In this paper, a purely displacement-based formulation is presented within the framework of the scaled boundary finite element method to model compressible and nearly incompressible materials. A selective reduced integration technique combined with an analytical treatment in the nearly incompressible limit is employed to alleviate volumetric locking. The stiffness matrix is computed by solving the scaled boundary finite element equation. The salient feature of the proposed technique is that it neither requires a stabilization parameter nor adds additional degrees of freedom to handle volumetric locking. The efficiency and the robustness of the proposed approach is demonstrated by solving various numerical examples in two and three dimensions. © 2019 John Wiley &amp; Sons, Ltd.

Sundararajan Natarajan

Department of Mechanical Engineering

Lakshmi Narasimha Pramod Aladurthi

Ean Tat Ooi

Chongmin Song

Degrees of freedom (mechanics)

Incompressible flow

Locks (fasteners)

Stiffness Matrix

Analytical treatment

DISPLACEMENT-BASED FORMULATIONS

FINITE ELEMENT EQUATIONS

NEARLY INCOMPRESSIBLE

SCALED BOUNDARY FINITE ELEMENT METHOD

SELECTIVE REDUCED INTEGRATION

STABILIZATION PARAMETERS

TAYLOR SERIES EXPANSIONS

finite element method

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

International Journal for Numerical Methods in Engineering

Scaled boundary finite element method for compressible and nearly incompressible elasticity over arbitrary polytopes

The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semi-analytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygons to represent arbitrary geometric shapes leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility. © 2017 Elsevier Ltd

Fulltext

Engineering Fracture Mechanics

A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

We discuss the application of non-uniform rational B-splines (NURBS) in the scaled boundary finite element method (SBFEM) for the solution of wave propagation problems at rather high frequencies. We focus on the propagation of guided waves along prismatic structures of constant cross-section. Comparisons are made between NURBS-based discretizations and high-order spectral elements in terms of the achievable convergence rates. We find that for the same order of shape functions, NURBS can lead to significantly smaller errors compared with Lagrange polynomials. The difference becomes particularly important at very high frequencies, where spectral elements are prone to instabilities. Furthermore, we analyze the behavior of NURBS for the discretization of curved boundaries, where the benefit of exact geometry representation becomes crucial even in the low-frequency range. © 2016 Elsevier B.V.

Computer Methods in Applied Mechanics and Engineering

On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems

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

Smoothed finite element methods (S-FEMs) with polynomial pressure projection (P3) for incompressible solids

Journal	Data powered by TypesetInternational Journal for Numerical Methods in Engineering
Publisher	Data powered by TypesetJohn Wiley and Sons Ltd
ISSN	00295981
Open Access	No