Initial tension in randomly disordered periodic lattices

E. G. Karpov; N. G. Stephen; Wing Kam Liu

doi:10.1016/S0020-7683(03)00290-7

Initial tension in randomly disordered periodic lattices

E. G. Karpov^*, N. G. Stephen, Wing Kam Liu

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

This paper is concerned with probabilistic analysis of initial member stress in geometrically imperfect regular lattice structures with periodic boundary conditions. Spatial invariance of the corresponding statistical parameters is shown to arise on the Born-von Kármán domains. This allows analytical treatment of the problem, where the parameters of stress distribution are obtained in a closed form. Several benchmark problems with beam- and plate-like lattices are considered, and the results are verified by the direct Monte-Carlo simulations. Behaviour of the standard deviation as a function of lattice repetitive cell number is investigated, and dependence on the lattice structural redundancy is pointed out.

Original language	English (US)
Pages (from-to)	5371-5388
Number of pages	18
Journal	International Journal of Solids and Structures
Volume	40
Issue number	20
DOIs	https://doi.org/10.1016/S0020-7683(03)00290-7
State	Published - Oct 2003

Keywords

Initial tension
Lack of fit
Periodic lattice
Repetitive structure

ASJC Scopus subject areas

Modeling and Simulation
Materials Science(all)
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Applied Mathematics

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@article{178c670d98bc4ae4b2266290fc5c3085,

title = "Initial tension in randomly disordered periodic lattices",

abstract = "This paper is concerned with probabilistic analysis of initial member stress in geometrically imperfect regular lattice structures with periodic boundary conditions. Spatial invariance of the corresponding statistical parameters is shown to arise on the Born-von K{\'a}rm{\'a}n domains. This allows analytical treatment of the problem, where the parameters of stress distribution are obtained in a closed form. Several benchmark problems with beam- and plate-like lattices are considered, and the results are verified by the direct Monte-Carlo simulations. Behaviour of the standard deviation as a function of lattice repetitive cell number is investigated, and dependence on the lattice structural redundancy is pointed out.",

keywords = "Initial tension, Lack of fit, Periodic lattice, Repetitive structure",

author = "Karpov, {E. G.} and Stephen, {N. G.} and {Kam Liu}, Wing",

note = "Funding Information: This research was supported by the National Science Foundation.",

year = "2003",

month = oct,

doi = "10.1016/S0020-7683(03)00290-7",

language = "English (US)",

volume = "40",

pages = "5371--5388",

journal = "International Journal of Solids and Structures",

issn = "0020-7683",

publisher = "Elsevier Limited",

number = "20",

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TY - JOUR

T1 - Initial tension in randomly disordered periodic lattices

AU - Karpov, E. G.

AU - Stephen, N. G.

AU - Kam Liu, Wing

N1 - Funding Information: This research was supported by the National Science Foundation.

PY - 2003/10

Y1 - 2003/10

N2 - This paper is concerned with probabilistic analysis of initial member stress in geometrically imperfect regular lattice structures with periodic boundary conditions. Spatial invariance of the corresponding statistical parameters is shown to arise on the Born-von Kármán domains. This allows analytical treatment of the problem, where the parameters of stress distribution are obtained in a closed form. Several benchmark problems with beam- and plate-like lattices are considered, and the results are verified by the direct Monte-Carlo simulations. Behaviour of the standard deviation as a function of lattice repetitive cell number is investigated, and dependence on the lattice structural redundancy is pointed out.

AB - This paper is concerned with probabilistic analysis of initial member stress in geometrically imperfect regular lattice structures with periodic boundary conditions. Spatial invariance of the corresponding statistical parameters is shown to arise on the Born-von Kármán domains. This allows analytical treatment of the problem, where the parameters of stress distribution are obtained in a closed form. Several benchmark problems with beam- and plate-like lattices are considered, and the results are verified by the direct Monte-Carlo simulations. Behaviour of the standard deviation as a function of lattice repetitive cell number is investigated, and dependence on the lattice structural redundancy is pointed out.

KW - Initial tension

KW - Lack of fit

KW - Periodic lattice

KW - Repetitive structure

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DO - 10.1016/S0020-7683(03)00290-7

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EP - 5388

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

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