Mixed meshless formulation for analysis of shell-like structures

Modelling of orthorhombic quasicrystal shallow shells

“…A nice review about the alleviation of the volumetric locking in the MLS meshfree methods can be found in Belytschko et al (2004). Earlier results with application of meshless methods to shallow shell problems (Krysl and Belytschko, 1996;Li et al, 2000Li et al, , 2008Noguchi et al, 2000;Sladek et al, 2007Sladek et al, , 2008Jarak et al, 2007;Soric and Jarak, 2010;Sladek et al, 2013a,b) showed excellent results for conventional elastic materials. In mesh-based methods, the mesh describes the geometry of the surface, and the elements provide local parametrical spaces where the shape functions and the local parameterizations of the surface can be defined.…”

Mixed Meshless Local Petrov-Galerkin Methods for Solving Linear Fourth-Order Differential Equations

“…Thereby, rigorous tests and Mixed Meshless Local Petrov-Galerkin Methods for T. Jarak, B. Jalušić, J. Sorić Solving Linear Fourth-Order Differential Equations theoretical analyses regarding the numerical and computational efficiency are needed, in line with those performed for the existing mixed MLPG methods, cf. [3,19,21,25], in order to correctly assess the applicability of the proposed methods. In addition, further research is needed to investigate the applicability of the presented methods to solving nonlinear problems.…”

“…In order to evaluate the potential of the developed methods more easily and to present the general idea and the applied methodology more clearly, only simple one-dimensional (1D) linear problems are considered here, without including any nonlinearities. The primary variable and its gradients up to the third order are approximated by the same interpolating Moving Least Square (IMLS) approximation [20,21]. Governing equations are based on the local weak forms of the principles of conservation of linear and angular momenta as well as on compatibility conditions between the approximated variables.…”

Review of Recent Literature on Static Analyses of Composite Shells: 2000-2010

“…Non-linear buckling and postbuckling of a moderately thick anisotropic laminated cylindrical shell of finite length subjected to lateral pressure, hydrostatic pressure and external liquid pressure based on a higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/ flexural and flexural/twist couplings were presented by Li and Lin [34] wherein the material property of each layer could be linearly elastic, anisotropic and fiber-reinforced. A mixed meshless computational method based on the Local Petrov-Galerkin approach for analysis of plate and shell structures was presented by Sorić and Jarak [35]. They overcame the undesired locking phe-nomena and demonstrated that this meshless method is numerically more efficient than the available meshless fully displacement approaches.…”