Static and dynamic boundary element analysis in incompressible linear elasticity

Equivalent-Linear Dynamic Stiffness of Surface Footings on Liquefiable Soil

“…In these analyses, isoparametric four-noded linear quadrilateral elements are used for meshing the surfaces. Note that ISoBEM has been successfully used to study several problems of applied mechanics [21][22] and soil mechanics [23]. Three-dimensional models simulating a rigid square footing on a three-layer liquefiable soil in ISoBEM were set up with a dual purpose: a) to provide comparisons and b) to yield fitted formulae for static stiffness.…”

A MLPG(LBIE) numerical method for solving 2D incompressible and nearly incompressible elastostatic problems

“…It should be noted here that the LBIEs (29) and (30) are also valid for nearly incompressible elastic materials, since their kernels are not infinite as Poisson ratio approaches 0.5 [14].…”

“…On the other hand, the boundary element method (BEM), as presented in [14], has the distinct advantage over the FEM of working without any problem for both compressible and incompressible linear elastic materials, providing results of high accuracy by discretizing only the boundary of the analysed structure and not the boundary plus the interior of the domain as the FEM does. Nevertheless, the requirement of using the fundamental solution of the differential equation or system of equations that describe the problem of interest renders the BEM less attractive than FEM when non-linear, non-homogeneous and anisotropic compressible and incompressible elastic problems are considered.…”

“…where a = 1 2 for x (k) belonging to a smooth boundary of , a = 1 for x (k) ∈ { − } and a = 0 elsewhere,ũ * ,t * are the incompressible fundamental displacement and traction tensors, respectively, given in [14].…”

“…with u * i jk and t * i jk given in [14]. The surface traction vector components are connected with stresses through the relation…”