Geometric Topology Optimization Under Residual Stresses For Machining
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The manufacturing of large monolithic metallic parts is sometimes subject to significant distortions during machining. These deformations arise from the redistribution of Bulk Residual Stresses (BRS) initially present in the forged or rolled raw material. Such distortions may cause critical interfaces to deviate from geometric tolerances, necessitating additional operations to ensure assembly. This work proposes a topology optimization methodology aimed at designing large monolithic structures that are intrinsically robust to machining distortions. The approach relies on the Moving Morphable Voids (MMV) method, which projects explicit geometries defined by closed B-splines onto a fixed finite element mesh. To guarantee the assembly of the part, a novel ”tolerance containment” constraint is formulated. This constraint ensures that assembly interfaces remain, after the relaxation of residual stresses, within a prescribed spatial tolerance zone (e.g., ±0.2 mm). The optimization problem addresses design-dependent internal loads using an interpolated force model to avoid numerical instabilities. The problem is solved using the Method of Moving Asymptotes (MMA) with analytical sensitivity calculation via the adjoint method. Results on a simplified large stiffened panel demonstrate that the optimizer successfully distributes material to counteract the principal deformation modes induced by internal stresses. This approach effectively ensures that assembly interfaces respect tolerance constraints where intuitive designs fail, paving the way for automated ”design for manufacturing” of large machined components.
