A unified simultaneous shape and topology optimization method for multi-material laminated shell structures

Shimoda, Masatoshi; Nakayama, Hirotaka; Suzaki, Shota; Tsutsumi, Ryo

doi:10.1007/s00158-021-03039-2

Cited by 16 publications

(4 citation statements)

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“…The H 1 gradient method was proposed by Azegami and Wu as a parameter-free (or node-based) shape optimization method for linear elastic bodies, 33 and many related papers have been published including topology and size optimization. 37,38,67,68 With the proposed method, the objective functional can be reduced while maintaining the smoothness of the design variable distributions (i.e., the design velocity field and the density variation fields in this study).…”

Section: H 1 Gradient Methodsmentioning

confidence: 99%

“…The material distribution of the macrostructure is obtained by the scalar-type H 1 gradient method. [36][37][38] The H 1 gradient method for topology optimization introduces the Poisson equation. A negative sensitivity function −G P 𝛼 is applied to F I G U R E 6 Schematics of vector-type H 1 gradient method for V 𝛼 .…”

Section: Topology Optimization Of Macrostructurementioning

confidence: 99%

“…The material distribution of the macrostructure is obtained by the scalar‐type H 1 gradient method 36–38 . The H 1 gradient method for topology optimization introduces the Poisson equation.…”

Section: Sensitivity Derivation and Multiscale Optimization Systemmentioning

confidence: 99%

“…35 Then, the H 1 gradient method for topology optimization was developed, 36 and applied to various design problems with scalar design variable. 37,38 Both scalar and vector types of optimization problems are formulated as distributed-parameter optimization problems, and sensitivity functions (called gradient functions) distributed over the design domain or boundary are theoretically derived using the Lagrange multiplier method, the associated variable method, and the material derivative method. The obtained gradient function is not directly used to update the design variables, but is applied by replacing the Neumann condition.…”

Section: Introductionmentioning

confidence: 99%

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Concurrent multiscale and multi‐material optimization method for natural vibration design of porous structures

Shimoda,

Fujita,

Al Ali

et al. 2024

Numerical Meth Engineering

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This paper proposes a concurrent multiscale optimization method of macrostructure topology and microstructure shapes for porous structures, aimed at maximizing a specified natural frequency. The multi‐material distribution of the macrostructure and the shape of the microstructures are optimized by topology and shape optimization, respectively. The homogenized properties of the porous materials are calculated using the homogenization method, and the homogenized elastic tensor and density are applied to the macrostructure. The optimum distribution of the porous material in the macrostructure is determined by a multi‐material topology optimization using the generalized solid isotropic material with penalization (GSIMP) method, which is a method to obtain multi‐material topology by implementing the successive binarization. The KS (Kreisselmeier–Steinhauser) function is introduced to solve the repeated natural frequencies issue that lies in the maximization of a specified natural frequency. An area‐constrained multiscale optimization problem is formulated as a distributed‐parameter optimization problem, and the sensitivity functions are derived using the Lagrange multiplier method and the adjoint variable method. Based on the obtained sensitivity functions, the design variables are updated using the H1 gradient method (i.e., a nonparametric shape/topology optimization method). The effectiveness of the proposed method for maximizing a specified natural frequency is confirmed through 2D and 3D numerical examples, in which the influences of sub‐regions of the macrostructure and anisotropic material of the microstructures are also investigated and the results are discussed.

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