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Nhon Nguyen-thanh - One of the best experts on this subject based on the ideXlab platform.

  • Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite Element method for structural analysis
    2013
    Co-Authors: Nhon Nguyen-thanh
    Abstract:

    This thesis presents two new methods in finite Elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite Element method using Triangular Elements. In this method, the piecewise constant strain field of Linear Triangular finite Element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a Linear Triangular Element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite Element method is coupled with a discrete shear gap technique for Triangular Elements to significantly improve the accuracy of the standard Triangular finite Elements. The basic idea behind this Element formulation is to approximate displacements and rotations as in the standard finite Element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results.

  • An alternative alpha finite Element method with discrete shear gap technique for analysis of laminated composite plates
    Applied Mathematics and Computation, 2011
    Co-Authors: C. Thai-hoang, Nhon Nguyen-thanh, Hung Nguyen-xuan, Timon Rabczuk
    Abstract:

    Abstract This paper presents an alternative alpha finite Element method using Triangular meshes (A α FEM) for static, free vibration and buckling analyses of laminated composite plates. In the A α FEM, an assumed strain field is carefully constructed by combining compatible strains and additional strains with an adjustable parameter α which can produce an effectively softer stiffness formulation compared to the Linear Triangular Element. The stiffness matrices are obtained based on the strain smoothing technique over the smoothing domains and the constant strains on Triangular sub-domains associated with the nodes of the Elements. The discrete shear gap (DSG) method is incorporated into the A α FEM to eliminate transverse shear locking and an improved Triangular Element termed as A α DSG3 is proposed. Several numerical examples are then given to demonstrate the effectiveness of the A α DSG3.

  • An alternative alpha finite Element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates
    Finite Elements in Analysis and Design, 2011
    Co-Authors: Nhon Nguyen-thanh, Timon Rabczuk, Hung Nguyen-xuan, Stéphane Bordas
    Abstract:

    An alternative alpha finite Element method (A@aFEM) 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 Mindlin-Reissner plates. In the A@aFEM, the piecewise constant strain field of Linear Triangular Elements is enhanced by additional strain terms with an adjustable parameter @a 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 A@a-DSG3 is obtained. Several numerical examples show that the A@a-DSG3 achieves high reliability compared to other existing Elements in the literature. Through selection of @a, under or over estimation of the strain energy can be achieved.

  • An alternative alpha finite Element method (AαFEM) for free and forced structural vibration using Triangular meshes
    Journal of Computational and Applied Mathematics, 2010
    Co-Authors: Nhon Nguyen-thanh, Timon Rabczuk, Hung Nguyen-xuan, Stéphane Bordas
    Abstract:

    An alternative alpha finite Element method ([email protected]) 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 [email protected], the piecewise constant strain field of Linear Triangular FEM models is enhanced by additional strain terms with an adjustable parameter @a 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 [email protected] achieves high reliability compared to other existing Elements in the literature.

Stéphane Bordas - One of the best experts on this subject based on the ideXlab platform.

  • An alternative alpha finite Element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates
    Finite Elements in Analysis and Design, 2011
    Co-Authors: Nhon Nguyen-thanh, Timon Rabczuk, Hung Nguyen-xuan, Stéphane Bordas
    Abstract:

    An alternative alpha finite Element method (A@aFEM) 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 Mindlin-Reissner plates. In the A@aFEM, the piecewise constant strain field of Linear Triangular Elements is enhanced by additional strain terms with an adjustable parameter @a 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 A@a-DSG3 is obtained. Several numerical examples show that the A@a-DSG3 achieves high reliability compared to other existing Elements in the literature. Through selection of @a, under or over estimation of the strain energy can be achieved.

  • An alternative alpha finite Element method (AαFEM) for free and forced structural vibration using Triangular meshes
    Journal of Computational and Applied Mathematics, 2010
    Co-Authors: Nhon Nguyen-thanh, Timon Rabczuk, Hung Nguyen-xuan, Stéphane Bordas
    Abstract:

    An alternative alpha finite Element method ([email protected]) 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 [email protected], the piecewise constant strain field of Linear Triangular FEM models is enhanced by additional strain terms with an adjustable parameter @a 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 [email protected] achieves high reliability compared to other existing Elements in the literature.

S.r. Sabbagh-yazdi - One of the best experts on this subject based on the ideXlab platform.

  • Unstructured finite volume method for matrix free explicit solution of stress–strain fields in two dimensional problems with curved boundaries in equilibrium condition
    Applied Mathematical Modelling, 2012
    Co-Authors: S.r. Sabbagh-yazdi, S. Ali-mohammadi, M K Pipelzadeh
    Abstract:

    Abstract In this paper, a plane stress structural solver which uses a matrix free unstructured finite volume method based on Galerkin approach is introduced for solution of weak form of two dimensional Cauchy equations on Linear Triangular Element meshes. The developed shape function free Galerkin finite volume structural solver explicitly computes stresses and displacements in cartesian coordinate directions for the two dimensional solid mechanic problems in equilibrium condition. The accuracy of the introduced algorithm is assessed by comparison of computed results of two plane-stress cases with curved boundaries under uniformly distributed loads with available analytical solutions. The results of the introduced method are presented in terms of stress and strain contours and its effective parameters on convergence behaviour to equilibrium condition are assessed.

  • Symmetric Conditions for Strain Analysis in a Long Thick Cylinder under Internal Pressure Using NASIR Unstructured GFVM Solver
    Jordan Journal of Civil Engineering, 2011
    Co-Authors: S.r. Sabbagh-yazdi, M. Esmaili, M.t. Alkhamis
    Abstract:

    Utilization of symmetric condition in NASIR Galerkin Finite Volume Method for Linear Triangular Element unstructured meshes is introduced for numerical solution of two dimensional strain and stress fields in a long thick cylinder section. The developed shape function free Galerkin Finite Volume structural solver explicitly computes stresses and displacements in Cartesian coordinate directions for the two- dimensional solid mechanic problems under either static or dynamic loads. The accuracy of the introduced algorithm is assessed by comparison of computed results of a thick cylinder under internal fluid pressure load with analytical solutions. The performance of the solver for taking advantage of symmetric conditions is presented by computation of stress and strain contours on a half and a quarter of the cylinder section.

  • Performance evaluation of iterative GFVM on coarse unstructured Triangular meshes and comparison with matrix manipulation based solution methods
    Scientia Iranica, 2011
    Co-Authors: S.r. Sabbagh-yazdi, S. Ali-mohammadi
    Abstract:

    Abstract A matrix free unstructured Galerkin Finite Volume Method (GFVM) is adopted for solving plane-stress two dimensional Cauchy equilibrium equations. The algorithm is developed based on the Galerkin method, for the solution of structural problems on unstructured Linear Triangular Element meshes. The developed shape function free Galerkin Finite Volume solver computes stresses and displacements of solid mechanic problems via some iteration. The performance of the introduced algorithm on coarse unstructured meshes is assessed by comparison with computed results of a plane-stress case (with uniformly distributed load on one of its elliptic boundaries and two straight sliding support boundaries), for which an analytical solution is available. The results of the introduced method are presented in terms of stress and strain contours, and the sensitivity of the GFVM solver to mesh coarseness, as well as to the utilized gradual load imposing parameter (which affects the convergence behavior of the model), is assessed. Furthermore, the accuracy of the present matrix free GFVM is compared to the previous matrix manipulation based solution methods.

  • Utilizing NASIR Galerkin Finite Volume Analyzer for 2D Plane Strain Problems under Static and Vibrating Concentrated Loads
    Jordan Journal of Civil Engineering, 2008
    Co-Authors: M.t. Alkhamis, S.r. Sabbagh-yazdi, Esmaeili, Falah M. Wegian
    Abstract:

    A Numerical Analyzer for Scientific and Industrial Requirements (NASIR) software which utilizes novel matrix free Finite Volume is applied for solving plane strain solid state problems on Linear Triangular Element meshes. The developed shape function free Galerkin Finite Volume structural solver explicitly computes stresses and displacements in Cartezian coordinate directions for the two dimensional solid mechanic problems under either static or dynamic loads. The accuracy of the introduced algorithm is assessed by comparison of computed results of cantilever structural Elements under static concentrated load with analytical solutions. Then, the performance of the introduced method to solve structural plane strain problem under forced and vibrating loads is demonstrated. The performance of the solver is presented in terms of stress and strain contours as well as convergence behavior of the method.

C.-c.j. Kuo - One of the best experts on this subject based on the ideXlab platform.

  • Shape from shading with a Linear Triangular Element surface model
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 1993
    Co-Authors: Kyoung Mu Lee, C.-c.j. Kuo
    Abstract:

    The authors propose to combine a Triangular Element surface model with a Linearized reflectance map to formulate the shape-from-shading problem. The main idea is to approximate a smooth surface by the union of Triangular surface patches called Triangular Elements and express the approximating surface as a Linear combination of a set of nodal basis functions. Since the surface normal of a Triangular Element is uniquely determined by the heights of its three vertices (or nodes), image brightness can be directly related to nodal heights using the Linearized reflectance map. The surface height can then be determined by minimizing a quadratic cost functional corresponding to the squares of brightness errors and solved effectively with the multigrid computational technique. The proposed method does not require any integrability constraint or artificial assumptions on boundary conditions. Simulation results for synthetic and real images are presented to illustrate the performance and efficiency of the method. >

Arun Kumar Baruah - One of the best experts on this subject based on the ideXlab platform.

  • • Linear Triangular Element APPROXIMATION IN THREE-PARAMETER STURM–LIOUVILLE PROBLEM
    International Journal of Mathematical Archive, 2015
    Co-Authors: Surashmi Bhattacharyya, Arun Kumar Baruah
    Abstract:

    T he purpose of this paper is to use Linear Triangular Element approximation, which is one of the forms of finite Element method, to find the eigenvalues of a three-parameter Linear Sturm-Liouville problem with homogeneous boundary conditions. We first reduce the original three-parameter problem into an equivalent system of one-parameter problem. We apply Linear Triangular Element approximation on reduced form of the given problem to find the rough estimates of the eigenvalues. Using the rough estimates as starting approximation in the corresponding shooting method, we obtained the actual values of the eigenvalues . A numerical example is given to illustrate the effectiveness of the method.

  • Linear Triangular Element approximation in three parameter sturm liouville problem
    International Journal of Mathematical Archive, 2015
    Co-Authors: Surashmi Bhattacharyya, Arun Kumar Baruah
    Abstract:

    T he purpose of this paper is to use Linear Triangular Element approximation, which is one of the forms of finite Element method, to find the eigenvalues of a three-parameter Linear Sturm-Liouville problem with homogeneous boundary conditions. We first reduce the original three-parameter problem into an equivalent system of one-parameter problem. We apply Linear Triangular Element approximation on reduced form of the given problem to find the rough estimates of the eigenvalues. Using the rough estimates as starting approximation in the corresponding shooting method, we obtained the actual values of the eigenvalues . A numerical example is given to illustrate the effectiveness of the method.