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a b s t r a c tIn most of structural optimization approaches, finite element method (FEM) has been employed for structural response analysis and sensitivity calculation. However, the approaches generally suffer certain drawbacks. In shape optimization, cumbersome parameterization of design domain is required and time consuming remeshing task is also necessary. In topology optimization, design results are generally restricted on the initial design space and additional post-processing is required for communication with CAD systems. These drawbacks are due to the use of different mathematical languages in design or geometric modeling and numerical analysis: spline basis functions are used in design and geometric modeling whereas Lagrangian and Hermitian polynomials in analysis. Isogeometric analysis is a very attractive and promising alternative to overcome the limitations resulting from the use of the conventional FEM in structural optimization. In isogeometric analysis, the same spline information such as control points and spline basis functions which represent geometries in CAD systems are also used in numerical analysis. Such unification of the mathematical languages in CAD, analysis and design optimization can resolve the issues mentioned above. In this work, structural shape optimization using isogeometric analysis is studied on 2D and shell problems. The proposed framework is extended to topology optimization using trimming techniques. New inner fronts are introduced by trimming spline curves in topology optimization. Trimmed surface analysis which was recently proposed to analyze arbitrary complex topology problems is employed for topology optimization. Some benchmarking problems in shape and topology optimization are treated using the proposed approach.

SUMMARYIn the present work, an isogeometric contact analysis scheme using mortar method is proposed. Because the isogeometric analysis is employed for contact analysis, the geometric exactness of the contact region is maintained without any loss of geometric data because of geometry approximation. Thus, the proposed method can overcome underlying shortcomings that result from the geometric approximation of contact surfaces in the conventional finite element (FE)-based contact analysis. For an isogeometric contact analysis, the schemes for treating the contact conditions and detecting the real contact surfaces are essentially required. In the proposed method, the mortar method is adopted as a nonconforming contact treatment scheme because it is expected to be in good harmony with the useful characteristics of nonuniform rational B-spline A new matching algorithm is proposed to combine the mortar method with the isogeometric analysis to guarantee consistent contact surface information with the nonuniform rational B-spline curve. The present scheme is verified by patch test and the well-known problems which have theoretical solutions such as interference fit and the Hertzian contact problem. It is shown that the problems with curved contact surfaces which are difficult to treat by conventional approaches can be easily dealt with.

SUMMARYA T-spline surface is a nonuniform rational B-spline (NURBS) surface with T-junctions, and is defined by a control grid called T-mesh. The T-mesh is similar to a NURBS control mesh except that in a T-mesh, a row or column of control points is allowed to terminate in the inner parametric space. This property of T-splines makes local refinement possible. In the present study, shell formulation based on the T-spline finite element method (FEM) is presented. Shell formulation based on NURBS or T-splines has fundamental limitations because rotational DOFs, which are necessary in the shell formulation, cannot be defined on control points. In this study, the simple mapping scheme, in which every control point is mapped into one geometric point on the surface, is employed to eliminate the limitations. Using this mapping scheme, T-spline FEM can be easily extended to the analysis of shells. The proposed shell formulation is verified through various benchmarking problems. This study is a part of the efforts by the authors for the integration of CAD-CAE processes.

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SUMMARYA new e cient meshfree method is presented in which the ÿrst-order least-squares method is employed instead of the Galerkin's method. In the meshfree methods based on the Galerkin formulation, the source of many di culties is in the numerical integration. The current method, in this respect, has di erent characteristics and is expected to remove some of the integration-related problems. It is demonstrated through numerical examples that the present formulation is highly robust to integration errors. Therefore, numerical integration can be performed with great ease and e ectiveness using very simple algorithms.