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Sven Klinkel - One of the best experts on this subject based on the ideXlab platform.

  • a finite element formulation in Boundary Representation for the analysis of nonlinear problems in solid mechanics
    Computer Methods in Applied Mechanics and Engineering, 2019
    Co-Authors: Sven Klinkel, Rainer Ernst Reichel
    Abstract:

    Abstract The contribution is concerned with a numerical element formulation in Boundary Representation. It results in a polynomial element description with an arbitrary number of nodes on the Boundary. Scaling the Boundary description determines the interior domain. The scaling approach is adopted from the so-called scaled Boundary finite element method (SBFEM), which is a semi-analytical formulation to analyze problems in linear elasticity. Within this method, the basic idea is to scale the Boundary with respect to a scaling center. The Boundary, which is denoted as circumferential direction, and the scaling direction span the parameter space. In the present approach, interpolations in scaling direction and circumferential direction are introduced. The interpolation in circumferential direction is independent of the scaling direction. The formulation is suitable to analyze problems in nonlinear solid mechanics. The displacement degrees of freedom are located at the nodes on the Boundary and in the interior element domain. The degrees of freedom located at the interior domain are eliminated by static condensation, which leads to a polygonal finite element formulation with an arbitrary number of nodes on the Boundary. The element formulation allows per definition for Voronoi meshes and quadtree mesh generation. Numerical examples give rise to the performance of the present approach in comparison to other polygonal element formulations, like the virtual element method (VEM). Some benchmark tests show the capability of the element formulation. A comparison to standard and mixed element formulations is presented. The present approach is perfectly suitable to model heterogeneous structures with inclusions and voids. It avoids also staircase approximation of curved boundaries.

  • a scaled Boundary isogeometric formulation for the elasto plastic analysis of solids in Boundary Representation
    Computer Methods in Applied Mechanics and Engineering, 2018
    Co-Authors: Margarita Chasapi, Sven Klinkel
    Abstract:

    Abstract This contribution deals with the nonlinear analysis of Boundary represented solids with elasto-plastic material behavior based on the so-called scaled Boundary isogeometric formulation (SB-IGA). The proposed approach combines the features of the scaled Boundary finite element method and isogeometric analysis. Based on the original Boundary Representation of the CAD model, a formulation is provided where the geometrical description of the Boundary is sufficient to define the entire surface. The domain is parameterized by a radial scaling parameter emanating from a scaling center and a parameter in circumferential direction along the Boundary. Non star-shaped domains are tackled by standard sub-structuring. Here, conforming discretizations are considered for the two-dimensional case. According to the isogeometric paradigm, NURBS basis functions are employed for the approximation of the solution. The displacement response is derived based on a multiplicative decomposition of the approximation in circumferential and radial scaling direction. The Boundary value problem is solved with the Galerkin method. The Newton–Raphson iterative scheme is employed to obtain the nonlinear response. Several benchmark tests demonstrate the accuracy and computational efficiency of the formulation.

  • a nurbs based galerkin approach for the analysis of solids in Boundary Representation
    Computer Methods in Applied Mechanics and Engineering, 2016
    Co-Authors: Bernd Simeon, Lin Chen, Sven Klinkel
    Abstract:

    Abstract The paper is concerned with a new numerical method to solve the elasticity problem of solids in Boundary Representation. A formulation is derived where the geometrical description of the Boundary is sufficient for defining the equations of elasticity of the complete solid. While the interior of the domain is described by a radial scaling parameter, the scaling of the Boundary with respect to the specified scaling center leads to the complete solid. This idea fits perfectly to the Boundary Representation modeling technique commonly employed in CAD. In the present approach the tensor-product structure of the solid will be reduced by one dimension to parametrize the physical domain, i.e., the three-dimensional solid exploits only two-dimensional NURBS objects, which parametrize the Boundary surfaces. For the analysis, the weak form of the equilibrium equations is enforced for the entire solid. In particular the weak form is employed in the scaling direction and the circumferential direction. Applying the isogeometric paradigm, the NURBS functions that describe the Boundary of the geometry form also the basis for the approximation of the displacement at the Boundary. The displacement response in the radial scaling direction, on the other hand, is approximated by a one-dimensional NURBS. Overall, the Galerkin projection of the weak form yields a linear system of equilibrium equations whose solution gives rise to the displacement response. The accuracy of the method is validated by means of analytical reference data. In conclusion, the proposed method allows the analysis of solids which are bounded by an arbitrary number of contour boundaries.

J Trevelyan - One of the best experts on this subject based on the ideXlab platform.

  • an isogeometric Boundary element method for elastostatic analysis 2d implementation aspects
    Computers & Structures, 2013
    Co-Authors: Robert Napier Simpson, Stephane Bordas, Haojie Lian, J Trevelyan
    Abstract:

    The concept of isogeometric analysis, whereby the parametric functions that are used to describe CAD geometry are also used to approximate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlining an isogeometric Boundary element Method (IGABEM) that only requires a Representation of the geometry of the domain for analysis, fitting neatly with the Boundary Representation provided completely by CAD. The method circumvents the requirement to generate a Boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional Boundary element implementations. Examples of Matlab(R) code are given whenever possible to aid understanding of the techniques used.

  • an isogeometric Boundary element method for elastostatic analysis 2d implementation aspects
    arXiv: Numerical Analysis, 2013
    Co-Authors: Robert Napier Simpson, Stephane Bordas, Haojie Lian, J Trevelyan
    Abstract:

    The concept of isogeometric analysis, whereby the parametric func- tions that are used to describe CAD geometry are also used to approx- imate the unknown fields in a numerical discretisation, has progressed rapidly in recent years. This paper advances the field further by outlin- ing an isogeometric Boundary Element Method (IGABEM) that only re- quires a Representation of the geometry of the domain for analysis, fitting neatly with the Boundary Representation provided completely by CAD. The method circumvents the requirement to generate a Boundary mesh representing a significant step in reducing the gap between engineering design and analysis. The current paper focuses on implementation details of 2D IGABEM for elastostatic analysis with particular attention paid towards the differences over conventional Boundary element implementa- tions. Examples of Matlab R{\deg} code are given whenever possible to aid understanding of the techniques used.

Manuel Tur - One of the best experts on this subject based on the ideXlab platform.

  • exact 3d Boundary Representation in finite element analysis based on cartesian grids independent of the geometry
    International Journal for Numerical Methods in Engineering, 2015
    Co-Authors: Onofre Marco, Ruben Sevilla, Yongjie Zhang, J J Rodenas, Manuel Tur
    Abstract:

    Summary This paper proposes a novel Immersed Boundary Method where the embedded domain is exactly described by using its Computer-Aided Design (CAD) Boundary Representation with Non-Uniform Rational B-Splines (NURBS) or T-splines. The common feature with other immersed methods is that the current approach substantially reduces the burden of mesh generation. In contrast, the exact Boundary Representation of the embedded domain allows to overcome the major drawback of existing immersed methods that is the inaccurate Representation of the physical domain. A novel approach to perform the numerical integration in the region of the cut elements that is internal to the physical domain is presented and its accuracy and performance evaluated using numerical tests. The applicability, performance, and optimal convergence of the proposed methodology is assessed by using numerical examples in three dimensions. It is also shown that the accuracy of the proposed methodology is independent on the CAD technology used to describe the geometry of the embedded domain. Copyright © 2015 John Wiley & Sons, Ltd.

C. A. Gonzalez - One of the best experts on this subject based on the ideXlab platform.

  • Shape optimisation of continuum structures via evolution strategies and fixed grid finite element analysis
    Structural and Multidisciplinary Optimization, 2004
    Co-Authors: Manuel García, C. A. Gonzalez
    Abstract:

    Evolution strategies (ES) are very robust and general techniques for finding global optima in optimisation problems. As with all evolutionary algorithms, ES apply evolutionary operators and select the most fit from a set of possible solutions. Unlike genetic algorithms, ES do not use binary coding of individuals, working instead with real variables. Many recent studies have applied evolutionary algorithms to structural problems, particularly the optimisation of trusses. This paper focuses on shape optimisation of continuum structures via ES. Stress analysis is accomplished by using the fixed grid finite element method, which reduces the computing time while keeping track of the Boundary Representation of the structure. This Boundary is represented by b-spline functions, circles, and polylines, whose control points constitute the parameters that govern the shape of the structure. Evolutionary operations are applied to each set of variables until a global optimum is reached. Several numerical examples are presented to illustrate the performance of the method. Finally, structures with multiple load cases are considered along with examples illustrating the results obtained.

Lin Chen - One of the best experts on this subject based on the ideXlab platform.

  • a nurbs based galerkin approach for the analysis of solids in Boundary Representation
    Computer Methods in Applied Mechanics and Engineering, 2016
    Co-Authors: Bernd Simeon, Lin Chen, Sven Klinkel
    Abstract:

    Abstract The paper is concerned with a new numerical method to solve the elasticity problem of solids in Boundary Representation. A formulation is derived where the geometrical description of the Boundary is sufficient for defining the equations of elasticity of the complete solid. While the interior of the domain is described by a radial scaling parameter, the scaling of the Boundary with respect to the specified scaling center leads to the complete solid. This idea fits perfectly to the Boundary Representation modeling technique commonly employed in CAD. In the present approach the tensor-product structure of the solid will be reduced by one dimension to parametrize the physical domain, i.e., the three-dimensional solid exploits only two-dimensional NURBS objects, which parametrize the Boundary surfaces. For the analysis, the weak form of the equilibrium equations is enforced for the entire solid. In particular the weak form is employed in the scaling direction and the circumferential direction. Applying the isogeometric paradigm, the NURBS functions that describe the Boundary of the geometry form also the basis for the approximation of the displacement at the Boundary. The displacement response in the radial scaling direction, on the other hand, is approximated by a one-dimensional NURBS. Overall, the Galerkin projection of the weak form yields a linear system of equilibrium equations whose solution gives rise to the displacement response. The accuracy of the method is validated by means of analytical reference data. In conclusion, the proposed method allows the analysis of solids which are bounded by an arbitrary number of contour boundaries.