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Background Mesh

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Ashok Kumar – 1st expert on this subject based on the ideXlab platform

  • Isoparametric B-Spline Elements for Immersed Boundary Explicit Dynamic Simulation
    Journal of Computing and Information Science in Engineering, 2020
    Co-Authors: Shashank Menon, Ashok Kumar

    Abstract:

    Abstract
    Explicit dynamic analysis has proven to be advantageous when simulating shock and impact loading, and very small time-scale events. In this article, the feasibility of using a Background Mesh of B-spline elements for immersed boundary explicit dynamic simulation is studied. In this approach, the geometry is immersed in a Background Mesh consisting of uniform regular shaped elements to avoid Mesh generation difficulties. The boundary conditions are applied using the step boundary method, which uses the equations of the boundaries to construct trial functions that satisfy the essential boundary conditions. An isoparametric formulation is presented for quadratic and cubic B-spline elements and their shape functions are derived from the classical recursive definition of B-splines. The effectiveness of mass diagonalization for B-spline elements is also explored. This approach is validated using several examples by comparing with modal superposition solutions as well as past work using traditional finite element analysis (FEA) and analytical solutions when available.

  • Survey of Immersed Boundary Approaches for Finite Element Analysis
    Journal of Computing and Information Science in Engineering, 2020
    Co-Authors: Ashok Kumar

    Abstract:

    Abstract
    Mesh generation for traditional finite element analysis has proven to be very difficult to fully automate especially using hexahedral elements for complex 3D geometry. Several modifications to the finite element method (FEM), such as the Meshless methods, have been proposed for avoiding Mesh generation. An alternative approach has recently gained popularity where the geometry, created as a solid model in cad software, is embedded or immersed in a nonconforming Background Mesh for analysis. In this approach, referred to here as the immersed boundary approach, a Background Mesh that is independent of the geometry is used for piecewise interpolation or approximation of the solution. Therefore, a uniform Mesh with regular-shaped or undistorted elements can be used, and such a Mesh is easy to generate automatically. When the geometry is immersed in the Background Mesh, the boundary elements are often only partly inside the geometry and the nodes of the Mesh may not be on the boundaries. Many new methods have been developed to integrate over partial elements and to apply boundary and interface conditions when the boundaries of the geometries do not conform to the Background Mesh. These methods are reviewed in this article with particular emphasis on the implicit boundary method and step boundary method for applying boundary conditions. In addition, B-spline elements and several applications of the immersed boundary approach are surveyed including composite microstructures and structural elements for plates and shells.

  • total lagrangian formulation for large deformation modeling using uniform Background Mesh
    ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2016
    Co-Authors: Nikhil Bhosale, Ashok Kumar

    Abstract:

    Mesh generation difficulties can be avoided when a Background Mesh rather than a Mesh that conforms to the geometry is used for the analysis. The geometry is represented by equations and is independent of the Mesh and is immersed in the Background Mesh. The solution to boundary value problems is approximated or piece-wise interpolated using the Background Mesh. The main challenge is in applying the boundary conditions because the boundaries may not have any nodes on them. Implicit boundary method has been used for linear static and dynamic analysis and has shown to be an effective approach for imposing boundary conditions but has never been applied to nonlinear problems. In this paper, this approach is extended to large deformation nonlinear analysis using the Total Lagrangian formulation. The equations are solved using the widely used modified Newton-Raphson method with loads applied over many load steps. Several test examples are studied and compared with traditional finite element analysis software for verification.Copyright © 2016 by ASME

Hailong Chen – 2nd expert on this subject based on the ideXlab platform

  • method for imposing boundary conditions on reissner mindlin plates for analysis using structured Background Mesh
    Computers & Structures, 2014
    Co-Authors: Hailong Chen, Ashok Kumar

    Abstract:

    Elements in a conforming Mesh are often distorted to fit the geometry which can cause numerical errors. If a Background Mesh is used for analysis, the elements can be regular shaped. The geometry must be represented independently using equations and implicit boundary method can be used to enforce essential boundary conditions. In this paper, this approach is extended to traditional Reissner–Mindlin plate elements that use mixed interpolation to avoid shear locking. The convergence of plate elements that use implicit boundary approach and a Background Mesh is studied in this paper using several benchmark problems to test their validity and robustness.

  • Method for imposing boundary conditions on Reissner–Mindlin plates for analysis using structured Background Mesh
    Computers & Structures, 2014
    Co-Authors: Hailong Chen, Ashok Kumar

    Abstract:

    Elements in a conforming Mesh are often distorted to fit the geometry which can cause numerical errors. If a Background Mesh is used for analysis, the elements can be regular shaped. The geometry must be represented independently using equations and implicit boundary method can be used to enforce essential boundary conditions. In this paper, this approach is extended to traditional Reissner–Mindlin plate elements that use mixed interpolation to avoid shear locking. The convergence of plate elements that use implicit boundary approach and a Background Mesh is studied in this paper using several benchmark problems to test their validity and robustness.

Charbel Farhat – 3rd expert on this subject based on the ideXlab platform

  • Accelerated Mesh sampling for the hyper reduction of nonlinear computational models
    International Journal for Numerical Methods in Engineering, 2017
    Co-Authors: Todd Chapman, P. Avery, Pat Collins, Charbel Farhat

    Abstract:

    We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a Background Mesh to curvilinear ones that conform exactly to the immersed domain. Constructing such a map relies on a novel way of parameterizing the immersed boundary over a collection of nearby edges with its closest point projection. By interpolating the mappings to curvilinear triangles at select points, we recover isoparametric mappings for the immersed domain defined over the Background Mesh. Indeed, interpolating the constructed mappings just at the vertices of the Background Mesh yields a fast Meshing algorithm that involves only perturbing a few vertices near the boundary. For the discretization of a curved domain to be robust, we have to impose restrictions on the Background Mesh. Conversely, these restrictions define a family of domains that can be discretized with a given Background Mesh. We then say that the Background Mesh is a universal Mesh for such a family of domains. The notion of universal Meshes is particularly useful in free/moving boundary problems because the same Background Mesh can serve as the universal Mesh for the evolving domain for time intervals that are independent of the time step. Hence it facilitates a framework for finite element calculations over evolving domains while using a fixed Background Mesh. Furthermore, since the evolving geometry can be approximated with any desired order, numerical solutions can be computed with high-order accuracy. We demonstrate these ideas with various numerical examples.

  • A FETI-preconditioned conjugate gradient method for large-scale stochastic finite element problems
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: Debraj Ghosh, P. Avery, Charbel Farhat

    Abstract:

    We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a Background Mesh to curvilinear ones that conform exactly to the immersed domain. Constructing such a map relies on a novel way of parameterizing the immersed boundary over a collection of nearby edges with its closest point projection. By interpolating the mappings to curvilinear triangles at select points, we recover isoparametric mappings for the immersed domain defined over the Background Mesh. Indeed, interpolating the constructed mappings just at the vertices of the Background Mesh yields a fast Meshing algorithm that involves only perturbing a few vertices near the boundary. For the discretization of a curved domain to be robust, we have to impose restrictions on the Background Mesh. Conversely, these restrictions define a family of domains that can be discretized with a given Background Mesh. We then say that the Background Mesh is a universal Mesh for such a family of domains. The notion of universal Meshes is particularly useful in free/moving boundary problems because the same Background Mesh can serve as the universal Mesh for the evolving domain for time intervals that are independent of the time step. Hence it facilitates a framework for finite element calculations over evolving domains while using a fixed Background Mesh. Furthermore, since the evolving geometry can be approximated with any desired order, numerical solutions can be computed with high-order accuracy. We demonstrate these ideas with various numerical examples.