Smooth size design for the natural frequencies of curved Timoshenko beams using isogeometric analysis

Curved thick beams with smoothly variable cross-section size are very common in practical engineering problems. Designing the variable size based on the traditional finite element methods often leads to non-smooth solutions. To guarantee the smoothness of size distribution, an isogeometric analysis (IGA)-based design approach is proposed in this work to optimize the cross-section size of curved Timoshenko beams for natural frequencies. Due to the geometric exactness and high-order continuity of IGA, there is high accuracy of natural frequency prediction and sensitivity analysis for design optimization. It is found that small numbers of design variables lead to parameterization-dependent solutions, while large numbers of design variables induce design fluctuation. To avoid the undesirable design fluctuation, a stability transformation method-based K-S aggregation constraint scheme is proposed to regularize the size distribution and also achieve the stable convergence of optimal solutions. Multiple design studies including the deterministic and reliability-based optimization problems are performed to demonstrate the applicability and effectiveness of the proposed approach.