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Upper and lower bound limit analysis of plates using FEM and second-order cone programming
Computers and Structures Số 02-Jan, năm 2010 (Tập 88, trang 65-73)
ISSN: 457949
ISSN: 457949
DOI: 10.1016/j.compstruc.2009.08.011
Tài liệu thuộc danh mục: Scopus
Article
English
Từ khóa: Criterion of mean; Displacement and equilibrium models; Limit analysis; Second order cone programming; Upper and lower bounds; Control theory
Tóm tắt tiếng anh
This paper presents two novel numerical procedures to determine upper and lower bounds on the actual collapse load multiplier for plates in bending. The conforming Hsieh-Clough-Tocher (HCT) and enhanced Morley (EM) elements are used to discrete the problem fields. A Morley element with enhanced moment fields is used. The constant moment fields is added a quadratic mode in which the pressure is equilibrated by corner loads only, ensuring that exact equilibrium relations associated with a uniform pressure can be obtained. Once the displacement or moment fields are approximated and the bound theorems applied, limit analysis becomes a problem of optimization. In this paper, the optimization problems are formulated in the form of a standard second-order cone programming which can be solved using highly efficient interior point solvers. The procedures are tested by applying it to several benchmark plate problems and are found good agreement between the present upper and lower bound solutions and results in the literature. 2009 Elsevier Ltd. All rights reserved.