Li, X., Mi, Y., Wang, Z.-P., Rosen, D. W., & Wang, Y. (2025). Barrier regularization for nonlinear isogeometric topology optimization with large mesh distortion. Engineering with Computers, 41(6), 4529–4548. https://doi.org/10.1007/s00366-025-02212-1
Abstract:
In topology optimization involving large nonlinear deformations, excessive mesh distortion in void regions often leads to ill-conditioned stiffness matrices and convergence failure. In isogeometric topology optimization (ITO), this issue is further exacerbated by the non-zero support of NURBS basis functions across multiple knot spans (elements): (i) distortion in voids can cause unrealistic deformation in neighboring solid regions, and (ii) conventional remedies for mesh distortion, built on C0 inter-element continuity, are not readily applicable. This paper introduces a barrier regularization method to robustly stabilize nonlinear ITO under extreme mesh distortion. The proposed regularization term penalizes the system’s potential energy at quadrature points where the Jacobian degenerates and the element tends to invert, providing a geometrically actuated and computationally simple mechanism for suppressing element irregularities. The method is first validated using isogeometric analysis on a C-shaped beam example, demonstrating improved mesh quality and enhanced numerical stability. It is subsequently applied to several benchmark problems (including a cantilever beam, a compliant mechanism, and a classical FEM- based case), exhibiting strong mesh control, robust optimization performance under diverse loading conditions, and seamless extensibility to FEM frameworks. The results verify the method’s effectiveness for large-deformation topology optimization, its broad applicability across different types of basis functions, and its ease of implementation within the standard optimization workflow.
License type:
Publisher Copyright
Funding Info:
This research / project is supported by the Agency for Science, Technology and Research - RIE2025 Manufacturing, Trade And Connectivity (MTC) Programmatic Fund - 4D Additive Manufacturing (4DAM) of Smart Structures
Grant Reference no. : M24N3b0028
Description:
This is a post-peer-review, pre-copyedit version of an article published in Engineering with Computers. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00366-025-02212-1