Analysis of laminated beams using the natural neighbour radial point interpolation method

Neste trabalho aplica‐se o método sem malha natural neighbour radial point interpolation method (NNRPIM) à análise unidimensional de vigas laminadas, considerando a teoria de Timoshenko. O NNRPIM combina o conceito matemático dos vizinhos naturais com a interpolação radial pontual. Os diagramas de Voronoï permitem impor a conectividade nodal e construir a malha de fundo para efeitos de integração, por intermédio das células de influência. É apresentada a construção das funções de interpolação NNRPIM, sendo, para estas, usada a função de base radial multiquadrática. As funções de interpolação geradas possuem continuidade infinita e a propriedade de delta Kronecker, o que facilita a imposição das condições de fronteira, uma vez que estas podem ser impostas com o método da imposição direta, tal como no método dos elementos finitos (FEM). De modo a obter o campo de deslocamentos e de deformações, a teoria de deformação de Timoshenko para vigas sujeitas a esforços transversos é considerada. Vários exemplos numéricos de vigas isotrópicas e vigas laminadas são apresentados de modo a demonstrar a convergência e a exatidão da aplicação proposta. Os resultados obtidos são comparados com soluções analíticas disponíveis na literatura.In this work, a meshless method, “natural neighbour radial point interpolation method” (NNRPIM), is applied to the one‐dimensional analysis of laminated beams, considering the theory of Timoshenko. The NNRPIM combines the mathematical concept of natural neighbours with the radial point interpolation. Voronoï diagrams allows to impose the nodal connectivity and the construction of a background mesh for integration purposes, via influence cells. The construction of the NNRPIM interpolation functions is shown, and, for this, it is used the multiquadratic radial basis function. The generated interpolation functions possess infinite continuity and the delta Kronecker property, which facilitates the enforcement of boundary conditions, since these can be directly imposed, as in the finite element method (FEM). In order to obtain the displacements and the deformation fields, it is considered the Timoshenko theory for beams under transverse efforts. Several numerical examples of isotropic beams and laminated beams are presented in order to demonstrate the convergence and accuracy of the proposed application. The results obtained are compared with analytical solutions available in the literature.Peer Reviewe

Analysis of laminated beams using the natural neighbour radial point interpolation method

In this work, a meshless method, “natural neighbour radial point interpolation method” (NNRPIM), is applied to the one‐dimensional analysis of laminated beams, considering the theory of Timoshenko. The NNRPIM combines the mathematical concept of natural neighbours with the radial point interpolation. Voronoï diagrams allows to impose the nodal connectivity and the construction of a background mesh for integration purposes, via influence cells. The construction of the NNRPIM interpolation functions is shown, and, for this, it is used the multiquadratic radial basis function. The generated interpolation functions possess infinite continuity and the delta Kronecker property, which facilitates the enforcement of boundary conditions, since these can be directly imposed, as in the finite element method (FEM). In order to obtain the displacements and the deformation fields, it is considered the Timoshenko theory for beams under transverse efforts. Several numerical examples of isotropic beams and laminated beams are presented in order to demonstrate the convergence and accuracy of the proposed application. The results obtained are compared with analytical solutions available in the literature