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An Algorithm to compute damage from load in composites ; Bordas, Stéphane ; et al in Frontiers of Architecture and Civil Engineering in China (2011), 5(2), 180-193 We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this ... [more ▼] We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this first step, the alkali-silica reaction is taken into account through damage mechanics though the process is more complex involving thermo-hygro-chemo-mechanical reaction. We use a non-local damage model that ensures the well-posedness of the boundary value problem (BVP). In contrast to existing methods, the interactions between degrees of freedom evolve with the damage evolutions. Numerical results are compared to analytical and experimental results and show good agreement. [less ▲] Detailed reference viewed: 96 (1 UL)Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics and Engineering (2011), 200(21-22), 1892-1908 Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite ... [more ▼] Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method. [less ▲] Detailed reference viewed: 134 (2 UL)Linear free flexural vibration of cracked functionally graded plates in thermal environment ; ; et al in Computers and Structures (2011), 89(15-16), 1535-1546 In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are ... [more ▼] In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack is studied using an 8-noded shear flexible element. The material properties are assumed to be temperature dependent and graded in the thickness direction. The effective material properties are estimated using the Mori-Tanaka homogenization scheme. The formulation is developed based on first-order shear deformation theory. The shear correction factors are evaluated employing the energy equivalence principle. The variation of the plates natural frequency is studied considering various parameters such as the crack length, plate aspect ratio, skew angle, temperature, thickness and boundary conditions. The results obtained here reveal that the natural frequency of the plate decreases with increase in temperature gradient, crack length and gradient index. © 2011 Elsevier Ltd. All rights reserved. [less ▲] Detailed reference viewed: 132 (1 UL)Lifetime prediction for solder joints with the extended finite element method ; ; et al in Proceedings of 12th Int. Conf. on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2011 (2011) Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical ... [more ▼] Predicting the lifetime of solder joints undergoing thermal cycling is crucial for the electronics industry in order to guarantee a certain performance of their products in the field. Semi-empirical methods are often used to predict the average lifetime of the critical joints. However, to get a reliable failure probability the standard deviation must also be addressed. The deviation of the lifetime from the mean value is a consequence of the variation in microstructure found in actual joints. We therefore propose a new methodology that calculates crack growth based on microstructural features of the joint. A series of random microstructures is generated. Crack growth calculations are performed for each of these structures. The structural problem is solved numerically with the extended finite element method which allows a complete automation of the process. The mean crack length and standard deviation are calculated from the crack growth simulations and the result is compared to experimental data. [less ▲] Detailed reference viewed: 84 (1 UL)Alleviating the Mesh Burden in Computational Solid Mechanics Bordas, Stéphane ; ; et al in Proceedings of ECT2010 (2010, December 12) The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment ... [more ▼] The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment; meshfree methods; extended finite element methods; isogeometric analysis; advanced remeshing techniques. [less ▲] Detailed reference viewed: 441 (3 UL)LINEAR BUCKLING ANALYSIS OF CRACKED ISOTROPIC PLATES USING THE EXTENDED FINITE ELEMENT METHOD ; ; et al Scientific Conference (2010, March) The behaviour of plate structures under compressive loads has been of great concern for engineering applications, especially in aeronautical and aerospace structures in which the demanding design of ... [more ▼] The behaviour of plate structures under compressive loads has been of great concern for engineering applications, especially in aeronautical and aerospace structures in which the demanding design of weight critical applications usually leads to stability problems. In this paper, the linear buckling problem of cracked isotropic plates is studied using the extended finite element method (XFEM). The mixed interpolation technique of the well-established MITC4 quadrilateral finite element with 12 standard degrees of freedom per element is used. The critical buckling load and mode shapes of simply supported square plates are computed as a function of crack length. [less ▲] Detailed reference viewed: 213 (0 UL)An alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes ; ; et al in Journal of Computational and Applied Mathematics (2010), 233(9), 2112-2135 An alternative alpha finite element method (AαFEM) using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent ... [more ▼] An alternative alpha finite element method (AαFEM) using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent solution in the energy norm for the static analysis of two-dimensional solid mechanics problems. In the AαFEM, the piecewise constant strain field of linear triangular FEM models is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to a linear triangular element. The element is further extended to the free and forced vibration analyses of solids. Several numerical examples show that the AαFEM achieves high reliability compared to other existing elements in the literature. [less ▲] Detailed reference viewed: 71 (0 UL)Modelling of crack growth behaviour in composite materials using the extended finite element method (XFEM) ; ; et al Scientific Conference (2010) Detailed reference viewed: 140 (0 UL)A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates ; ; et al in Computational Mechanics (2010), 46(5), 679-701 In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete ... [more ▼] In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation.Aso-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method. [less ▲] Detailed reference viewed: 130 (0 UL)On numerical integration of discontinuous approximations in partition of unity finite elements ; Bordas, Stéphane ; in IUTAM Bookseries (2010), 19 This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal ... [more ▼] This contribution presents two advances in the formulation of discontinuous approximations in finite elements. The first method relies on Schwarz-Christoffel mapping for integration on arbitrary polygonal domains [1]. When an element is split into two subdomains by a piecewise continuous discontinuity, each of these polygonal domains is mapped onto a unit disk on which cubature rules are utilized. This suppresses the need for the usual two-level isoparametric mapping. The second method relies on strain smoothing applied to discontinuous finite element approximations. By writing the strain field as a non-local weighted average of the compatible strain field, integration on the surface of the finite elements is transformed into boundary integration, so that the usual subdivision into integration cells is not required, an isoparametric mapping is not needed and the derivatives of the shape (enrichment) functions do not need to be computed. Results in fracture mechanics and composite materials are presented and both methods are compared in terms of accuracy and simplicity. The interested reader is referred to [1,6,13] for more details and should contact the authors to receive a version of the MATLAB codes used to obtain the results herein. © 2010 Springer Science+Business Media B.V. [less ▲] Detailed reference viewed: 204 (1 UL)Analysis of thermoelastic waves in a two-dimensional functionally graded materials domain by the Meshless Local Petrov-Galerkin (MLPG) method ; ; Bordas, Stéphane et al 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 (Al2O3) 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. [less ▲] Detailed reference viewed: 55 (4 UL)Analysis of thermoelastic waves in a two-dimensional functionally graded materials domain by the Meshless Local Petrov-Galerkin (MLPG) method ; ; Bordas, Stéphane et al 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 ▲] Detailed reference viewed: 186 (6 UL)An element nodal force-based large increment method for elastoplasticity ; ; et al in AIP Conference Proceedings (2010), 1233(PART 1), 1401-1405 This paper presents a new method for establishing the basic equations in the novel force-based large increment method (LIM) for continuum elastoplastic problems. In LIM, unlike traditional displacement ... [more ▼] This paper presents a new method for establishing the basic equations in the novel force-based large increment method (LIM) for continuum elastoplastic problems. In LIM, unlike traditional displacement methods, the (generalised) elemental force variables are adopted as system unknowns. The equilibrium equations can then be obtained directly at every nodal degree of freedom without physical equations (i.e., constitutive equations) involved. The generalised inverse of the non-square system of equations is employed to obtain the set of solutions of the non-square matrix equations directly. A conjugate gradient procedure is then used to find the correct solution from this set of solutions by optimising the compatibility of the solution based on the fact that the correct solution should also satisfy the constitutive equations and the compatibility equations. In this paper, the generalised elemental force variables are defined based on the element nodal forces. The LIM framework is therefore successfully applied to elements based on this definition. The efficiency and accuracy of the LIM are illustrated with a few benchmark problems and the results are compared with the analytical solution and the conventional displacement-based finite element method. [less ▲] Detailed reference viewed: 99 (0 UL)XFEM modelling of delamination in composite materials ; ; et al Scientific Conference (2010) Detailed reference viewed: 140 (0 UL)A cell-based smoothed finite element method for kinematic limit analysis ; ; et al in International Journal for Numerical Methods in Engineering (2010), 83(12), 1651-1674 This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of ... [more ▼] This paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second-order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged. [less ▲] Detailed reference viewed: 117 (2 UL)On the approximation in the smoothed finite element method (SFEM) Bordas, Stéphane ; in International Journal for Numerical Methods in Engineering (2010), 81(5), 660-670 This letter aims at resolving the issues raised in the recent short communication (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295. DOI: 10.1002/nme.2460) and answered by (Int. J. Numer. Meth. Engng 2009 ... [more ▼] This letter aims at resolving the issues raised in the recent short communication (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295. DOI: 10.1002/nme.2460) and answered by (Int. J. Numer. Meth. Engng 2009; DOI: 10.1002/nme.2587) by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique advantages of the smoothed finite element method (SFEM) (Comput. Mech. 2007; 39(6):859-877. DOI: 10.1007/s00466-006-0075-4; Commun. Numer. Meth. Engng 2009; 25(1):19-34. DOI: 10.1002/cnm.1098; Int. J. Numer. Meth. Engng 2007; 71(8):902-930; Comput. Meth. Appl. Mech. Engng 2008; 198(2):165-177. DOI: 10.1016/j.cma.2008.05.029; Comput. Meth. Appl. Mech. Engng 2007; submitted; Int. J. Numer. Meth. Engng 2008; 74(2):175-208. DOI: 10.1002/nme.2146; Comput. Meth. Appl. Mech. Engng 2008; 197 (13-16):1184-1203. DOI: 10.1016/j.cma.2007.10.008) and resolve the existence, linearity and positivity deficiencies pointed out in (Int. J. Numer. Meth. Engng 2008; 76(8):1285-1295). We show that Wachspress interpolants (A Rational Basis for Function Approximation. Academic Press, Inc.: New York, 1975) computed in the physical coordinate system are very well suited to the SFEM, especially when elements are heavily distorted (obtuse interior angles). The proposed approximation leads to results that are almost identical to those of the SFEM initially proposed in (Comput. Mech. 2007; 39(6):859-877. DOI: 10.1007/s00466-006-0075-4). These results suggest that the proposed approximation scheme forms a strong and rigorous basis for the construction of SFEMs. © 2009 John Wiley & Sons, Ltd. [less ▲] Detailed reference viewed: 173 (4 UL)On three-dimensional modelling of crack growth using partition of unity methods ; Bordas, Stéphane ; in Computers and Structures (2010), 88(23-24), 1391-1411 This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the ... [more ▼] This paper reviews different crack tracking techniques in three-dimensions applicable in the context of partition of unity methods, especially meshfree methods. Issues such as describing and tracking the crack surface are addressed. A crack tracking procedure is proposed in detail and implemented in the context of the extended element-free Galerkin method (XEFG). Several three-dimensional cracking examples are compared to other results from the literature or the experimental data and show good agreement. [less ▲] Detailed reference viewed: 148 (9 UL)Strain smoothing in FEM and XFEM Bordas, Stéphane ; ; et al 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 ▲] Detailed reference viewed: 178 (1 UL)Enriched finite elements (XFEM) for multi-crack growth simulations in orthotropic materials ; ; et al Scientific Conference (2010) Detailed reference viewed: 124 (0 UL)On the structure of a new superhard hexagonal carbon phase ; ; et al in AIP Conference Proceedings (2010), 1233(PART 1), 489-493 Molecular dynamics simulations show that graphite will transform into a superhard phase under cold compression. Recent experiments show that there is a sp 3-rich hexagonal carbon polymorph (a 0=2.496 Å, c ... [more ▼] Molecular dynamics simulations show that graphite will transform into a superhard phase under cold compression. Recent experiments show that there is a sp 3-rich hexagonal carbon polymorph (a 0=2.496 Å, c 0=4.123Å) with a bulk modulus of 447 GPa and average density about 3.6g/cm 3, restricted to the space group of P-62c (No. 190), but the detailed atomic structure was not obtained [Wang et al., P. Natl. Acad. Sci. 101(38), 13699]. Here we set carbon atoms occupying P-62c 4f Wyckoff positions of P-62c, and calculate the total energy of the different structures changing the internal parameter z by first-principles calculations using geometry optimisation algorithm in CASTEP code, which shows that the stable structures in energy (at local minimum points) are hexagonal carbon (z=1/4) and hexagonal diamond (z=1/16). The calculated mechanical properties and lattice parameters of the structure P-62c 4f (z=1/4) are in good agreement with those of the new hexagonal carbon proposed by Wang et al., which indicates that the atomic structure is a possible candidate. © 2010 American Institute of Physics. [less ▲] Detailed reference viewed: 101 (0 UL) |
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