Analysis of thermoelastic waves in a two-dimensional functionally graded materials domain by the Meshless Local Petrov-Galerkin (MLPG) method

in Computer Modeling in Engineering and Sciences (2010), 65(1), 27-74

This contribution focuses on the simulation of two-dimensional elastic wave propagation in functionally graded solids and structures. Gradient volume fractions of the constituent materials are assumed to ... [more ▼]

This contribution focuses on the simulation of two-dimensional elastic wave propagation in functionally graded solids and structures. Gradient volume fractions of the constituent materials are assumed to obey the power law function of position in only one direction and the effective mechanical properties of the material are determined by the Mori-Tanaka scheme. The investigations are carried out by extending a meshless method known as the Meshless Local Petrov-Galerkin (MLPG) method which is a truly meshless approach to thermo-elastic wave propagation. Simulations are carried out for rectangular domains under transient thermal loading. To investigate the effect of material composition on the dynamic response of functionally graded materials, a metal/ceramic (Aluminum (Al) and Alumina (Al 2O 3) are considered as ceramic and metal constituents) composite is considered for which the transient thermal field, dynamic displacement and stress fields are reported for different material distributions. Copyright © 2010 Tech Science Press. [less ▲]

Strain smoothing in FEM and XFEM

in Computers and Structures (2010), 88(23-24), 1419-1443

We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The ... [more ▼]

We present in this paper recent achievements realised on the application of strain smoothing in finite elements and propose suitable extensions to problems with discontinuities and singularities. The numerical results indicate that for 2D and 3D continuum, locking can be avoided. New plate and shell formulations that avoid both shear and membrane locking are also briefly reviewed. The principle is then extended to partition of unity enrichment to simplify numerical integration of discontinuous approximations in the extended finite element method. Examples are presented to test the new elements for problems involving cracks in linear elastic continua and cracked plates. In the latter case, the proposed formulation suppresses locking and yields elements which behave very well, even in the thin plate limit. Two important features of the set of elements presented are their insensitivity to mesh distortion and a lower computational cost than standard finite elements for the same accuracy. These elements are easily implemented in existing codes since they only require the modification of the discretized gradient operator, B. © 2008 Elsevier Ltd. All rights reserved. [less ▲]

APPLICATION OF EXTENDED ELEMENT-FREE GALERKIN METHOD TO MULTIPLE FLAWS UNDER BRITTLE FRACTURE CONDITIONS

in PROCEEDINGS OF THE ASME PRESSURE VESSELS AND PIPING CONFERENCE - 2008, VOL 6, PT A AND B (2009)

The extended element-free Galerkin (XEFG) method incorporates cracks through partition of unity enrichment of the standard basis functions. Discontinuous functions are added to capture the jump through ... [more ▼]

The extended element-free Galerkin (XEFG) method incorporates cracks through partition of unity enrichment of the standard basis functions. Discontinuous functions are added to capture the jump through the crack faces and near-front enrichment is added to capture the asymptotic behaviour in the vicinity of the crack fronts. Depending on the material behaviour, these functions can be of various type. The method can treat initiation, growth and coalescence of cracks seamlessly in both linear elastic and non-linear settings. The method is a powerful tool for modelling and studying crack paths, which are a central feature in the assessment of multiple flaws.The method is applied to the problem of multiple non-aligned flaws in a ferritic plate under cleavage failure. Fracture paths from two nonaligned notches in a plate are modelled. Based on the observations of crack paths the critical flaw alignment distance is established for nonaligned through-wall flaws. [less ▲]

Meshless methods: A review and computer implementation aspects

in Mathematics and Computers in Simulation (2008), 79(3), 763-813

The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our ... [more ▼]

The aim of this manuscript is to give a practical overview of meshless methods (for solid mechanics) based on global weak forms through a simple and well-structured MATLAB code, to illustrate our discourse. The source code is available for download on our website and should help students and researchers get started with some of the basic meshless methods; it includes intrinsic and extrinsic enrichment, point collocation methods, several boundary condition enforcement schemes and corresponding test cases. Several one and two-dimensional examples in elastostatics are given including weak and strong discontinuities and testing different ways of enforcing essential boundary conditions. © 2008 IMACS. [less ▲]

The smoothed extended finite element method

in Proceedings of the 6th International Conference on Engineering Computational Technology (2008)

This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite ... [more ▼]

This paper shows how the strain smoothing technique recently proposed by G.R.Liu [1] coined as smoothed finite element method (SFEM) can be coupled to partition of unity methods, namely extended finite element method (XFEM) [2] to give birth to the smoothed extended finite element method (SmXFEM), which shares properties both with the SFEM and the XFEM. The proposed method suppresses the need to compute and integrate the derivatives of shape functions (which are singular at the tip in linear elastic fracture mechanics). Additionally, integration is performed along the boundary of the finite elements or smoothing cells and no isoparametric mapping is required, which allows elements of arbitrary shape. We present numerical results for cracks in linear elastic fracture mechanics problems. The method is verified on several examples and comparisons are made to the conventional XFEM. © 2008 Civil-Comp Press. [less ▲]