TY - JOUR

T1 - Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process

AU - Takezawa, Akihiro

AU - To, Albert C.

AU - Chen, Qian

AU - Liang, Xuan

AU - Dugast, Florian

AU - Zhang, Xiaopeng

AU - Kitamura, Mitsuru

N1 - Funding Information:
This work was partially supported by the JSPS KAKENHI ( 18H01351 , 18KK0412 and 19H05625 ) and the JST , A-Step, Seeds development type ( JPMJTR192A ). Partial financial support from the U.S. National Science Foundation ( CMMI-1634261 ) is also gratefully acknowledged.
Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2020/10/1

Y1 - 2020/10/1

N2 - Compensation of the thermal distortion that occurs during the fabrication process is an important issue in the field of metal additive manufacturing. Considering the problem in forming a lattice structure inside an object to reduce the thermal distortion, we developed a lattice volume fraction distribution optimization method. Assuming that the linear elastic problem is solved using the finite element method (FEM), an inherent strain method applying a layer-by-layer process utilizing the element activation during the FEM is formed as a recurrence relation, and the sensitivity of an objective function is derived based on the adjoint method. The unit lattice shape is a simple cube with a cube or a sphere-shaped air hole, and its distribution is optimized by considering the minimum thickness of the wall surrounding it as a design variable. The effective stiffness tensor of the lattice is derived using a homogenization method. The functions of the effective properties with respect to the design variables are approximated through polynomial functions. The optimization problem is formulated as an unconstrained minimization problem. The design variables are optimized using the method of moving asymptotes. Herein, the validity of the proposed method is discussed based on quasi two-dimensional and three-dimensional numerical studies including a re-analysis through full-scale thermo-mechanical analysis.

AB - Compensation of the thermal distortion that occurs during the fabrication process is an important issue in the field of metal additive manufacturing. Considering the problem in forming a lattice structure inside an object to reduce the thermal distortion, we developed a lattice volume fraction distribution optimization method. Assuming that the linear elastic problem is solved using the finite element method (FEM), an inherent strain method applying a layer-by-layer process utilizing the element activation during the FEM is formed as a recurrence relation, and the sensitivity of an objective function is derived based on the adjoint method. The unit lattice shape is a simple cube with a cube or a sphere-shaped air hole, and its distribution is optimized by considering the minimum thickness of the wall surrounding it as a design variable. The effective stiffness tensor of the lattice is derived using a homogenization method. The functions of the effective properties with respect to the design variables are approximated through polynomial functions. The optimization problem is formulated as an unconstrained minimization problem. The design variables are optimized using the method of moving asymptotes. Herein, the validity of the proposed method is discussed based on quasi two-dimensional and three-dimensional numerical studies including a re-analysis through full-scale thermo-mechanical analysis.

KW - Additive manufacturing

KW - Inherent strain method

KW - Lattice density optimization

KW - Recurrence relation

KW - Sensitivity analysis

KW - Thermal distortion

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U2 - 10.1016/j.cma.2020.113231

DO - 10.1016/j.cma.2020.113231

M3 - Article

AN - SCOPUS:85087908476

SN - 0045-7825

VL - 370

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 113231

ER -