Two-dimensional beams in rectangular coordinates using the radial point interpolation method.
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2020
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Resumo
The three-dimensional Theory of Elasticity equations lead to a complex solution
for most problems in engineering. Therefore, the solutions are typically developed for
reduced systems, usually symmetrical or two-dimensional. In this context, compu-
tational resources allow the reduction of these simplifications. The most recognized
methods of algebraic approximation of the differential equations are the Finite Differ-
ences Method and the Finite Element Method (FEM). However, they have limitations
in mesh generation and/or adaptation. As follows, Meshless Methods appear as an al-
ternative to these options. The present work uses the Radial Point Interpolation Meth-
od (RPIM) to evaluate the stress in two-dimensional beams in regions close to loading
(Saint Venant’s Principle). Formulations based on the Fourier Series Theory and the
RPIM are presented. Multiquadrics Radial Basis Functions were used to obtain the
stiffness matrix. Two numerical examples demonstrate the validity of the RPIM for
the proposed theme. The results were obtained from the formulations cited and the
Finite Element Method for comparison.
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Saint-Venant’s principle, Stress analysis
Citação
FERNANDES, W. L. et al. Two-dimensional beams in rectangular coordinates using the radial point interpolation method. REM - International Engineering Journal, Ouro Preto, v. 73, p. 9-16, jan./mar. 2020. Disponível em: <https://www.scielo.br/j/remi/a/VST96kr8VQB7xpynGRzWRBj/?lang=en>. Acesso em: 29 abr. 2022.