Computational morphogenesis of three-dimensional free-form structures using isosurfaces based on space mapping

Abstract

This paper presented a novel computational morphogenesis method based on space mapping that employed isosurfaces to generate three-dimensional free-form continuum structures from design domains of arbitrary complexity. To achieve the interaction between form and performance, a mapping was established between the parameter space and the physical space of the design domain using B-spline volume modelling. Two assumptions were introduced to ensure that the entire parameter space has mechanical properties equivalent to those of the physical space. The isosurfaces of criterion thresholds were extracted from the entire parameter space and mapped into the physical space as the boundaries of the new design. The proposed methodology effectively addresses the limitations of the non-orthogonal body-fitted meshes for structural analysis. It comprehensively reflected the redistribution of mechanical performance and yielded an optimal design at the global-structural level. Furthermore, a geometric matrix was developed for the marching cubes algorithm, which streamlines the process of extracting isosurfaces. Numerical examples were presented to validate the method, demonstrating its ability to generate free-form structures with smooth boundaries, innovative shapes, and rational topology. The unexpected architectural form can provide valuable references for conceptual design in engineering applications.