TOPOLOGY OPTIMIZATION OF THIN SHELL STRUCTURES BASED ON ADAPTIVE BUBBLE METHOD

Combined with the isogeometric shell analysis (IGA) method, a new optimization design framework based on the adaptive bubble method (ABM) is proposed in this work, in order to effectively solve the topology optimization design problem of thin shell structures, and meet the high standards for the accuracy of analysis models as well as the quality of optimization results. The IGA technique has its natural advantages in thin shell analysis: on one hand, precise analysis models for thin shell structures are established with IGA, and model transformation operations and the resulting errors could therefore be avoided; on the other hand, the high-order continuity of physical fields to be solved can be guaranteed without setting the rotational degrees of freedom. Thanks to the mapping relationship related to the NURBS surface (i.e., the middle surface of thin shell), the structural topology evolution of a given shell surface can be achieved easily in the 2D regular parametric domain. In view of this, the ABM is adopted to carry out topology optimization in the parametric domain, and it contains three modules: the modeling of holes with closed B-splines (CBS), the insertion of holes via the topological derivative theory, and the fixed-grid analysis based on the finite cell method (FCM). It should be noted that holes are expressed in both parametric and implicit forms with CBS. The parametric form makes it convenient to import the structural model into the CAD system exactly. The implicit form not only facilitates the merging and separating operations of holes, but also can be well combined with the FCM which is far more convenient than trimming surface analysis (TSA). Theoretical analysis and numerical examples indicate that the proposed design framework could convert the complicated thin shell structural topology optimization problem into the simple one in the 2D domain, and optimized results with clear and smooth boundaries can be obtained with relatively few design variables.