Structural Topology Optimization Using a Nodal Density-based Level Set Method

Hong Kong Polytechnic University
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Conference Proceeding
Proceedings of The 14th Asia-Pacific Vibration Conference. Dynamics for Sustainable Engineering, 2011, pp. 1144 - 1151
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This paper aims to present a nodal density-based level set method for shape and topology optimization of continuum structures. Structural boundary is implicitly embedded into constant level sets of the level set function of higher dimension, to implement shape fidelity and topology changes in time via the propagation of the discrete level set function. A point-wise nodal density field, non-negative and range-bounded, is used to parameterize the level set function with the compactly supported radial basis functions (CSRBFs) at a scattered set of points. The set of densities are used to interpolate practical material properties in finite element approximation via the standard Lagrangian shape function. CSRBFs knots are supposed to be consistent with finite element nodes only for the sake of numerical simplicity. By doing so, the discrete values of the level set function are related to practical material properties via the physically meaningful interpolation. The original more difficult shape and topology optimization is transformed to a relatively easier size optimization of the nodal densities, to which many more efficient optimization algorithms such as optimality criteria and mathematical programming methods can be directly applied. In this way, the dynamic motion of the design boundary is just a question of transporting the discrete level set function by updating the design variables of the size optimization until the optimal criteria of the structure is satisfied. Two widely studied numerical examples are applied to demonstrate the effectiveness of the proposed method.
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