A novel cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields. The domain is discretized with arbitrary polygons and on each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The plate is made of functionally graded material with effective properties computed using the rule of mixtures. The influence of various parameters, viz., the plate aspect ratio and the material gradient index on the static bending response and the first fundamental frequency is numerically studied. It is seen that the proposed element: (a) has proper rank; (b) does not require derivatives of shape functions and hence no isoparametric mapping required; (c) independent of shape and size of elements and (d) is free from shear locking. © 2019

Sundararajan Natarajan

Department of Mechanical Engineering

Irwan Katili

Imam Jauhari Maknun

Andi Makarim Katili

Stéphane P.A. Bordas

Aspect ratio

BEAMS AND GIRDERS

finite element method

Functionally graded materials

Locks (fasteners)

Numerical methods

Shear strain

KIRCHHOFF

Mindlin Theory

Numerical integrations

SHEAR-LOCKING

SMOOTHED FINITE ELEMENT METHOD

MINDLIN PLATES

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IIT Madras

Composite Structures

A unified polygonal locking-free thin/thick smoothed plate element

The extended finite element method was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak, and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and the convergence of the numerical solution. The smoothed extended finite element method (XFEM), for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in the literature that the strain smoothing is inaccurate when non-polynomial functions are in the basis. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure which provides better approximation to higher-order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics are solved and the results are compared with existing approaches. We observe that the stress intensity factors computed through the proposed linear smoothed XFEM is more accurate than that obtained through smoothed XFEM. Copyright © 2017 John Wiley &amp; Sons, Ltd.

Fulltext

International Journal for Numerical Methods in Engineering

Linear smoothed extended finite element method

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

The strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision. Copyright © 2016 John Wiley &amp; Sons, Ltd. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Linear smoothed polygonal and polyhedral finite elements

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.

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

Journal	Data powered by TypesetComposite Structures
Publisher	Data powered by TypesetElsevier Ltd
ISSN	02638223
Open Access	No