops. In the computer program, the frame is subjected to the time history of an earthquake accelerogram, the equations of motion are stepwise integrated, and the various structural responses - displacement, bending moments, incurred yielding, etc. - are determined. The agreement between the response parameters resulting from excitation by seven different earthquake ground motions indicates that these response characteristics are determined more by the properties of the structure than by the earthquake. These results throw some light on extreme value statistics of the response of yielding structures subjected to earthquakes. The characteristic patterns observed in the computed responses of the nonlinear structure can be related to analytical studies of linear elastic, shear-type, uniform and tapered continuous cantilever beams.

The classical step-by-step integration method is commonly used for solving structural dynamic responses, but its performance is highly sensitive to the choice of time step. A large time step can significantly reduce accuracy and stability, while a very small time step greatly diminishes computational efficiency. Data-driven modeling and analysis methods are particularly favored for their potential to replace traditional structural analysis methods. However, traditional data-driven machine learning approaches require substantial amounts of training data to predict structural dynamic responses. Moreover, these methods often function as black boxes, lacking physical interpretability, and acquiring the necessary data can be challenging in practice. To address these limitations, this paper employs a physics-informed neural network (PINN) method for structural dynamic response analysis. The PINN approach incorporates the governing equations of structural dynamics into the neural network’s loss function as physical constraints, endowing the model with physical interpretability. The feasibility and effectiveness of this method are demonstrated through case studies on structural dynamic responses under different excitation scenarios. Numerical results show that the PINN method can accurately analyze structural dynamic responses without relying on system response data, a key advantage over traditional data-driven models. Moreover, unlike the classical step-by-step integration method, the PINN approach operates as a spatial domain optimization process and is independent of time step. Given the critical role of hyperparameters in the performance of the PINN model, this paper systematically investigates the influence of various hyperparameter settings on accuracy and efficiency, uncovering patterns of their impact on structural response analysis. Replication code for this paper will be available on GitHub:https://github.com/duke-iem/AIStructDynSolve.

[Introduction] The bucket foundation is a kind of emerging environment-friendly offshore wind turbine foundation, with the characteristic of simple construction, high construction efficiency and low comprehensive cost. It has been gradually received attention and recognition from the offshore wind power engineering community. The bottom is an open structure, which can displace an amount of water by the air pressure generated by the compression of the internal air cushion, and form a buoyancy force by forming a water pressure difference between the inside and the outside of the bucket. This self-floating property is a prerequisite for the bucket foundation to perform air-floating towing. [Method] This paper summarized the floating characteristics of air cushion structures at home and abroad, and discussed the related theories, test methods and research results of air flotation structures applied in different fields. [Result] The influence law of air cushion, subdivision form and resonance sloshing on structural dynamic response is analyzed in depth. [Conclusion] The summary analysis of the air-floating towing characteristics of this paper has important practical and theoretical significance for the promotion and application of the bucket foundation.

On the theory of molecular polarization in gases: II. Effect of molecular interactions on the Clausius-Mosotti function for systems of spherical nonpolar molecules

Numerical analysis of dynamic responses of laminated glass window subjected to gas explosions

A well-validated Finite Element (FE) model of a jacket structure (OC4 jacket) with pile foundation together with a Computational Fluid Dynamic (CFD) model (OpenFOAM-based) set-up for extreme waves on the structure are applied to perform systematic comparative analyses of the dynamic response of the structure to extreme wave loads with and without scour effects. The pile foundation model is considered by implementing a non-linear soil model to the foundation using load-deflection (p-y) approach to capture the non-linear behaviour of the soil for large pile foundation displacements. The results show that, the scour protection improves the foundation bearing capacity and consequently, decreases the failure probability in terms of both serviceability and ultimate limit states. Moreover, it enhances the dynamic response of the structure under extreme load events caused by breaking waves. Accordingly, an innovative solution for scour protection of offshore-fixed bottom structures has been introduced by “Biodegradable Soft Rock” (sand filled containers produced from bio-degradable geotextile product) which is the newest development in this section.

As composite materials have been used for marine structures such as boats, ships, offshore structures, etc., the effect of FSI should be understood.In particular, FSI effect is expected to be significant for polymer composites because the water density is very comparable to the composites' densities.For example, the density of a carbon composite is approximately 50% greater than the water density.Sandwich composites consisting of very low densities of core materials have lower densities than that of water.As a result, the hydrodynamic mass associated with FSI would be very critical to composite structures under water.The growing use of composites in ship masts, superstructures, deck grates, piping, ducting, rudders, propellers, stacks, and various submarine structures requires extensive modeling and testing to help designers, builders and operators better understand composite response [Mouritz, et al., 2001].These materials are subjected to a wide spectrum of loads during manufacturing and service life.Dynamic loadings, in particular, impact type event, represent a serious design concern for use of composite.Composite structures are more susceptible to impact damage than similar metallic structures which are more ductile in nature and can absorb typically large amounts of energy without failure.Furthermore, the damage in composites from impact can go undetected even when the mechanical properties may be drastically reduced from an impact.For these reasons, numerous experimental and analytical studies have been conducted to study the dynamic response of composites subjected to impact loading [Abrate, 1994;Aslan, et al., 2003;Kwon & Wojcik, 1998].According to the review of past works, most of the research effort has been focused on low velocity impact damage, specifically, the damage predictions, and the evaluation and prediction of residual properties of damaged laminates.All of the research completed thus far has focused on damage in composites under impact loading in dry environments to support development of composites in aircraft structures.As far as dynamic response of structures under water is concerned, a great deal amount of analytical and experimental studies have been conducted on the effect of fluid force on the natural frequencies, damping ratios and mode shapes of vibrating structures in contact with fluid.This is commonly known as the Fluid Structure Interaction (FSI) problem.FSI investigations have supported many problems in submarine signaling, offshore oil structure stability, and ship structure vibrations.Through these studies, many numerical and analytical methods have been developed in order to predict the added mass and the www.intechopen.com Advances in Composites Materials -Ecodesign and Analysis 338resulting changes in natural frequency of a structure in contact with fluid.It has been determined and widely proven that the effect of fluid surrounding a structure decreases the natural frequency of a structure due to the increase in total kinetic energy of the vibrating structure and fluid from the addition of kinetic energy of the fluid.This effect can be interpreted as an added mass to the vibrating structure in the analysis of the dynamic response.Essentially as the structure vibrates, its mass is increased by the mass of the vibrating fluid with which it is in contact, consequently decreasing its natural frequency.Studies of fluid structure interaction and the added mass effect, also known as virtual mass effect, hydrodynamic mass, and hydroelastic vibration of structures, started with Lamb [Lamb, 1921] who calculated the first bending mode of a submerged circular plate.In response to a problem of submarine signaling, Lamb investigated the vibrations of a thin elastic circular plate in contact with water.In his investigation he discovered that the natural frequencies for structures in contact with fluid are lower than the frequencies in air, based on the assumption that the modes shapes are virtually the same in water as in a vacuum.The resonant frequency was determined using Rayleigh's method.Lamb's theortical results were verified experimentally [Powell & Roberts, 1923].Much later, more research was conducted for measuing and calculating natural frequencies of free vibartions of beams and plates under water [Lindholm, et al., 1965; Fu & price, 1979;Kwak, 1996].Another branch of FSI studies is underwater explosion.Both experimental and numerical studies have been conducted for metallic structures [

Corrected method for scaling the dynamic response of stiffened plate subjected to blast load

A study of the dynamic response of offshore structures to simultaneous loadings by random earthquake ground motions and random sea waves is presented. Emphasis is placed on the evaluation of dynamic soil‐structure interaction effects and also on the evaluation of non‐linear hydrodynamic damping effects due to sea waves for the seismic response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider's power spectrum and the Morison equation defines the wave forcing function. The Tajimi‐Kanai power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency‐domain random vibration approach.It is found that the first few vibrational modes contribute significantly to the dynamic response. The response due to earthquake loadings is larger when the soil‐structure interaction effects are considered. The hydrodynamic damping forces are higher in random seas than in still water and sea waves reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquake forces.

Nowadays, it is common to see large public buildings, e.g., stadiums, with some equipment or substructure suspended from the center of the roof. These substructures will tend to be larger and heavier the more gear is needed, which may have negative impacts on the dynamic performance of the roof structures. In this paper, to explore the dynamic response of a large-span roof structure with a suspended substructure, a real structure model is simplified into a two-degrees-of-freedom system. The essential consideration of nonlinear vibration is elaborated in the equations of motions. Approximate analytical solutions for free and forced vibrations are derived using perturbation methods, while numerical analysis is carried out to validate the solutions. The ratio of linear to nonlinear amplitude is proposed to represent the nonlinear effect of the primary structure, and the nonlinear effect, varying with structural parameters of frequency ratio, mass ratio, excitation ratio, and external force to the primary structure, is investigated. It is shown that internal resonance occurs when the structural frequency ratio is close to 1:2 and that secondary resonance takes place due to certain external excitations; internal resonance and secondary resonance will magnify the amplitude of the primary structure during vibration. Finally, a case of a designed practical dome with a suspended substructure is studied to verify the outcomes from the above research. According to these findings, some design proposals for this type of structure are provided.

Insulators are regulatory DNA elements restricting gene activation by enhancers. Interactions between insulators can lead to both insulation and activation of promoters by enhancers. In this work, we analyzed the effects of interaction of two Drosophila insulators, Wari and Su(Hw). The functional interaction between these insulators was found to enhance the activity of the Su(Hw) insulator only, but not of the Wari insulator. This suggests that the formation of a chromatin loop between interacting insulators is not a key factor for enhancement of insulation, which is in disagreement with the main idea of structural models. In addition, the effect of interaction between Wari and Su(Hw) depends on a distance between them and on the position in the system relative to other regulatory elements.

BackgroundAssociation mapping studies offer great promise to identify polymorphisms associated with phenotypes and for understanding the genetic basis of quantitative trait variation. To date, almost all association mapping studies based on structured plant populations examined the main effects of genetic factors on the trait but did not deal with interactions between genetic factors and environment. In this paper, we propose a methodological prospect of mixed linear models to analyze genotype by environment interaction effects using association mapping designs. First, we simulated datasets to assess the power of linear mixed models to detect interaction effects. This simulation was based on two association panels composed of 90 inbreds (pearl millet) and 277 inbreds (maize).ResultsBased on the simulation approach, we reported the impact of effect size, environmental variation, allele frequency, trait heritability, and sample size on the power to detect the main effects of genetic loci and diverse effect of interactions implying these loci. Interaction effects specified in the model included SNP by environment interaction, ancestry by environment interaction, SNP by ancestry interaction and three way interactions. The method was finally used on real datasets from field experiments conducted on the two considered panels. We showed two types of interactions effects contributing to genotype by environment interactions in maize: SNP by environment interaction and ancestry by environment interaction. This last interaction suggests differential response at the population level in function of the environment.ConclusionsOur results suggested the suitability of mixed models for the detection of diverse interaction effects. The need of samples larger than that commonly used in current plant association studies is strongly emphasized to ensure rigorous model selection and powerful interaction assessment. The use of ancestry interaction component brought valuable information complementary to other available approaches.

Among different types of loads on jacket structures, wave loads, especially breaking wave loads, are the most likely to threat the stability of the structure; therefore, the correct estimation of the wave loading of an offshore jacket structure is crucial for the design of these structures. Despite the importance of the correct estimation of breaking wave induced forces on jacket structures, so far, no slamming formulae to predict these forces are available in the design standards and guidelines or in other publications. Moreover, the implications of such extreme wave load events and the associated uncertainties for the dynamic response of the entire jacket structure, including the response of the foundation piles, are still not fully clarified. This PhD study attempts to improve the understanding of processes associated with the interaction of waves and jacket structures and to develop reliable wave slamming formulae for the prediction of breaking wave-induced loads on jacket structures. First, the present knowledge is analysed to identify the processes involved in the interaction as well as the related knowledge gaps. Second, the data available from previous tests performed on a truss structure under breaking and non-breaking waves in the Large Wave Flume (GWK tests) in Hannover are analysed to identify the most relevant influencing parameters and to provide reliable slamming formulae for breaking waves on legs and braces of jacket structures. Third, using a CFD model set-up for the waves generated in the large wave flume GWK and a CSD model for the truss structure tested in GWK, the laboratory tests are reproduced and a methodology is proposed to predict total forces induced by near-breaking and breaking waves on jacket structures. Finally, the proposed methodological approach including the slamming force formulae developed in this study is implemented to calculate total forces by breaking waves on a full-scale jacket structure (OC4 jacket). The Finite Element FE model of the OC4 jacket is extended by pile foundation model and the structural performance of the entire structure was examined by comparing the results by those of the numerical models developed for the same jacket structure. Finally, the dynamic response of the jacket structure with pile foundation to breaking waves is systematically analysed to achieve a substantially improved understanding of the processes involved in the wave-jacket-pile foundation interaction.

It is pointed out that the damping matrix deduced by active members in the finite element vibration equation of a truss adaptive structure generally can not be decoupled, which leads to the difficulty in the process of modal analysis by classical superposition method. This paper focuses on the computational method of the dynamic response for truss adaptive structures. Firstly, a new technique of state vector approach is applied to study the dynamic response of truss adaptive structures. It can make the coefficient matrix of first derivative of state vector a symmetric positive definite matrix, and particularly a diagonal matrix provided that mass matrix is derived by lumped method, so the coefficient matrix of the first derivative of state vector can be exactly decomposed by CHOLESKY method. In this case, the proposed technique not only improves the calculation accuracy, but also saves the computing time. Based on the procedure mentioned above, the mathematical formulation for the system response of truss adaptive structures is systematically derived in theory. Thirdly, by using FORTRAN language, a program system for computing dynamic response of truss adaptive structures is developed. Fourthly, a typical 18 bar space truss adaptive structure has been chosen as test numerical examples to show the feasibility and effectiveness of the proposed method. Finally, some good suggestions, such as how to choose complex mode shapes practically in determining the dynamic response are also given. The new approach can be extended to calculate the dynamic response of general adaptive structures.

Prediction of the dynamic response of a slender marine structure under an irregular ocean wave using the NARX-based quadratic Volterra series