Abstract

Two-dimensional digital image correlation (DIC) is one of the most commonly used measurement methods for displacement and deformation of specimen surfaces in the field of experimental mechanics. Since its presentation, DIC has been evolving with many new ideas and assets. This paper proposes a new displacement field, based on Legendre polynomials and compares it with conventional second-order polynomial, commonly used in DIC's method.

Abstract

Beams on elastic foundation are basic elements within structural analysis, which are used to model foundation beams, foundation piles, retaining walls, and more complex structures that include some of these elements. For their analysis, the finite element method is usually used [1], which produces an approximate solution of the problem; and the Green’s function stiffness method [2], which produces an exact solution. This article presents a methodology 100 % based on the use of Green function’s (response to a unit point force), to obtain the exact response of beams on elastic foundation. The main advantage of this formulation is its computational low cost compared to the aforementioned alternatives, and even for a large number of problems, it can be expressed only by means of sums and integrals, which can be easily performed numerically.

Also, a great variety of Green function’s for finite and infinite beams on elastic foundations with different boundary conditions are also presented, as well as some examples with the implementation of the proposed methodology.