Maximum thickness control in topology optimization using an inflection-point-based geometric constraint

In density-based topology optimization, the design space is parameterized by assigning a density to each element that discretizes the domain. However, establishing a limit on the maximum attainable thickness of the structural components in this framework is non-trivial. To control the thickness, knowledge of both the central axis of the components and the elements that reside beyond a specified thickness is required for penalizing the correct design variables. This study proposes a geometric constraint-based method for exerting control over the maximum allowable thickness of the structural members in topology optimization. The central axis of the structural components is traced by identifying the inflection points of the density distribution, where the density is locally maximum. By computing the angle of the spatial gradient of the density distribution and taking their divergence, the inflection points can be reliably located in all regions of the design domain. Based on geometric information, domains of elements beyond the specified thickness from the inflection points are constructed. Then, a constraint is defined to penalize material formation only in these elements. As a result, control over the maximum thickness of the structural components can be achieved during topology optimization. The framework can also be utilized to regulate the minimum thickness of the structural components by enforcing material formation within a specified thickness. Special measures are implemented to enable the formation of junction regions within the domain while preserving the imposed thickness constraint. The proposed method is applied to topology optimization of minimum compliance and heat conduction problems to demonstrate its applicability. & COPY; 2023 Elsevier B.V. All rights reserved.