Multimaterial topology optimization often leads to members containing composite materials. However, in some instances, designers might be interested in using only one material for each member. Therefore, we propose an...
详细信息
Multimaterial topology optimization often leads to members containing composite materials. However, in some instances, designers might be interested in using only one material for each member. Therefore, we propose an algorithm that selects a single preferred material from multiple materials per overlapping set. We develop the algorithm, based on the evaluation of both the strain energy and the cross-sectional area of each member, to control the material profile (ie, the number of materials) in each subdomain of the final design. This algorithm actively and iteratively selects materials to ensure that a single material is used for each member. In this work, we adopt a multimaterial formulation that handles an arbitrary number of volume constraints and candidate materials. To efficiently handle such volume constraints, we employ the ZPR (Zhang-Paulino-Ramos) design variable update scheme for multimaterial optimization, which is based upon the separability of the dual objective function of the convex subproblem with respect to Lagrange multipliers. We provide an alternative derivation of this update scheme based on the Karush-Kuhn-Tucker conditions. Through numerical examples, we demonstrate that the proposed material selection algorithm, which can be readily implemented in multimaterial optimization, along with the ZPR update scheme, is robust and effective for selecting a single preferred material among multiple materials.
Topology optimization is a practical tool that allows for improved structural designs. This thesis focuses on developing both theoretical foundations and computational algorithms for topology optimization to effective...
详细信息
Topology optimization is a practical tool that allows for improved structural designs. This thesis focuses on developing both theoretical foundations and computational algorithms for topology optimization to effectively and efficiently handle many materials, many constraints, and many load cases. Most work in topology optimization is restricted to linear material with limited constraint settings for multiple materials. To address these issues, we propose a general multi-material topology optimization formulation with material nonlinearity. This formulation handles an arbitrary number of materials with flexible properties, features freely specified material layers, and includes a generalized volume constraint setting. To efficiently handle such arbitrary constraints, we derive an update scheme, named ZPR, that performs robust updates of design variables associated with each constraint independently. The derivation is based on the separable feature of the dual problem of the convex approximated primal subproblem with respect to the Lagrange multipliers, and thus the update of design variables in each constraint only depends on the corresponding Lagrange multiplier. This thesis also presents an efficient filtering scheme, with reduced-order modeling, and demonstrates its application to 2D and 3D topology optimization of truss networks. The proposed filtering scheme extracts valid structures, yields the displacement field without artificial stiffness, and improve convergence, leading to drastically improved computational performance. To obtain designs under many load cases, we present a randomized approach that efficiently optimizes structures under hundreds of load cases. This approach only uses 5 or 6 stochastic sample load cases, instead of hundreds, to obtain similar optimized designs (for both continuum and truss approaches). Through examples using Ogden-based, bilinear, and linear materials, we demonstrate that proposed topology optimization frameworks with the ne
暂无评论