A new n-noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed element: (a)has proper rank; (b)passes patch test for both thin and thick plates; (c)is free from shear locking and (d)yields optimal convergence rates in L2-norm and H1-semi-norm. The accuracy and the convergence properties are demonstrated with a few benchmark examples. © 2019 Elsevier Ltd

Sundararajan Natarajan

Department of Mechanical Engineering

Javier Videla

Stéphane P.A. Bordas

Locks (fasteners)

Shear strain

INTERPOLANTS

Mindlin Theory

Numerical integrations

POLYGONAL ELEMENT

Shape functions

SHEAR-LOCKING

MINDLIN PLATES

Fulltext

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IIT Madras

Computers and Structures

In this paper, a displacement based finite element framework for general three-dimensional convex polyhedra is presented. The method is based on a semi-analytical framework, the scaled boundary finite element method. The method relies on the definition of a scaling center from which the entire boundary is visible. The salient feature of the method is that the discretizations are restricted to the surfaces of the polyhedron, thus reducing the dimensionality of the problem by one. Hence, an explicit form of the shape functions inside the polyhedron is not required. Conforming shape functions defined over arbitrary polygon, such as the Wachpress interpolants are used over each surface of the polyhedron. Analytical integration is employed within the polyhedron. The proposed method passes patch test to machine precision. The convergence and the accuracy properties of the method is discussed by solving few benchmark problems in linear elasticity. © 2017 Elsevier Ltd

Engineering Analysis with Boundary Elements

A scaled boundary finite element formulation over arbitrary faceted star convex polyhedra

This manuscript presents the development of novel high-order complete shape functions over star-convex polygons based on the scaled boundary finite element method. The boundary of a polygon is discretised using one-dimensional high order shape functions. Within the domain, the shape functions are analytically formulated from the equilibrium conditions of a polygon. These standard scaled boundary shape functions are augmented by introducing additional bubble functions, which renders them high-order complete up to the order of the line elements on the polygon boundary. The bubble functions are also semi-analytical and preserve the displacement compatibility between adjacent polygons. They are derived from the scaled boundary formulation by incorporating body force modes. Higher-order interpolations can be conveniently formulated by simultaneously increasing the order of the shape functions on the polygon boundary and the order of the body force mode. The resulting stiffness-matrices and mass-matrices are integrated numerically along the boundary using standard integration rules and analytically along the radial coordinate within the domain. The bubble functions improve the convergence rate of the scaled boundary finite element method in modal analyses and for problems with non-zero body forces. Numerical examples demonstrate the accuracy and convergence of the developed approach. Copyright © 2016 John Wiley &amp; Sons, Ltd. Copyright © 2016 John Wiley &amp; Sons, Ltd.

International Journal for Numerical Methods in Engineering

Construction of high-order complete scaled boundary shape functions over arbitrary polygons with bubble functions

Computer Methods in Applied Mechanics and Engineering

A polytree-based adaptive polygonal finite element method for multi-material topology optimization

A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures

International Journal of Mechanical Sciences

A polygonal finite element method for laminated composite plates

A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields

Journal	Data powered by TypesetComputers and Structures
Publisher	Data powered by TypesetElsevier Ltd
ISSN	00457949
Open Access	Yes