Formulação do método dos elementos de contorno para placas delgadas apoiadas em bases elásticas de kerr

Abstract

Due to a simpler mathematical representation and computationally effortlessly smaller effort than pure continuum-besed techniques to simulate soil´structure interaction problmes, structures resting on elastic foundations models have aroused great interest in the academic comunity and engineering professionals. The present work aims to establish a boundary element method for thin plates supported on Kerr elastic foundation, where all the steps required by this numerical method are properly addressed.Initially, the derivation of the fundamental solutions associated with three distinct sets of roots which are dependent on the mechanical properties of both thin plate and Kerr elastic foundation is done. Then, the partial differential equations of the problem are transformed into equivalent integral equations, involving integrals defined on the problem boundary containing the problem variables and integrals defined across the domain problem containing the external load. In addition, these domain integrals are also transformed into boundary integrals when a constant loading is applied on the plate. From the discretization of problem boundary using boundary elements (definition of functional nodes and interpolating functions for the variables), and calculation of the resulting integrals, the integral representations of the problem are transformed into an algebraic system which is solved to determine the variables in the boundary problem. The fields of interest defined on the plate domain and shear layer domain can be calculated by discretization of integral equations using the known values of boundary variables. Finally, numerical examples are presented in which BEM solutions are compared to other results, based on analytical or numerical solutions according to their availabilities, showing a good performance of the proposed BEM solution