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In the realm of sustainable construction within a circular economy, the study of demountable buildings garners significant interest. Achieving the full potential of reusing materials from disassembled structures demands innovative assembly methods surpassing conventional fasteners like nails. Although traditional joinery has addressed this challenge to some extent, it faces design limitations. Modern digital fabrication technologies, such as CNC milling and additive manufacturing, have expanded the horizons for manufacturable assemblies. This paper builds upon prior research to introduce a flexible method for crafting 2D assemblies adaptable to various geometric assumptions. It offers two contributions. Firstly, it provides a versatile numerical model for analyzing the mechanical properties of diverse designs, uncovering novel assemblies with superior mechanical performance compared to traditional configurations. Secondly, it presents an optimization approach enabling precise control over assembly and disassembly of imperfect parts by optimizing joint geometry. By integrating advanced fabrication techniques, adaptable design methods, and mechanical analysis, this research paves the way for the development of sustainable and mechanically efficient demountable buildings. [Display omitted] • A numerical model to systematically evaluate the mechanical behavior of assemblies with strange-looking geometrical features. • A method to robustly optimise assemblies so that they can be (dis)assembled even if the parts have imperfect geometries. [ABSTRACT FROM AUTHOR]