A BEM formulation based on Reissner's hypothesis for analysing the coupled stretching–bending problem of building floor structures

Multi-scale modelling for bending analysis of heterogeneous plates by coupling BEM and FEM

“…where ∇ Sũ i μ is determined through the solution of the microscopic equilibrium problem defined by (35).…”

“…As the present work deals with non-linear analysis, all variables are expressed in rates, i.e., ð_ xÞ ¼ dx=dt, their time derivatives. The basic equilibrium equations for the plate problem will be omitted here, but they can be found in several works ( [31][32][33][34][35])…”

“…The Boundary Element Method (BEM) has already proved to be a suitable numerical tool to deal with plate bending problems (see [31][32][33][34][35]). The method is particularly recommended to evaluate internal force concentrations due to loads distributed over small regions that very often appear in practical problems.…”

FEM/BEM formulation for multi-scale analysis of stretched plates

“…As the present work deals with non-linear analysis, all variables are expressed in rates, i.e., ð_ xÞ ¼ dx=dt, their time derivatives. The basic equilibrium equations for the plate stretching problem will be omitted here, but they can be found in several works [32][33][34][35][36][37].…”

“…On the other hand, the BEM is a suitable tool to deal with plate problems (see [32][33][34][35][36]), being specially indicated to compute displacements and forces due to stress or strain concentration problems. This can occur when the plate is subjected to loads distributed over small regions or due to a fracture process leading to strain localisation, for example.…”