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<p>We integrate compliant mechanisms into our Thermodynamic Topology Optimization framework. By applying <span>Hamilton</span>’s principle we obtain the governing system of equations for both the physical variables and the design variable, all derived from a single <span>Hamilton</span> functional. In this context, the <span>Helmholtz</span> free energy is modeled by using <span>Betti</span>’s reciprocal theorem taking into account two load cases. The first load case defines the acting force, while the second load case determines the location where displacement should be maximized. Since a pure SIMP approach results in large intermediate material regions, we introduce a smoothed Heaviside function in order to enforce binary material states. As a consequence, the topology develops one-node connections. To prevent this, we propose a simple but effective multi-objective approach for their avoidance.</p>

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Thermodynamic Topology Optimization of compliant mechanisms including a multi-objective approach to prevent one-node connections

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月20日

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  • Sebastian Wolf,
  • Dustin R. Jantos,
  • Philipp Junker

摘要

We integrate compliant mechanisms into our Thermodynamic Topology Optimization framework. By applying Hamilton’s principle we obtain the governing system of equations for both the physical variables and the design variable, all derived from a single Hamilton functional. In this context, the Helmholtz free energy is modeled by using Betti’s reciprocal theorem taking into account two load cases. The first load case defines the acting force, while the second load case determines the location where displacement should be maximized. Since a pure SIMP approach results in large intermediate material regions, we introduce a smoothed Heaviside function in order to enforce binary material states. As a consequence, the topology develops one-node connections. To prevent this, we propose a simple but effective multi-objective approach for their avoidance.