<p>Topology optimization has become an essential tool for achieving lightweight, high-performance, and functionally efficient structures in modern engineering design. Although isogeometric topology optimization provides a promising pathway for integrating design, simulation, and optimization, existing implementations often suffer from mesh-dependence, high computational cost, and incompatibility with existing topology optimization code. In this paper, we propose an isogeometric topology optimization framework based on Bézier extraction, referred to as E-ITO–SIMP, which integrates isogeometric analysis with the solid isotropic material with penalization approach. The non-uniform rational B-spline (NURBS) basis functions are expressed as a linear combination of Bernstein polynomials, and the design variables are assigned to elements rather than control points. This setting significantly reduces the computational cost of sensitivity analysis and allows seamless integration into existing topology optimization code. Furthermore, a systematic comparative study is conducted to evaluate convergence behavior, mesh-dependence, computational efficiency, and robustness, supported by some benchmark cases including multiple-load, 2D crack, and mechanical–electrical coupling problems. Numerical results demonstrate that the presented E-ITO–SIMP can double computational efficiency compared with traditional approaches and reduce the number of iterations by approximately 15%, while producing mesh-independent and physically consistent topology. These findings highlight the potential of E-ITO–SIMP for advancing integrated isogeometric design and optimization.</p>

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Robust and Efficient Isogeometric Topology Optimization via Bézier Elements for Continuum Structures

  • Yajun Cao,
  • Junjun Che,
  • Gang Xu

摘要

Topology optimization has become an essential tool for achieving lightweight, high-performance, and functionally efficient structures in modern engineering design. Although isogeometric topology optimization provides a promising pathway for integrating design, simulation, and optimization, existing implementations often suffer from mesh-dependence, high computational cost, and incompatibility with existing topology optimization code. In this paper, we propose an isogeometric topology optimization framework based on Bézier extraction, referred to as E-ITO–SIMP, which integrates isogeometric analysis with the solid isotropic material with penalization approach. The non-uniform rational B-spline (NURBS) basis functions are expressed as a linear combination of Bernstein polynomials, and the design variables are assigned to elements rather than control points. This setting significantly reduces the computational cost of sensitivity analysis and allows seamless integration into existing topology optimization code. Furthermore, a systematic comparative study is conducted to evaluate convergence behavior, mesh-dependence, computational efficiency, and robustness, supported by some benchmark cases including multiple-load, 2D crack, and mechanical–electrical coupling problems. Numerical results demonstrate that the presented E-ITO–SIMP can double computational efficiency compared with traditional approaches and reduce the number of iterations by approximately 15%, while producing mesh-independent and physically consistent topology. These findings highlight the potential of E-ITO–SIMP for advancing integrated isogeometric design and optimization.