Consistent Infinitesimal Finite-element Cell Method Research Articles

Three-Dimensional Nonlinear Seismic Analysis of Pile Groups Using FE-CIFECM Coupling in a Hybrid Domain and HISS Plasticity Model

AbstractThis paper reports the three-dimensional (3D) nonlinear dynamic analysis of floating pile groups subjected to seismic loading. For the nonlinear dynamic analysis of foundations in general, and pile foundations in particular, a perfect accuracy in modeling the frequency dependence of the unbounded soil support, as well as the local temporal nonlinearities, was ensured. In the current work, the finite elements (FEs) and boundary FEs were coupled in a hybrid domain of alternating frequency-time domains, to analyze the nonlinear dynamics of pile foundations in a 3D space. The frequency dependence of the stiffness and the damping of the unbounded far-field soil were completely accounted for by the consistent infinitesimal finite-element cell method (CIFECM) in the frequency domain, whereas the nonlinearities and transient conditions of the near-field were accounted for by the FE in the time domain. The hybrid frequency time domain algorithm is used for coupling the two domains. For the evaluation of no...

Dynamic impedances of pile groups with embedded caps in homogeneous elastic soils using CIFECM

Significant research has been reported on the dynamic analysis of pile groups. However, in most of the cases, the effect of pile cap is neglected despite the fact that there may be additional interactions due to the presence of the cap. This paper presents the dynamic impedances for the pile groups with caps embedded in isotropic homogeneous elastic soils. A general three-dimensional finite element procedure is developed. The system is sub-structured into bounded near-field and an unbounded far-field. The pile-soil system of the near-field is modeled using solid finite elements, and the unbounded elastic soil system of the far-field is modeled using the consistent infinitesimal finite element cell method (CIFECM) in the frequency domain. The method has shown excellent agreement with the published results for dynamic response of pile groups with a free-standing pile-cap. The dynamic impedances of pile groups with embedded cap are presented. Each pile group is capped with a thick pile-cap, embedded in the near-field soil domain. The dynamic impedances of 2×2 pile groups are presented, for different spacing of piles and thickness of the pile-cap with different embedment ratios. It was found that even for a small embedment ratio, the dynamic interactions due to cap can be significant.

Simulation methods for seismic behaviour of buildings in unbounded soil media with radiation damping

Mathematical and computer methods have been used by others to predict the seismic behaviour of viscous damped structures, yet most analyses have not accounted for the influence of an unbounded foundation. In order to better understand the motional behaviour of structures during earthquakes, this study considers the effects of radiation damping and flexibility when characterizing the interaction between damped structures and unbounded soil media. Two numerical methods, the consistent-infinitesimal finite element cell method and a new quiet boundary method, are introduced here. Also, computer simulation is used to demonstrate the effects of radiation damping for far field, unbounded media. The differences in seismic responses of structures with and without consideration of radiation damping are significant. The results also make clear the importance of accounting for such effects when, for example, structural engineers incorporate structural control devices into their designs.

Interactive Behavior of Structures with Multiple Friction Pendulum Isolation System and Unbounded Foundations

In the last two decades, base isolation has been used for enhanced seismic performance to protect structures against severe earthquakes. The reduction in earthquake forces on a structure is achieved by adding horizontal soft isolation elements between the superstructure and the foundation. The efficiency of the isolator in reducing the seismic energy imparted to a structure is dependent on the flexibility of the supporting soil. The effects of radiation damping and the flexibility of the soil media are the deciding factors for structural design against earthquakes. In order to ensure the safety of isolated structures, the interactive behavior of isolated structures and the unbounded foundation during earthquakes must be considered. In this paper, an advanced analytical model based on the viscoplasticity theory and rigorous finite element derivations for the Multiple Friction Pendulum System (MFPS) is presented. To yield better design accuracy, the consistent infinitesimal finite element-cell method, accounting for the radiation damping of the unbounded soil, was adopted. Significant differences between the system with and without radiation damping were observed. It is implied from this study that to obtain better accuracy, radiation damping should be properly taken into account for structural analysis and design. Quantitative results also reveal that the interaction effects of an isolated building and the unbounded soil medium are important.

Effect of non-linear soil–structure interaction on seismic response of tall slender structures

Some structures may be very massive and may have to be located on relatively soft soil. In such cases, the soil adjacent to the structure behaves in a non-linear fashion and affects the response of the structure to the dynamic loading. An approximate hybrid approach to analyse soil–structure systems accounting for soil non-linearities has been developed in this paper. The approach combines the consistent infinitesimal finite-element cell method (CIFECM) and the finite-element method (FEM). The CIFECM is employed to model the non-linear (near-field) zone of the soil supporting the structure as a series of bounded media. The material properties of the bounded media are selected so that they are compatible with the average effective strains over the whole bounded medium during the excitation. The linear zone of soil away from the foundation, the far-field, is modelled as an unbounded medium using the CIFECM for unbounded media. The structure itself is represented by the FEM. The proposed method is used to model the dynamic response of a one-mass structure and a TV-tower supported on a homogenous stratum and excited by an earthquake. It was found that the secondary soil non-linearity might increase or decrease the base forces of tall slender structures depending on the type of structure, frequency content of the input motion and the dynamic properties of the near-field soil.

A combined finite element based soil–structure interaction model for large-scale systems and applications on parallel platforms

A finite element (FE) based soil–structure interaction (SSI) model is presented and parallelized for applications on distributed systems. The SSI model is established by combining two methods: the Consistent Infinitesimal FE Cell Method (also referred to as ‘the scaled boundary-finite element method’) proposed by Wolf and Song (Finite-element modelling of unbounded media, Wiley, England, 1996) for modelling the soil region extending to infinity (far-field), and the standard FE for the finite region (near-field) and the structure. By using this combined model, a computer program for harmonic and transient analyses of soil–structure systems is coded. The model is investigated by solving various example problems existing in the literature. The results of the model agree with the results presented in the literature for selected problems. The advantages of the model are demonstrated through these comparisons. In order to decrease the computation time and achieve the solution of large-scale problems, the model is parallelized. As a result of this parallel solution, significant time is saved for large-scale problems.

The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics

The scaled boundary finite-element method, alias the consistent infinitesimal finite-element cell method, is developed starting from the governing equations of linear elastodynamics. Only the boundary of the medium is discretized with surface finite elements yielding a reduction of the spatial dimension by one. No fundamental solution is necessary, and thus no singular integrals must be evaluated. General anisotropic material is analysed without any increase in computational effort. Boundary conditions on free and fixed surfaces and on interfaces between different materials are enforced exactly without any discretization. This method is exact in the radial direction and converges to the exact solution in the finite-element sense in the circumferential directions. For a bounded medium symmetric static-stiffness and mass matrices with respect to the degrees of freedom on the boundary result without any additional assumption. A stress singularity is represented very accurately, as the condition on the boundary in the vicinity of the point of singularity is satisfied without spatial discretization.

CONSISTENT INFINITESIMAL FINITE‐ELEMENT CELL METHOD IN FREQUENCY DOMAIN

To calculate the dynamic-stiffness matrix at the structure–medium interface of an unbounded medium for the range of frequencies of interest, the consistent infinitesimal finite-element cell method based on finite elements is developed. The derivation makes use of similarity and finite-element assemblage, yielding a non-linear first-order ordinary differential equation in frequency. The asymptotic expansion for high frequency yields the boundary condition satisfying the radiation condition. In an application only the structure–medium interface is discretized resulting in a reduction of the spatial dimension by one. The boundary condition on the free surface is satisfied automatically. The consistent infinitesimal finite-element cell method is exact in the radial direction and converges to the exact solution in the finite-element sense in the circumferential directions. Excellent accuracy results.

CONSISTENT INFINITESIMAL FINITE-ELEMENT CELL METHOD IN FREQUENCY DOMAIN

To calculate the dynamic-stiffness matrix at the structure–medium interface of an unbounded medium for the range of frequencies of interest, the consistent infinitesimal finite-element cell method based on finite elements is developed. The derivation makes use of similarity and finite-element assemblage, yielding a non-linear first-order ordinary differential equation in frequency. The asymptotic expansion for high frequency yields the boundary condition satisfying the radiation condition. In an application only the structure–medium interface is discretized resulting in a reduction of the spatial dimension by one. The boundary condition on the free surface is satisfied automatically. The consistent infinitesimal finite-element cell method is exact in the radial direction and converges to the exact solution in the finite-element sense in the circumferential directions. Excellent accuracy results.

CONSISTENT INFINITESIMAL FINITE-ELEMENT CELL METHOD: THREE-DIMENSIONAL VECTOR WAVE EQUATION

To calculate the unit-impulse response matrix of an unbounded medium for use in a time-domain analysis of unbounded medium–structure interaction, the consistent infinitesimal finite-element cell method is developed for the three-dimensional vector wave equation. This is a boundary finite-element procedure. The discretization is only performed on the structure–medium interface, yielding a reduction of the spatial dimension by 1. The procedure is rigorous in the radial direction and exact in the finite-element sense in the circumferential directions. In contrast to the boundary-element procedure, the consistent infinitesimal finite-element cell method does not require a fundamental solution and incorporates interfaces extending from the structure–medium interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed. The derivation is based on the finite-element formulation and on similarity.

Consistent infinitesimal finite-element cell method for diffusion equation in unbounded medium

To calculate the unit-step response matrix of an unbounded medium for use in a time-domain analysis of unbounded medium-structure interaction for the diffusion equation, the consistent infinitesimal finite-element cell method is developed for the three-dimensional case. Its derivation is based on the finite-element formulation and on similarity. The discretization is only performed on the structure-medium interface, yielding a reduction of the spatial dimension by 1. The procedure is rigorous in the radial direction and exact in the finite-element sense in the circumferential directions. In contrast to the boundary-element procedure, the consistent infinitesimal finite-element cell method does not require a fundamental solution and incorporates interfaces extending from the structure-medium interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed.

Static Stiffness of Unbounded Soil by Finite-Element Method

To calculate the static-stiffness matrix of the unbounded soil for use in a time-domain analysis of soil-structure interaction, the consistent infinitesimal finite-element cell method is developed. Its derivation is based on the finite-element formulation and on similarity. The discretization is only performed on the structure-soil interface, yielding a reduction of the spatial dimension by 1. The procedure is exact in the radial direction and exact in the finite-element sense in the circumferential directions. In contrast to the boundary-element procedure, the consistent infinitesimal finite-element cell method does not require a fundamental solution and incorporates interfaces extending from the structure-soil interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed. Applications of the consistent infinitesimal finite-element cell method to problems of increasing complexity ranging from a spherical cavity with uniform pressure to a tunnel in inhomogeneous transversely isotropic unbounded rock show excellent accuracy.

Consistent infinitesimal finite-element cell method: in-plane motion

To calculate the unit-impulse response matrix of an unbounded medium for use in a time-domain analysis of medium-structure interaction, the consistent infinitesimal finite-element cell method is developed. Its derivation is based on the finite-element formulation and on similarity. The limit of the cell width is performed analytically yielding a rigorous representation in the radial direction. The discretization is only performed on the structure-medium interface. Explicit expressions of the coefficient matrices for the in-plane motion of anisotropic material are specified, which depend only on the geometry of the structure-medium interface and the material properties of the unbounded medium. For each time step a linear system of equations is solved. The calculated unit-impulse response matrix is symmetric. In contrast to the boundary-element formulation, no fundamental solution is necessary and equilibrium and compatibility on the layer interfaces extending from the structure-medium interface to infinity, if present, are incorporated automatically. Excellent accuracy is achieved for an inhomogeneous semi-infinite wedge and a rectangular foundation embedded in an inhomogeneous half-plane.

Matrix Quadratic Solutions

Matrix quadratic equation solution derivation applied in finding steady state solutions of Riccati differential equations with constant coefficients