On the design of multimaterial structural topologies using Integer Programming

This paper presents a framework for the discrete design of optimal multimaterial structural topologies using integer design variables and mathematical programming. The structural optimization problems: compliance minimization subject to mass constraint, and mass minimization subject to compliance co...

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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 384; S. 114000
Hauptverfasser: Sivapuram, Raghavendra, Picelli, Renato, Yoon, Gil Ho, Yi, Bing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.10.2021
Elsevier BV
Schlagworte:
Binary variables
Extended SIMP
Hydrostatic pressure
Inactive constraint
Integer programming
Interpolation
Iterative methods
Loads (forces)
Mathematical programming
Modulus of elasticity
Multimaterial
Optimization
Pressure dependence
Pressure loads
Sensitivity
Structural design
Topology optimization
Truncation error
Truncation errors
Multimaterial
Extended SIMP
Pressure loads
Binary variables
Inactive constraint
Truncation error
ISSN:0045-7825, 1879-2138
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Zusammenfassung:This paper presents a framework for the discrete design of optimal multimaterial structural topologies using integer design variables and mathematical programming. The structural optimization problems: compliance minimization subject to mass constraint, and mass minimization subject to compliance constraint are used to design the multimaterial topologies in this work. The extended SIMP interpolation is used to interpolate the different materials available for structural design, and the material phases in each element are represented using binary design variables, one variable per available material. The Topology Optimization of Binary Structure (TOBS) method (Sivapuram and Picelli, 2018) is employed, wherein the nonlinear objective/constraint functions of optimization are sequentially approximated (herein, linearized) to obtain a sequence of Integer Linear Programs (ILPs). A novel truncation error-regulating constraint in terms of the Young’s moduli of the elements is introduced to maintain the sequential approximations valid, by restricting large changes in successive structural topologies. A commercial branch-and-bound solver is used to solve the integer subproblems yielding perfectly binary solutions which guarantee discrete structural topologies with clear material interfaces at each iteration. Adjoint sensitivities are computed to generate the integer subproblems, and the sensitivities are filtered using a conventional mesh-independent sensitivity filter. Few examples show the design of multimaterial structures in the presence of design-dependent loads: hydrostatic pressure loads and self-weight loads. This work also demonstrates through few examples, convergence of optimal multimaterial topologies at inactive constraint values when different type of loadings simultaneously act on the structure. •Integer programming is used in multimaterial structural optimization.•The optimized structures have clear boundaries and clear material interfaces.•A novel truncation error-regulating constraint is proposed for multimaterial problems.•Examples include models with design-dependent pressure and self-weight loads.•Convergence at inactive mass constraint values is demonstrated through few examples.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114000