Vol. 3, No. 7, 2008

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ISSN: 1559-3959
Plastic yield and collapse mechanism of planar lattice structures

Yihui Zhang, Zhenyu Xue, Xinming Qiu and Daining Fang

Vol. 3 (2008), No. 7, 1257–1277
Abstract

Lattice structures possess a huge potential for energy absorbing applications, and the postinitial collapse region should be analyzed with respect to design principles in such cases. This paper presents an analytical method to calculate the ultimate yield surfaces of statically indeterminate planar lattice structures, based on the assessment of static equilibrium of the unit cell before and after initial yielding. The material of the unit cell wall is assumed to be elastic, perfectly plastic. Three statically indeterminate planar lattice structures: the diamond cross cell, the statically-indeterminate square cell (SI-square cell), the new Kagome cell (N-Kagome), are analyzed. The parametric studies reveal the roles of various geometrical parameters on the performance of each structure. The SI-square cell is utilized as an example to demonstrate the evolution of structural yielding, thus providing an insight into the collapse mode of lattice structures. Furthermore, the stress-strain relationships of the SI-square and N-Kagome cells are also calculated, and the effective constitutive relations of both lattices are found to be linearly hardening, which is validated by finite element (FE) simulations.

Keywords
planar lattice structures, plasticity, yield surface, structural collapse
Milestones
Received: 3 January 2008
Revised: 30 May 2008
Accepted: 4 June 2008
Published: 1 September 2008
Authors
Yihui Zhang
Department of Engineering Mechanics FML
Tsinghua University
Beijing, 100084
China
Zhenyu Xue
Department of Engineering Mechanics FML
Tsinghua University
Beijing, 100084
China
Xinming Qiu
Department of Engineering Mechanics FML
Tsinghua University
Beijing, 100084
China
Daining Fang
Department of Engineering Mechanics FML
Tsinghua University
Beijing, 100084
China