Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 100215

100215 - Strength-Based Topology Optimization Considering Multiple Materials 

Composite structures are extensively used across various engineering fields owing to their unique mechanical and physical properties enabled by material heterogeneity. To harness these properties in stress-constrained topology optimization, the incorporation of multiple materials is necessary. Established stress-constrained topology optimization studies typically assume the same yield criterion, e.g., von-Mises, for all the candidate materials while vary their stiffness and strengths. Yet, the capability of accounting for distinct yield/failure criteria in different candidate materials is crucial for many practical applications, as many real-world composite structures are made of dissimilar materials governed by distinct yield/failure criteria. For instance, in reinforced concrete structures, the steel rebars are governed by a hydrostatically independent yield criterion, e.g., von-Mises, whereas the concrete is controlled by a hydrostatically dependent yield criterion, e.g., Drucker-Prager. However, this capability of simultaneously incorporating dissimilar material strength information has been rarely explored and is currently underdeveloped in multimaterial stress-constrained topology optimization. To open up the full design capability for composite structures, this work puts forward a multimaterial stress-constrained topology optimization formulation capable of accounting for multiple candidate materials with distinct elastic properties (i.e., stiffness), strengths, and yield/failure criteria simultaneously. This is achieved by the introduction of a novel yield function interpolation scheme, which effectively encodes various yield functions of different forms into the multimaterial design parameterization. An Augmented Lagrangian algorithm, which preserves the local nature of the stress constraints, is employed to efficiently solve the optimization problem with many constraints.
Using this proposed framework, we numerically investigate several two-dimensional (2D) and three-dimensional (3D) design problems that aim to minimize the total structural volume. The obtained optimized composite structures exhibit unconventional distributions of both geometry and material phases. The optimized designs do not only prevent local material failure by addressing strong geometrical singularity such as re-entrant corners through topological morphing, but also reveal several fundamental advantages provided by heterogeneity in stiffness, strength, and yield/failure criteria. These advantages from material heterogeneity include the enlarged design space achieved by the inclusion of different yield criteria, the stress deconcentration effect enabled by stiffness and strength heterogeneity, and the exploitation of diverse tension-compression symmetry/asymmetry in both hydrostatically independent and dependent materials. The unique advantages of dissimilar candidate materials are comprehensively and effectively harnessed by the proposed formulation to generate optimized composite designs with significantly improved structural efficiency and reduced structural volume relative to single-material structures. The findings facilitate the discovery of novel composite structure designs with superior performance across various fields.

Presenting Author: Rahul Dev Kundu University of Illinois at Urbana-Champaign

Presenting Author Biography: Rahul Dev Kundu is a Ph.D. student at the Department of Civil and Environmental Engineering at the University of Illinois at Urbana-Champaign. His research interest focuses on topology optimization involving material heterogeneity for strong and sustainable structures.

Authors:

Rahul Dev Kundu University of Illinois at Urbana-Champaign
Weichen Li University of Illinois at Urbana-Champaign
Xiaojia Shelly Zhang University of Illinois at Urbana-Champaign