Dynamic layout optimization of truss subjected to a time-dependent load by isogeometric-analysis-based stiffness spreading method

• An efficient isogeometric analysis based stiffness spreading method is proposed for transient dynamic layout optimization of truss • A POD-Incremental SVD based reduced order model strategy is proposed for isogeometric transient dynamic analysis of a truss structure • Primal-dual reduced-order modeling of truss layout optimization is provided • Several large-scale cases demonstrate the effectiveness of the proposed method An innovative and efficient truss layout optimization framework under the transient load is proposed based on the isogeometric analysis-based stiffness spreading method (IGA-based SSM), integrated with the proper orthogonal decomposition (POD). The IGA-based SSM is featured with a small number of truss elements independently moving in weak IGA background grids to represent the truss layout during optimization, without considering the connectivity of the truss elements, and hence a low computational cost due to few design variables. We use the IGA-based SSM to spread the stiffness, mass and damping matrices of a truss element to weak IGA background grids, according to energy conservation. As such, its shape and size can be simultaneously optimized during dynamic layout optimization of truss. For achieving additional savings in computational cost, the POD procedure with incremental singular value decomposition (SVD) is leveraged to reduce the primal and adjoint equations. To mitigate the consistent error in the sensitivity computation, the reduced adjoint equation is constructed based on the “discretize-then-differentiate” approach. Moreover, we tackle the computational cost and scalability of the reduced order model (ROM) learning and updating phases. Consequently, we can attain almost the same truss optimization results as the full order model (FOM), in addition to achieving high computational speed with the speedup ratio of at least 2.02 referring to FOM, which are verified by 2D and 3D benchmark problems.