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国际多尺度计算工程期刊
影响因子: 1.016 5年影响因子: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.v4.i4.20
pages 429-444

Multiscale Modeling for Planar Lattice Microstructures with Structural Elements

Isao Saiki
Department of civil Engineering, Tohoku University, Sendai 980-8579, Japan
Ken Ooue
Kawada Construction Co., Ltd, Tokyo 114-8505, Japan
Kenjiro Terada
Department of civil Engineering, Tohoku University, Sendai 980-8579, Japan
Akinori Nakajima
Department of Civil Engineering, Utsunomiya University, Utsunomiya 321-8585, Japan

ABSTRACT

Formulations of linear and nonlinear multiscale analyses for media with lattice periodic microstructures based on the homogenization theory are proposed. For continuum media, the conventional homogenization theory leads to boundary value problems of continuum for both micro- and macroscales. However, it is rational to discretize lattice microstructures, such as cellular solids, by frame elements since they consist of slender members. The main difficulty in utilizing structural elements, such as frame elements, for microscale problems is due to the inconsistency between the kinematics assumed for the frame elements and the periodic displacement field for the microscale problem. In order to overcome this difficulty, we propose a formulation that does not employ the periodic microscale displacement, but the total displacement, including the displacement due to uniform deformation as well as periodic deformation, as the independent variable of the microscale problem. Some numerical examples of cellular solids are provided to show both the feasibility and the computational efficiency of the proposed method.


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