A BEM formulation based on Reissner’s theory to perform simple bending analysis of plates reinforced by rectangular beams

Abstract

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.

A BEM formulation for analysing the coupled stretching–bending problem of plates reinforced by rectangular beams with columns defined in the domain

“…Regarding the displacement w along the axis A and B (see Figs. 27,28) there was no significant difference between the three meshes. In Figs.…”

“…In [26,27] the authors have improved the model presented in [25] to consider a nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams. Also leading with simple bending analysis of plates reinforced by rectangular beams, Fernandes and Konda [28] presented a BEM formulation based on Reissner's hypothesis, where some approximations are adopted for both tractions and displacements, along the beams width, to reduce the number of degrees of freedom. Moreover, in [29] Fernandes and Venturini have extended the BEM formulation developed in [24] to perform non-linear analysis of stiffened plates.…”

Análise da influência de microestruturas heterogêneas na resposta macromecânica do problema bidimensional de placas

“…Assim, as variáveis relacionadas ao problema bidimensional são: forças (̇ e ̇) e deslocamentos (̇ e ̇), onde (n, s) é o sistema de coordenadas locais, sendo n e s, respectivamente, as direções normal e tangencial ao contorno da placa. As equações básicas do problema bidimensional serão omitidas aqui, mas as mesmas podem ser encontradas em [18][19][20][21][22][23][24].…”

Formulação multi-escala para a análise de flexão de placas considerando processos dissipativos na microestrutura e acoplamento MEC/MEF

“…Observe que os valores de momentos Δ definidos na equação (1), assim como o tensor [ ] definido na equação (17), são calculados numericamente usando a fórmula e a quadratura de Gauss. Para isso, devem ser definidos pontos de Gauss ao longo da espessura da placa (veja [21], [22], [23]). Assim, após o cálculo das curvaturas nodais na placa (equação (14)), o incremento de deformações Δ referente a um ponto de Gauss de um determinado nó de célula pode ser obtido.…”