The interaction action between structures and supporting soil media is of fundamental importance in foundation design and it has always attracted the attention of both researchers and engineers. This paper reviews the state-of-the-art in this field, highlighting the key areas of development, including the modelling of the soil media and various analytical as well as numerical approaches in analysing the interaction action between the foundation and soil. Copyright © 2005 John Wiley & Sons, Ltd.

Beams and plates on elastic foundations: a review

The axially symmetric flexural interaction of a uniformly loaded circular plate resting in smooth contact with an isotropic elastic halfspace is examined by using an energy method. In this development the deflected shape of the plate is represented in the form of a power series expansion which satisfies the kinematic constraints of the plate deformation. The flexural behavior of the plate is described by the classical Poisson-Kirchhoff thin plate theory. Using the energy formulation, analytical solutions are obtained for the maximum deflection, the relative deflection, and the maximum flexural moment in the circular plate. The results derived from the energy method are compared with equivalent results derived from numerical techniques. The solution based on the energy method yields accurate results for a wide range of relative rigidities of practical interest.

The Interaction between a Uniformly Loaded Circular Plate and an Isotropic Elastic Halfspace: A Variational Approach

The elastic buckling of square and skew thin functionally graded material (FGM) plates with cutout resting on an elastic foundation is investigated using the isoparametric spline finite strip method. It is assumed that the material properties of FGM plates vary smoothly through the thickness according to the power law model. The elastic foundation is simulated by the Winkler and two-parameter Pasternak models. The isoparametric spline finite strip method is also applied to investigate initial inelastic local buckling loads of skew homogenous plates with cutout based on the Ramberg–Osgood representation of the stress–strain curve using the deformation theory of plasticity. The critical buckling load of the plate is achieved by minimizing its total potential energy and solving the corresponding eigenvalue problem. In addition, the effects of elastic foundation coefficients and hole size on the local buckling of plates with different boundary conditions are determined and discussed.

Elastic and inelastic buckling of square and skew FGM plates with cutout resting on elastic foundation using isoparametric spline finite strip method

Analysis of circular plate-elastic half-space interaction using an energy approach

The interaction problem associated with a cylindrical storage tank-(plate) foundation system resting in frictionless contact on an isotropic halfspace is examined by using an energy formulation. The thin-plate and the thin-shell theories are considered in describing the flexural behavior of the foundation and the tank wall, respectively. The tank is assumed to be rigidly connected to the foundation. A power series in terms of the radial coordinate is used to represent the deflected shape of the plate. A variational technique is utilized to obtain the deflections and flexural moments at any point on the plate. The effects of interaction between various components of the tank-(plate) foundation-halfspace system are investigated in detail. A parametric nondimensional study shows that factors such as the relative stiffness and location of the tank wall may result in a more economical design of the (plate) foundation.

A cylindrical tank-foundation-halfspace interaction using an energy approach

In the present work the authors have developed a finite difference method of analysis for any circular plate with any kind of loading on semi-infinite elastic foundations. No assumption regarding the contact pressure distribution has been made. The equations have been developed in non-dimensional form and also the results have been obtained in non-dimensional form. These results have been compared with the available experimental results and the agreement between them is found to be much better than that of the previous works. The same method with slight modification can be applied for Winkler type foundations and problems of circular plates with varying thickness.

Finite difference solution for circular plates on elastic foundations

Data structures known as k-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local regression, and so forth. In this article we present a scalable mechanism to construct k-d trees for distributed data, based on approximating medians for each recursive subdivision of the data. We provide theoretical guarantees of the quality of approximation using this approach, along with a simulation study quantifying the accuracy and scalability of our proposed approach in practice.

Scalable k-d trees for distributed data

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Finite difference solution for circular plates on elastic foundations

Scalable k-d trees for distributed data