Adaptive strut cross-section design of lattice structure incorporating direct stiffness method with a geometric stiffness matrix

Abstract

This study introduces an adaptive analytical framework for designing strut cross-sections in lattice structures using the direct stiffness method while explicitly considering lateral deformation effects. The model incorporates a geometric stiffness matrix to capture axial load-induced lateral instability and simulate displacement-controlled compression to generate load-displacement responses. Mechanical responses were evaluated for three representative unit cell topologies (octet-truss, Kelvin, and hybrid body-centered cubic-cubic) under uniaxial quasi-static compressive load by varying elliptical aspect ratios assigned to orientation-specific strut cross-sections (horizontal, diagonal, and vertical). The framework demonstrates that the mechanical influence of cross-sectional geometry is highly dependent on strut orientation and nodal connectivity. Based on this positional dependency, aspect ratios tailored to individual strut orientations were derived and combined within single unit cells, forming lattice configurations with different cross-section geometries on each strut. Experimental validation using lattice cube specimens fabricated via laser powder bed fusion confirmed the analytical predictions, with deviations generally within approximately 10%. The proposed approach enables explicit and systematic exploration of geometry-performance relationships in lattice structures, supporting refined cross-sectional design strategies to enhance the mechanical behaviour of additively manufactured components.