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Isogeometric Analysis of Laminated Composite Plates Using the Higher-Order Shear Deformation Theory ; ; Bordas, Stéphane et al in Mechanics of Advanced Materials and Structures (2015), 22(6), 451-469 Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown ... [more ▼] Isogeometric analysis (IGA) aims at simplifying the computer aided design (CAD) and computer aided engineering (CAE) pipeline by using the same functions to describe the geometry (CAD) and the unknown fields (Analysis). IGA can be based on a variety of CAD descriptions, the most widely used today being non-uniform rational B-splines (NURBS). In this article, the suitability of NURBS-based isogeometric analysis within a third-order shear deformation theory for the simulation of the static, dynamic, and buckling response of laminated composite plates is investigated. The method employs NURBS basis functions to both represent the geometry (exactly) and the unknown field variables. One of the main advantages of the present method is directly inherited from IGA, that is to easily increase the approximation order. To avoid using a shear correction factor, a third-order shear deformation theory (TSDT) is introduced. It requires C1-continuity of generalized displacements and the NURBS basis functions are well suited for this requirement. Several numerical examples are used to demonstrate the performance of the present method compared with other published ones. [less ▲] Detailed reference viewed: 96 (2 UL)A staggered cell-centered finite element method for compressible and nearly-incompressible linear elasticity on general meshes ; ; Bordas, Stéphane et al in SIAM Journal on Numerical Analysis (2015), 53(4), 2051-2073 We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its ... [more ▼] We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost. [less ▲] Detailed reference viewed: 106 (2 UL)Isogeometric analysis of functionally graded plates using a refined plate theory ; ; et al in Composites : Part B, Engineering (2014), 64 We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of ... [more ▼] We present in this paper a simple and effective approach that incorporates isogeometric finite element analysis (IGA) with a refined plate theory (RPT) for static, free vibration and buckling analysis of functionally graded material (FGM) plates. A new inverse tangent distributed function through the plate thickness is proposed. The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions namely B-splines or non-uniform rational B-splines (NURBS) which reach easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field with four degrees of freedom per each control point allowing an efficient solution process. [less ▲] Detailed reference viewed: 105 (3 UL)An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics & Engineering (2013), 253 This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded ... [more ▼] This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. © 2012 Elsevier B.V. [less ▲] Detailed reference viewed: 351 (5 UL)Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity ; ; et al in Computational Mechanics (2013), 52(1), 37-52 An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown ... [more ▼] An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features. © 2012 Springer-Verlag. [less ▲] Detailed reference viewed: 295 (4 UL)A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis ; ; et al in Computer Modeling in Engineering & Sciences (2011), 73(4), 331-355 This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture ... [more ▼] This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks when we replace interior integration by boundary integration, simplifying integration of the discontinuous approximation. The key advantage of the NS-XFEM is that it provides more accurate solutions compared to the XFEM-T3 element. We will show for two numerical examples that the NS-XFEM significantly improves the results in the energy norm and the stress intensity factors. For the examples studied, we obtain super-convergent results. [less ▲] Detailed reference viewed: 36 (1 UL)An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates ; ; et al in Finite Elements in Analysis and Design (2011), 47(5), 519-535 An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite ... [more ▼] An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved. [less ▲] Detailed reference viewed: 79 (2 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 & 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: 114 (1 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: 104 (2 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: 59 (0 UL)A simple and robust three-dimensional cracking-particle method without enrichment ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics & Engineering (2010), 199(37-40), 2437-2455 A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal ... [more ▼] A new robust and efficient approach for modeling discrete cracks in meshfree methods is described. The method is motivated by the cracking-particle method (Rabczuk T., Belytschko T., International Journal for Numerical Methods in Engineering, 2004) where the crack is modeled by a set of cracked segments. However, in contrast to the above mentioned paper, we do not introduce additional unknowns in the variational formulation to capture the displacement discontinuity. Instead, the crack is modeled by splitting particles located on opposite sides of the associated crack segments and we make use of the visibility method in order to describe the crack kinematics. We apply this method to several two- and three-dimensional problems in statics and dynamics and show through several numerical examples that the method does not show any "mesh" orientation bias. © 2010 Elsevier B.V. [less ▲] Detailed reference viewed: 134 (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: 107 (0 UL)A smoothed finite element method for plate analysis ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics & Engineering (2008), 197(13-16), 1184-1203 A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending ... [more ▼] A quadrilateral element with smoothed curvatures for Mindlin-Reissner plates is proposed. The curvature at each point is obtained by a non-local approximation via a smoothing function. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements (smoothing cells). Numerical results show that the proposed element is robust, computational inexpensive and simultaneously very accurate and free of locking, even for very thin plates. The most promising feature of our elements is their insensitivity to mesh distortion. [less ▲] Detailed reference viewed: 86 (1 UL)A smoothed finite element method for shell analysis ; ; et al in Computer Methods in Applied Mechanics & Engineering (2008), 198(2), 165-177 A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on ... [more ▼] A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples. [less ▲] Detailed reference viewed: 110 (1 UL) |
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