• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.794-801
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• 2006

The linkage framework of geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating the given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES format file which is generated by the commercial CAD systems in the present study. Numerical examples shows the rate of displacement convergence according to the paramterization methods of the NURBS surface. NURBS can generate quadric surfaces in an exact manner. It is the one of the advantages of the NURBS. A trimmed NURBS surface that is often encountered in the modeling process of the CAD systems is also presented in the present study. The performance of the developed geometrically exact shell element integrated with the exact geometric representations by the NURBS equation is compared to those of the previous reported FE shell elements in the selected benchmark problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.105-112
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• 2007

The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.37 no.5
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• pp.345-352
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• 2024

In this paper, a multipatch isogeometric analysis method is developed for a multi-connected NURB patch model and applied to geometrically exact shell element analysis. When connecting different NURBS patches, isogeometric analysis may become inaccurate due to the density of control point meshes and discontinuity between patches. To solve this problem, Nitsche's method is applied to the isogeometric analysis method to ensure the compatibility of the displacement and traction between two patches by using a potential function defined as the product of the displacement difference and traction of the two patches. The final derived governing equation is formed as a symmetric stiffness matrix from this potential function. Since the added system matrices from the compatibility boundary conditions are calculated as a boundary integral between patches, the computational cost does not increase significantly. For the positive definiteness of the system equation, appropriate stability parameters are calculated through generalized eigenvalue analysis, and the stability parameters and solution accuracy are analyzed according to the density of the integration meshes between the two patches. This multipatch isogeometric analysis method is applied to geometrically exact shell elements considering first-order shear deformation, and it is confirmed that by using Nitsche's method in this shell analysis with multiple connected patches results in improved stress continuity as well as displacement continuity between patches.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.71-78
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• 2018

This paper presents the assembling of multiple patches based on the single patch isogeometric formulation for the shear deformable shell element given in the previous study. The geometrically exact shell formulation has been accomplished with the shell theory based formulation and the generalized curvilinear coordinate system directly derived from the given NURBS geometry. For the knot elements matching across adjacent surfaces, the zero-th and first parametric continuity conditions are considered and the corresponding coupling constraints are implemented by a master-slave formulation between adjacent patches. The constraints are then enforced by a substitution method for condensation of the slave variables, thereby reducing the model size. Through numerical investigations, the important features of the first parametric continuity condition are confirmed. The performance of the multi-patch shell models is also examined comparing the rate of convergence of response coefficients for the zero and first order continuity conditions and continuity in coupling boundary between two patches is confirmed.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.10a
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• pp.69-72
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection, which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the eigenvalue problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The present shell element should serve as a powerful tool in the prediction of natural frequency and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.505-511
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• 2002

In the present study, we visualize the linkage framework between geometric modeling and shell finite element based on B-spline representation. For the development of a consistent shell element, geometrically exact shell elements based on general curvilinear coordinates is provided. The NUBS(Non Uniform B-Spline) is used to generate the general free form shell surfaces. Employment of NUBS makes shell finite element handle the arbitrary geometry of the smooth shell surfaces. The proposed shell finite element .model linked with NUBS surface representation provides efficiency for the integrated design and analysis of shell surface structures. The linkage framework can potentially provide efficient integrated approach to the shape topological design optimizations for shell structures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.229-236
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• 2004

A new three-node triangular shell element based on higher order zig-zag theory is developed for laminated composite shells with multiple delaminations. The present higher order zig-zag shell theory is described in a general curvilinear coordinate system and in general tensor notation. All the complicated curvatures of surface including twisting curvatures can be described in an exact manner in the present shell element because this element is based on geometrically exact surface representation. The displacement field of the proposed finite element includes slope of deflection. which requires continuity between element interfaces. Thus the nonconforming shape function of Specht's three-node triangular plate bending element is employed to interpolate out-of-plane displacement. The present element passes the bending and twisting patch tests in flat surface configurations. The developed element is evaluated through the buckling problems of composite cylindrical shells with multiple delaminations. Through the numerical examples it is demonstrated that the proposed shell element is efficient because it has minimal degrees of freedom per node. The accuracy of the present element is demonstrated in the prediction of buckling loads and buckling modes of shells with multiple delaminations. The present shell element should serve as a powerful tool in the prediction of buckling loads and modes of multi-layered thick laminated shell structures with arbitrary-shaped multiple delaminations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.317-324
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• 2004

Shape design optimization of shell structure is implemented on a basis of integrated framework of geometric modeling and finite element analysis which is constructed on the geometrically exact shell theory. This shell theory enables more accurate and robust analysis for complicated shell structures, and it fits for the nature of B-spline function which Is popular modeling scheme in CAD field. Shape of laminated composite shells is optimized through genetic algorithm and sequential linear programming, because there ire numerous optima for various configurations, constraints, and searching paths. Sequential adaptation of global and local optimization makes the process more efficient. Two different optimized results of laminated composite shell structures to minimize strain energy are shown for different layup sequence.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.301-308
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• 2005

In this study, we implement a framework that directly links a general tensor-based shell finite element to NURBS geometric modeling. Generally, in CAD system the surfaces are represented by B-splines or non-uniform rational B-spline(NURBS) blending functions and control points. Here, NURBS blending functions are composed by two parameters defined in local region. A general tensor-based shell element also has a two-parameter representation in the surfaces, and all the computations of geometric quantities can be performed in local surface patch. Naturally, B-spline surface or NURBS function could be directly linked to the shell analysis routine. In our study, we use NLib(NURBS libraray) to generate NURBS for shell finite analysis. The NURBS can be easily generated by interpolating or approximating given set of data points through NLib.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.181-190
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• 2007

The linkage framework of surface geometric modeling based on the NURBS and shell finite element analysis is developed in this study. In the geometrically exact shell finite element analysis, the accuracy of the analysis strongly depends upon the accurate computation of the surface geometric quantities. Therefore if we obtain the necessary geometric quantities from the NVRBS surface equation, it's possible to construct the effective linkage framework of surface modeling in the CAD systems and shell finite element analysis using geometrically exact shell finite element. Besides, the linkage framework can be applied to the analysis of general and complex surfaces as well as simple surfaces. In this study, the shell surfaces are generated by interpolating given set of data points based on the NURBS surfaces. These data points usually can be obtained from surface scanning. But the representations of the generated NURBS surface are not same to one another. The accuracy depends on the chosen parameterization methods used in NURBS. Therefore, it is needed to select the suitable parameterization method according to the geometry of the surfaces. To verify the performance and accuracy of our developed linkage framework, we solve several well-known benchmark problems and assess the performance of the developed method.