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Hybrid collocation-Galerkin approach for the analysis of surface represented 3D-solids employing SB-FEM

  • This paper presents a numerical method to solve the three-dimensional elasticity problem of surface represented solids. A surface oriented formulation is derived, in which the three-dimensional solid is described by its boundary surfaces and a radial scaling center. Scaling the boundary surfaces with respect to the scaling center yields a parameterization of the complete solid. The definition of the boundary surfaces is sufficient for the description of the solid. Thus, the formulation conforms ideally to the boundary representation modeling technique used in CAD. In the present approach, no tensor-product structure of three-dimensional objects is exploited to parameterize the physical domain. The weak form of the equation of motion and the weak form of the Neumann boundary conditions are enforced only at the boundary surfaces. It leads to a transformation of the governing partial differential equations of elasticity to an ordinary differential equation (ODE) of Euler type. Solving the ODE leads to the displacement in the radialThis paper presents a numerical method to solve the three-dimensional elasticity problem of surface represented solids. A surface oriented formulation is derived, in which the three-dimensional solid is described by its boundary surfaces and a radial scaling center. Scaling the boundary surfaces with respect to the scaling center yields a parameterization of the complete solid. The definition of the boundary surfaces is sufficient for the description of the solid. Thus, the formulation conforms ideally to the boundary representation modeling technique used in CAD. In the present approach, no tensor-product structure of three-dimensional objects is exploited to parameterize the physical domain. The weak form of the equation of motion and the weak form of the Neumann boundary conditions are enforced only at the boundary surfaces. It leads to a transformation of the governing partial differential equations of elasticity to an ordinary differential equation (ODE) of Euler type. Solving the ODE leads to the displacement in the radial scaling direction. In the present approach, the isogeometric Galerkin finite element method is employed to describe the geometry of the boundary surfaces and also to approximate the displacement response of the boundary surfaces. It exploits two-dimensional NURBS objects to parameterize the boundary surfaces. The final Euler type ODE is solved by the NURBS based collocation method. The displacement response in the radial scaling direction is approximated by the NURBS basis functions. Hence, the method can be extended to nonlinear problems. The accuracy of the method is validated against analytical solutions. In general, the proposed formulation is able to model solids bounded by an arbitrary number of surfaces.show moreshow less

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Metadaten
Author: Lin Chen, Sven Klinkel, Wolfgang DornischORCiD
DOI:https://doi.org/10.1016/j.cma.2015.07.004
ISSN:0045-7825
Title of the source (English):Computer Methods in Applied Mechanics and Engineering
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2015
Tag:Hybrid collocation-Galerkin method; NURBS basis functions; Scaled boundary finite element method; Surface represented solid
Volume/Year:295
First Page:268
Last Page:289
Faculty/Chair:Fakultät 6 Architektur, Bauingenieurwesen und Stadtplanung / FG Statik und Dynamik
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