Engineering Analysis with Boundary Elements 99 (2019) 46–59 Contents lists available at ScienceDirect Engineering Analysis with Boundary Elements journal homepage: www.elsevier.com/locate/enganabound A meshless Reissner plate bending procedure using local radial point interpolation with an efficient integration scheme D.H. Konda a,b,∗ , J.A.F. Santiago b , J.C.F. Telles b , J.P.F. Mello b , E.G.A. Costa b a Exact Sciences and the Earth Institute, ICET/CUA/UFMT, Avenida Valdon Varjão N o 6390, Barra do Garças, MT, Brazil b Civil Engineering Program, COPPE/UFRJ, Caixa Postal 68506, Rio de Janeiro, RJ CEP 21941-972, Brazil a r t i c l e i n f o Keywords: Reissner’s plate Meshless method Plate bending Shear locking MLPG a b s t r a c t This paper presents a numerical analysis of bending plates considering Reissner’s hypothesis. A truly meshless method designated Meshless Local Petrov-Galerkin (MLPG) method is used to obtain a linear system of equation. A simplified Radial Point Interpolation Method (RPIM) approximation scheme, by centering both quadrature and local interpolation subdomains in the same field point, is proposed to increase the computational efficiency of the MLPG. Moreover, the shear locking effect is also analyzed. Results obtained by the application of the presented formulation are discussed in this work, considering plates with different geometries and boundary conditions, and compared, in terms of precision and efficiency, with solutions obtained via Finite Element Method. 1. Introduction Plate structures are widely applied in most diverse fields in engineer- ing. Nevertheless, the analysis of plate bending is not a simple problem to solve, especially when shear deformation effects are taken into con- sideration, as presented in Reissner’s plate bending theory. Therefore, the use of meshless methods in the solution of plate bend- ing problem occurs initially for Kirchhoff plates [1], as observed in [2], in which the Element-Free Galerkin meshless approach is used to an- alyze arbitrary plates. Another meshless method used to analyze thin plates presented in [3] is the Hermite collocation method based on Ra- dial Basis Function (RBF). Initially, the meshless methods required cells or elements to evalu- ate the domain integrations, associated to the energy, over the entire problem domain. A truly meshless method, in which no element or cell type is needed, was presented in [4], being the precursor of MLPG. The method developed in [4] introduced difficulties in the treatment of sin- gular integrals, leading part of the authors to the development of a new formulation [5], based on symmetric local weak form, MLPG. Then, the method was generalized in [6] with the definition of six variants and their characteristics. A variant of the MLPG, the Local Boundary Integral Equation (LBIE) method is used to analyze thin plates in [7] and produced good results. Once the efficiency of the method has been demonstrated, MLPG became widely used to solve thick-plate bending problems, as can be seen in [8], in which the author considers the complete set of three-dimensional constitutive equations. ∗ Corresponding author at: Exact Sciences and the Earth Institute, ICET/CUA/UFMT, Avenida Valdon Varjão N o 6390, Barra do Garças, MT, Brazil. E-mail addresses: danilokonda@ufmt.br (D.H. Konda), santiago@coc.ufrj.br (J.A.F. Santiago), telles@coc.ufrj.br (J.C.F. Telles). In [9] MLPG is applied in the static and dynamic analysis of thick plates considering an orthotropic material, elastic foundation and thick- ness variation. Thereafter, the same authors extend the formulation to consider viscoelasticity [10]. Recently, Xia et al. [11] used the MLPG to elastoplastic analysis of plate bending with shear deformation. The authors use a polynomial base and RBF composition to obtain the shape function, maintaining the property of the delta of Kronecker and consequently not requir- ing additional treatments to impose boundary conditions. Subsequently, the formulation is extended in [12] to consider fracture problems on elastoplastic behavior. In [13], the three-dimensional MLPG is applied in thermo-elastoplastic analysis of thick functionally graded plates us- ing brick-shapes local domains, in order to facilitate and improve the procedures of integration and approximation. In [14] the solution for thin plate bending is obtained from a mod- ified differentiation technique for the approximation of the derivatives of field variables. The proposed technique presents good results with the drawback of increasing the computational cost. As a matter of fact, the meshless methods already displaying flexibility and great potential, for example, the iterative coupling between the fundamental solution method and the MLPG is developed in [15] for crack problems. In order to simplify the computational process and the numerical implementa- tion, [16] proposes a new meshless method based on Shepard function and partition of unity, in which the subdomain near to the crack area is divided into triangular segments and a link elements are used to connect adjacent triangles. https://doi.org/10.1016/j.enganabound.2018.11.004 Received 24 July 2018; Received in revised form 12 October 2018; Accepted 8 November 2018 0955-7997/© 2018 Elsevier Ltd. All rights reserved.