Through recent advances in modern production techniques, particularly in the field of additive manufacturing, new previously unthinkable geometries have become feasible. This vast realm of new possibilities cannot be adequately addressed by classical methods in engineering, which is why numerical design techniques are becoming more and more valuable. In this context, this work aims to present concepts that exploit the emerging possibilities and facilitate numerical optimization. The numerical optimization is built on a microstructured grid, where the geometry is constructed by means of functional composition between splines [1], resulting in a regular patern of building blocks. Here, a macro-spline defines the outer contour, a micro-geometry sets the individual tiles and a parameter-spline controls the local parametrization of the microstructure, e.g., acting on the thickness or material density in a specific region [2]. This approach opens up a broad design space, where the adaptivity of the resultong microstructure can be easily extended by increasing the number of control variables in the parameters-spline via h- or p-refinement.