The Direct Boundary Element Method Applied to Modeling Differential and Integral Elastic Thin and Thick Plates Equations

Resumo

Differential and integral elastic plates equations are frequently performed using

numerical methods like the Finite Element Method (FEM) or the Boundary Element

Method (BEM). One of the main differences between these techniques is a direct treatment

of boundary value problem in BEM analysis. It must be pointed out that corner forces are

introduced in the direct boundary integral equation when polygonal plates are studied using

classical theory. This parameter appears as a consequence of classical plate hypothesis in

which curvatures are related with the second derivative of the out-of-plane displacement and

it is the necessary condition to reduce boundary variables. However, when thick plate theory

is considered curvatures are not directly related with out-of-plane displacement derivative

and no corner forces are introduced even in BEM analysis. Further, three boundary

conditions should be satisfied in thick plate analysis rather than two of classical theory. This

study intends to present results obtained from plate bending problems using classical and

thick plate theories in order to understand the differences in plate behavior due the features

above mentioned. The classical plate analysis will be performed using Dansons

fundamental solutions and Reissner theory will be used in thick plates analysis with

Weeëns fundamental solution. The numerical implementation is carried out for continuous

or discontinuous isoparametric linear elements. A classical example is solved to show the

aim of this paper and the results are compared with those available in the literature.