Isogeometric sizing and shape optimization of 3D beams and lattice structures at large deformations

Abstract A computational method for optimizing the shape of centerline curve and spatial variation geometric material sizing parameters cross-sections elastic, 3-dimensional beams beam structures subject to large deformations is presented in this work. The approach based on concept isogeometric analysis, i.e., representation geometry discretization numerical solution using spline functions. Here, mixed collocation methods are used discretize geometrically exact 3D model. These representations extended parameterization design variables, which initial curves beams, as well cross-sectional properties, may be varying along axis can functionally graded through cross-sections. To tailor mechanical deformation behavior a or structure, nonlinear optimization problem formulated solved gradient-based methods. For purpose, all required gradients sensitivities derived analytically. potential holistic demonstrated application tailoring elastic metamaterials lattice structures, 4D printing multi-material laminate beams.