Simultaneous node-based shape and thickness optimization of thin-walled structures using the explicit Vertex Morphing method

Node-based shape optimization has been successfully and consistently formulated via shape and sensitivity filtering methods. This work studies the union of the Vertex Morphing method, a shape parameterization technique that uses an explicit shape filtering approach, and shell thickness optimization. On this occasion, thickness variables are explicitly filtered similarly to the shape, but their filter is computed on the initial geometry configuration throughout the optimization. The problem is formulated such that both design variable types are optimized concurrently. Gradient-based algorithms are employed to solve the optimization problem, which have proven well suited for the Vertex Morphing method. Due to the different dimensionalities of the shape and thickness variables, a design variable scaling method between the two types is proposed, improving the convergence behavior without the necessity of second-order information. Academic examples and the application of a structure with industrial significance illustrate the method’s success.