Multi-material topology optimization considering interface behavior via XFEM and level set method

Self Cite

Summary The velocity field level‐set topological shape optimization method combines the implicit representation in the standard level‐set method and the capabilities of general mathematical programming algorithms in handling multiple constraints and additional design variables. The key concept is to construct the normal velocity field using basis functions and the velocity design variables at specified points (referred to as velocity knots) in the entire design domain. In this study, the velocity design variables are decoupled from the level‐set grid points. Making use of this property, we can adaptively change the arrangement of the velocity knots as the structural boundary evolves. This provides more design freedom in the optimization and allows for a significant reduction in the number of design variables. Several numerical examples in two‐ and three‐dimensional design domains are presented to demonstrate the robustness and efficiency of the proposed method. We also show that changing the number of velocity knots may implicitly exert certain control on topological complexity and length scale.

Section: Introductionmentioning

confidence: 99%

Velocity field level‐set method for topological shape optimization using freely distributed design variables

Wang

Kang

Liu

2019

Self Cite

“…Wang and Wang introduced the colour level set method, which combines multiple level set equations in a principle similar to mixing colours to create new colours . Liu et al combined the colour level set method with the extended FE method to model separation at dissimilar material interfaces in MMTO and were able to produce results that favorably loaded dissimilar material interfaces in compression rather than in tension . Hard‐kill approaches include heuristic schemes developed by Ramani where a user‐defined proportion of elements are changed to another material after calculating and ranking the “pseudo‐sensitivities” of every element in each iteration …”

Section: Introductionmentioning

confidence: 99%

“…20 Liu et al combined the colour level set method with the extended FE method to model separation at dissimilar material interfaces in MMTO and were able to produce results that favorably loaded dissimilar material interfaces in compression rather than in tension. 21 Hard-kill approaches include heuristic schemes developed by Ramani where a user-defined proportion of elements are changed to another material after calculating and ranking the "pseudo-sensitivities" of every element in each iteration. 22,23 Topology optimization can be used to determine not only the optimal topology of multiple components but also the optimal quantity and distribution of joints in a multicomponent design.…”

Section: Introductionmentioning

confidence: 99%

Multimaterial multijoint topology optimization

Woischwill

Kim

2018

Summary In this paper, a methodology that solves multimaterial topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials is proposed. Multimaterial topology optimization has become a popular design optimization technique since the enhanced design freedom typically leads to superior solutions; however, the conventional assumption that all elements are perfectly fused together as a single piece limits the usefulness of the approach since the mutual dependency between optimal multimaterial geometry and optimal joint design is not properly accounted for. The proposed methodology uses an effective decomposition approach to both determine the optimal topology of a structure using multiple materials and the optimal joint design using multiple joint types. By decomposing the problem into two smaller subproblems, gradient‐based optimization techniques can be used and large models that cannot be solved with nongradient approaches can be solved. Moreover, since the joining interfaces are interpreted directly from multimaterial topology optimization results, the shape of the joining interfaces and the quantity of joints connecting dissimilar materials do not need to be defined a priori. Three numerical examples, which demonstrate how the methodology optimizes the geometry of a multimaterial structure for both compliance and cost of joining, are presented.

“…Later, Gao and Zhang proposed a modified formulation for three materials plus void elements . Another widely adopted method for multimaterial representation is the multimaterial level‐set method in which a unique level‐set function is optimized for each material phase …”

Section: Introductionmentioning

confidence: 99%

Multimaterial topology design for optimal elastic and thermal response with material‐specific temperature constraints

Kang

James

2018

Summary We present an original method for multimaterial topology optimization with elastic and thermal response considerations. The material distribution is represented parametrically using a formulation in which finite element–style shape functions are used to determine the local material properties within each finite element. We optimize a multifunctional structure that is designed for a combination of structural stiffness and thermal insulation. We conduct parallel uncoupled finite element analyses to simulate the elastic and thermal response of the structure by solving the two‐dimensional Poisson problem. We explore multiple optimization problem formulations, including structural design for minimum compliance subject to local temperature constraints so that the optimized design serves as both a support structure and a thermal insulator. We also derive and implement an original multimaterial aggregation function that allows the designer to simultaneously enforce separate maximum temperature thresholds based upon the melting point of the various design materials. The nonlinear programming problem is solved using gradient‐based optimization with adjoint sensitivity analysis. We present results for a series of two‐dimensional example problems. The results demonstrate that the proposed algorithm consistently converges to feasible multimaterial designs with the desired elastic and thermal performance.