Isogeometric-analysis-based stiffness spreading method for truss layout optimization

Abstract

A novel isogeometric analysis-based stiffness spreading method (IGA-based SSM) is proposed for the truss layout optimization design within a continuum, where the topology, geometry, and cross-sectional areas of the truss elements can be simultaneously optimized. The IGA-based SSM based on energy conservation is employed to obtain the spreading stiffness matrices of the truss elements that are embedded in weak IGA background grids. The IGA background grids are constructed using high-order continuous isogeometric elements that can overcome the limitation of discontinuous sensitivity derived by traditional C0 elements. Because the sensitivity required for the optimization can be obtained analytically, gradient-based optimization algorithms can be easily implemented. To verify the effectiveness of the IGA-based SSM for truss layout optimization design, typical illustrative examples are used, considering the compliance minimization optimization problem. The proposed method can provide a continuous and smooth sensitivity field and overcome the numerical inaccuracy caused by interpolation methods, such as the radial basis function. The different background mesh sizes, initial layouts, and orders p of nonuniform rational B-splines basis functions are investigated in truss layout optimization. The results indicate that the selection of the appropriate background mesh size can avoid the problem of discontinuous truss connections, C1-continuous isogeometric elements can provide better optimization designs with a lower computational cost, and the proposed method can provide a clear layout for different initial layouts. Moreover, the spatial truss layout optimization problem and the min–max displacement optimization problem are also studied to further verify the effectiveness of the proposed method. Finally, the proposed method is extended to solve the concentrated force diffusion problem that widely exists in the interstage adapters of launch vehicles by adding the variance constraint of reaction forces. The results indicate that the proposed method can obtain required concentrated force diffusion results with reasonable stiffness distributions.