engleski

On elimination of locking phenomena in a Meshless Local Petrov-Galerkin (MLPG) shell formulation

A new meshless formulation based on the Local Petrov-Galerkin approach for analysis of shell structures is proposed. Special attention is directed to the elimination of thickness and shear locking effects. A variety of meshless approaches has been used to derive shell formulations including remedies to minimize the shear and membrane locking in thin shell limit, such as stabilized conforming nodal integration or approximation of displacement field by using the MLS basis functions of sufficiently high order. In contrast to those formulations based on the classical Reisner-Mindlin shell theory, a 3D solid concept, allowing the use of complete 3D constitutive equations, is adopted in the present formulation. Besides minimization of shear and membrane locking effects, the proposed computational strategy enables elimination of thickness locking as well. In this contribution, the well-known MLS approximation is employed in the in-plane shell directions and polynomial interpolations are used in the thickness direction. The linear functions are applied for the in-plane displacement components, while the hierarchical quadratic interpolation is adopted for the transversal displacement component in order to avoid the undesired thickness locking phenomena. To define such quadratic interpolation properly, an additional unknown is required. For derivation of a closed global system of equations, two computational strategy are applied: by means of the test function as quadratic polynomial over the thickness and by enforcing additional collocation requirements of equilibrium at the points located on the shell middle surface. In contrast to other formulations, where the shear locking has been minimized by suitable interchanging of nodal variables leading to a kind of meshless mixed shell formulation, here the shear locking phenomena in the case of thin structures are alleviated by applying a sufficiently high order of the MLS basis function. The numerical efficiency of the proposed meshless formulations will be demonstrated by numerical examples.

meshless; local Petrov-Galerkin approach; shells; thickness locking; shear locking

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