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This study investigates the seismic response of a horizontal axis wind turbine on two bottom-fixed support structures for transitional water depths (30-60 m), a tripod and a jacket, both resting on pile foundations. Fully coupled, nonlinear time-domain simulations on full system models are carried out under combined wind-wave-earthquake loadings, for different load cases, considering fixed and flexible foundation models. It is shown that earthquake loading may cause a significant increase of stress resultant demands, even for moderate peak ground accelerations, and that fully coupled nonlinear time-domain simulations on full system models are essential to capture relevant information on the moment demand in the rotor blades, which cannot be predicted by analyses on simplified models allowed by existing standards. A comparison with some typical design load cases substantiates the need for an accurate seismic assessment in sites at risk from earthquakes.

The classical calculation method of additional stresses in foundation soils was established based on the Flamant and Boussinesq solutions in elasticity theory. This method can only calculate the additional stresses in foundations with regular shapes and under regularly distributed base pressures. Based on the Gauss–Legendre numerical product formula, which is independent of the specific form of the product function, a suitable method for calculating the additional stresses in irregularly shaped foundation soils under non-uniform loads was established in this study. Using Simpson’s formula to perform integration over the domain, Gaussian summation calculation methods for the additional stresses in foundation soil under non-uniform loads in rectangular domains, under loads in non-rectangular domains, and under irregular loads and loads in irregular integration regions were derived. The combination of the complex product algorithm and a computer program further efficiently improved the calculation accuracy. Validation examples showed that the Gaussian product calculation method of additional stresses in foundation soil was completely consistent with classical elasticity theory, and the results of the Gaussian product calculation method converged to the classical elasticity theory prediction when the complex product formula was applied. Based on validation and application examples, the method has advantages over the finite element method in terms of modeling difficulty, computational accuracy, computational volume, and computational cost when calculating additional stresses in foundation soil. The research results provide a new method and idea for the calculation of additional stresses in irregularly shaped flexible foundation soils under non-uniform loads.

In many tasks of railway vibration, the structure, that is, the track, a bridge, and a nearby building and its floors, is coupled to the soil, and the soil–structure interaction and the damping by the soil should be included in the analysis to obtain realistic resonance frequencies and amplitudes. The stiffness and damping of a variety of foundations is calculated by an indirect boundary element method which uses fundamental solutions, is meshless, uses collocation points on the boundary, and solves the singularity by an appropriate averaging over a part of the surface. The boundary element method is coupled with the finite element method in the case of flexible foundations such as beams, plates, piles, and railway tracks. The results, the frequency-dependent stiffness and damping of single and groups of rigid foundations on homogeneous and layered soil and the amplitude and phase of the dynamic compliance of flexible foundations, show that the simple constant stiffness and damping values of a rigid footing on homogeneous soil are often misleading and do not represent well the reality. The damping may be higher in some special cases, but, in most cases, the damping is lower than expected from the simple theory. Some applications and measurements demonstrate the importance of the correct damping by the soil.

In order to enhance the vibration isolation effectiveness of an underwater vehicle power plant, and alleviate the mechanical vibration of the outer housing, initially discrete vibration isolators were improved, and three new types of ring vibration isolators designed, i.e., ring metal rubber isolators, magnesium alloy isolators and modified ultra-high polyethylene isolators (MUHP). A vibrator excitation test was carried out, and the isolation effectiveness of the three types of vibration isolators was evaluated, adopting insertion loss and vibration energy level drop. The results showed that compared with the initial isolators and the other two new types of isolators, MUHP showed the most significant vibration isolation effectiveness. Furthermore, its effectiveness was verified by a power vibration test of the power plant. To improve the vibration isolation effectiveness, in addition to vibration isolators, it is essential to carry out investigations on high-impedance housings.

The problem of settlement of shallow foundations is among the most important ones in classical soil mechanics. And while for the settlement of flexible foundations elastic solutions are widely used, for rigid rectangular foundations where the actual contact pressure distribution is still unknown, the problem is approximated either analytically assuming a contact pressure distribution or semi‐empirically combining the theory of elasticity with experimental and/or numerical results. A third and often attractive choice is the use of simple empirical relationships or relevant tabulated values relating the elastic settlement of rigid foundations ( ρ R ) with the settlement of the respective flexible foundations (e.g. at the center, ρ Ce ). Reviewing the relathionships of this third approach, the author revealed serious lack of consesous between the various sources; for example, according to the literature, ρ R ranges between 68 and 125% of ρ Ce , the time when it is well-known that ρ R  <  ρ Ce . In this paper, comparison of the settlement of 210 rigid foundation cases derived from 3D elastic finite element analysis, with the settlement of the respective flexible foundations derived from the theory of elasticity, led to simple empirical relationships between ρ R and ρ Ce as well as between ρ R and ρ Av ( ρ Av  = average settlement of the flexible foundation) with coefficient of determination (R 2 ) almost unity. The analysis showed that these relationships are largely independent of the aspect ratio of foundations and the thickness and Poisson’s ratio ( ν ) of the compressible medium, although separate relationships are given for ν  = 0.5, slightly increasing R 2 . Finally, a correction factor for foundation rigidity is given exploting the known linear relationship that exists between the relative stiffness factor of foundations and settlement.

This study investigates model errors caused by the rigid-foundation assumption in dynamic Soil-Structure Interaction (SSI), which has been widely accepted in the past decades to reduce computational effort. A linear two-dimensional model is used for a qualitative analysis that compares the dynamic responses of a rigid system, comprising a rigid foundation embedded in a layered half-space with a superstructure mounted on top, and a corresponding flexible system with the same parameters but a flexible foundation with a variable stiffness. The Indirect Boundary Element Method combined with non-singular Green’s functions of distributed line loads is employed to calculate the system responses accurately. Transfer functions computed for a range of parameters show that the rigid-foundation assumption leads to overestimating the system natural frequency and changes the peak deformations to a different extent. It is also shown through a case study of 42 earthquakes that the rigid-foundation assumption may either overestimate or underestimate the system responses by up to approximately 50%, and in some cases even by approximately 100%, depending on the frequency content of excitation and SSI dynamic characteristics.

This article is devoted to solving problems with known theoretical solutions in the Fidesys software package. Within the framework of the work, modeling of a biaxial shear test of the ground and simulating a draft of a flexible foundation was done. The solutions obtained were correlated with the solutions of such problems in the Plaxis software package. According to the results of the study, it can be concluded that the Fidesys software complex allows solving problems in the field of geomechanics. At the same time, it is not inferior to recognized solutions in terms of functionality.

Background This study introduces a numerical model designed to simulate interactions occurring between a wind turbine's tower and the surrounding soil, as well as between the nacelle, blades, and the surrounding environment. This simulation accounts for both fore–aft and side-to-side movements. To describe these interactions, the model leverages the Euler–Lagrange equations. It calculates wave loads utilizing the Morison equation, with wave data generated based on the JONSWAP spectrum. Furthermore, aerodynamic loads are determined using the blade element moment theory, and the wind spectrum is generated using the Von Karman turbulence model. The tower is represented as a variable cross-sectional beam, employing a two-noded Euler beam element with two degrees of freedom: transverse displacement and rotation, and utilizing Hermite polynomial shape functions. Results In a comparative analysis against experimental data, this modified model demonstrates significant enhancements in accurately reproducing the dynamic behavior of wind turbines with variable cross-sectional towers, outperforming models that approximate the tower with a constant cross section. Our findings reveal that the modified model achieves a remarkable improvement of 15% in replicating the tower's dynamic response when compared to the constant cross-sectional models. As a case study, a 5 MW monopile wind turbine with a flexible foundation, specifically the one provided by the National Renewable Energy Laboratory (NREL), is employed to simulate its dynamic response. Conclusions This research presents a robust numerical model for simulating wind turbine behavior in various environmental conditions. The incorporation of variable cross-sectional tower representation significantly improves the model's accuracy, making it a valuable tool for assessing wind turbine dynamics. The study's findings highlight the importance of considering tower flexibility in wind turbine simulations to enhance their real-world applicability.

Recently, Roller Compacted Concrete (RCC) dams have become one of the most applicable types of dams across the globe. However, the basic challenge in analysis of RCC dams is evaluation of the actual response under earthquake excitations with considering flexible foundation and impounded water. For this purpose, a finite element model of RCC Dam-Reservoir-Foundation is accurately developed and dynamic time history analysis is utilized to assess the seismic responses in terms of acceleration, displacements, stresses, cracking patterns and crack propagation by implementation of concrete damaged plasticity model. A verification model is carried out to show the work accuracy. Based on these explanations, the obtained results showed that, however, the hydrodynamic pressure due to the reservoir water had great influence on seismic responses of the RCC dam with rigid foundation especially in terms of displacement response but overall responses of the dam are greatly fluctuated while flexible foundation is taken into consideration.

Soil-structure interaction (SSI) of a building and shear wall above a foundation in an elastic half-space has long been an important research subject for earthquake engineers and strong-motion seismologists. Numerous papers have been published since the early 1970s; however, very few of these papers have analytic closed-form solutions available. The soil-structure interaction problem is one of the most classic problems connecting the two disciplines of earthquake engineering and civil engineering. The interaction effect represents the mechanism of energy transfer and dissipation among the elements of the dynamic system, namely the soil subgrade, foundation, and superstructure. This interaction effect is important across many structure, foundation, and subgrade types but is most pronounced when a rigid superstructure is founded on a relatively soft lower foundation and subgrade. This effect may only be ignored when the subgrade is much harder than a flexible superstructure: for instance a flexible moment frame superstructure founded on a thin compacted soil layer on top of very stiff bedrock below. This paper will study the interaction effect of the subgrade and the superstructure. The analytical solution of the interaction of a shear wall, flexible-rigid foundation, and an elastic half-space is derived for incident SH waves with various angles of incidence. It found that the flexible ring (soft layer) cannot be used as an isolation mechanism to decouple a superstructure from its substructure resting on a shaking half-space.