Infinite Foundation Research Articles

Numerical Analyses for Layered Foundation by Coupling Finite and Axis-Radiate Infinite Elements

The model of the axis-radiate infinite element is developed for simulation of the infinite layered foundation underlain by a rigid base. Within the infinite element, the coordinate and displacement of any point are expressed by those of the nodes located on the artificial boundary, and concise mapping functions can easily express the attenuation character of the displacement field. By coupling finite and infinite elements, the elastic recovery capacity and radiation damping of the infinite layered foundation are simulated. In the numerical calculation, the infinite element mesh is performed only on the artificial boundary. Compared to FEM, the present approach needs less nodes and elements, and shows good accuracy and efficiency.

Static and dynamic damage analysis of mass concrete in hydropower house of Three Gorges Project

This paper establishes a 3D numerical model for 15# hydropower house of the Three Gorges Project (TGP) and performs a nonlinear static and dynamic damage analysis. In this numerical model, a coupling model of finite and infinite elements for simulating infinite foundation of hydropower station is adopted. A plastic-damage model based on continuum damage mechanics, which includes the softening and damage behavior under tension is considered for the concrete material. The dynamic equilibrium equations of motion are solved by using the Hilber-Hughes-Taylor (HHT) time integration method. Firstly, the static damage response analysis of the hydropower station is conducted due to high tensile stress resulting from large water head and diameter of an inlet pipe. Then, on the basis of static simulation, the dynamic damage analysis of hydropower house subjected to earthquake motion is simulated. Numerical results show that under large water head and diameter of an inlet pipe of the project, the damages are mainly located near the top of the spiral case from the inlet section to the 0° section; under combined loadings of static loads and earthquake, the damages of the concrete surrounding the spiral case increase insignificantly; however, some damages occur on the side walls of the main powerhouse.

Coupled FEM-BEM Approach for Axisymetrical Heat Transfer Problems

This work deals with a stationary axisymmetrical heat transfer problem in a combined domain. This domain consists of half-space joined with a bounded cylinder. An important feature of the problem is the possible flux singularity along the edge points of the transmission surface. Domain decomposition is used to separate the subdomains. The solution for an auxiliary mixed boundary value problem in the half space is found analytically by means of Hankel integral transform. This allows us to reduce the main problem in the infinite domain to another problem defined in the bounded subdomain. In turn, the new problem contains a nonlocal boundary conditions along the transmission surface. These conditions incorporate all basic information about the infinite sub-domain (material properties, internal sources etc.). The problem is solved then by means of the Finite Element Method. In fact it might be considered as a coupled FEM-BEM approach. We use standard MATLAB PDE toolbox for the FEM analysis. As it is not possible for this package to introduce directly a non-classical boundary condition, we construct an appropriate iterative procedure and show the fast convergence of the main problem solution. The possible solution singularity is taken into account and the corresponding intensity coefficient of the heat flux is computed with a high accuracy. Numerical examples dealing with heat transfer between closed reservoir (filled with some substance) and the infinite foundation are discussed.

Transient elastic wave propagation in an infinite Timoshenko beam on viscoelastic foundation

This paper presents an effective numerical method for solving elastic wave propagation problems in an infinite Timoshenko beam on viscoelastic foundation in time domain. In order to use the finite element method to model the local complicated material properties of the infinite beam as well as foundation, two artificial boundaries are needed in the infinite system so as to truncate the infinite beam into a finite beam. This treatment requires an appropriate boundary condition derived and applied on the corresponding truncated boundaries. For this purpose, the time-dependent equilibrium equation of motion for beam is changed into a linear ordinary differential equation by using the operator splitting and the residual radiation methods. Simultaneously, an artificial parameter is employed in the derivation. As a result, the high-order accurate artificial boundary condition, which is local in time, is obtained by solving the ordinary differential equation. The numerical examples given in this paper demonstrate that the proposed method is of high accuracy in dealing with elastic wave propagation problems in an infinite foundation beam.

3‐D infinite boundary elements and simulation of monolithic dam foundations

AbstractBased on the asymptotic behaviour of the fundamental solution for 3‐D elasticity problems, this paper presents an infinite boundary element model (IBEM) and its interpolation form. By using the analytical solution for half‐space under a vertical loading, excellent accuracy of this model has been verified. As an engineering application, the infinite foundation of a monolithic gravity dam was modelled by IBEM and the dam itself by normal BEM, and the displacement and stress distributions of the dam were analysed. It was concluded that large structure and foundation problems can be solved by this coupling system with the advantage of having fewer degrees of freedom and less data preparations. The results also clearly show the great improvement of the 3‐D model for critical stresses of the dam over the 2‐D plane model for narrow canyons having a width‐height ratio less than 2·4. Thus, a more economical cross‐section for dams can be achieved by 3‐D analysis.