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Node-based shape optimization methods like Vertex Morphing use every node of the surface mesh as design variables. The method's key advantages are the minimal effort for problem setup and the resulting largest possible design space that allows finding new and innovative shapes. Due to a large number of design variables, the application of gradient-based optimization methods becomes mandatory, and adjoint sensitivity analysis is the preferred way for efficient computation of the shape gradients.For some industrial applications, it is necessary to restrict the large design freedom in some sense, for example by limiting the geometric design space. In recent work, nodal nonpenetration constraints have been successfully applied in the context of Vertex Morphing, resulting in a potentially large number of active constraints. Aggregation methods are commonly used to reduce the number of constraints in the optimization problem and are investigated here to combine nodal geometric constraints in a single global constraint function.

There is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an existing design and proposing or ideally generating an optimal design using numerical optimization. In this context, efficient and robust realization of such a framework for numerical shape optimization is of prime importance. Another requirement of such a framework is modularity, such that the shape optimization can involve different physics. This requires that different physics solvers should be handled in black-box nature. The current contribution discusses the conceptualization and applications of a general framework for numerical shape optimization using the vertex morphing parametrization technique. We deal with both 2D and 3D shape optimization problems, of which 3D problems usually tend to be expensive and are candidates for special attention in terms of efficient and high-performance computing. The paper demonstrates the different aspects of the framework, together with the challenges in realizing them. Several numerical examples involving different physics and constraints are presented to show the flexibility and extendability of the framework.

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