The calculation of critical buckling loads for externally constrained structures

Hexiang, Lu; Feng, Minghui; Lark, Robert John; Williams, F.W.

doi:10.1002/(sici)1099-0887(199903)15:3<193::aid-cnm235>3.0.co;2-5

Cited by 11 publications

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“…Besides these techniques, there exist methodologies where the unilateral constraints are maintained in the formulation of the problem. These techniques lead to quadratic programming or linear complementarity problems which can be solved by a variety of mathematical methods, for example, Lemke's or Dantig's algorithms (Lemke, 1968;Ascione and Grimaldi, 1984;Joo and Kwak, 1986;Barbosa, 1986;Silveira, 1995;Koo and Kwak, 1996;Hexiang et al, 1999;Silva et al, 2001;Silveira and Concalves, 2001;Wriggers, 2002;Pereira, 2003;Hollanda and Concalves, 2003). Mathematical programming resembles the force method of structural analysis, thus the local contact loads are set as unknowns and the solution is obtained by minimizing a given function (Chand et al, 1976;Fisher and Melosh, 1987).…”

Section: Methodologies For the Analysis Of Unilateral Systemsmentioning

confidence: 99%

The unilateral contact buckling problem of geometrically perfect and imperfect beams

Tzaros¹

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Section: Methodologies For the Analysis Of Unilateral Systemsmentioning

confidence: 99%

The unilateral contact buckling problem of geometrically perfect and imperfect beams

Tzaros¹

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Calculation of critical buckling loads for finite length externally constrained thin circular cylinders

Hexiang

Jinhua

Williams

2005

Commun. Numer. Meth. Engng.

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SUMMARYThe problem of the buckling of ÿnite length externally constrained thin circular cylinders is solved to yield a generalized eigenvalue problem with constraint conditions. The solution is based on an inverse iteration procedure in which the non-linear complementary equation is solved by a non-smooth version of Newton's method that saves computer time and space when compared to a linear complementary algorithm. The numerical results show that the method proposed is e ective and that the critical buckling load of the constrained cylinder is almost independent of the length of the cylinder, unlike the critical load of free (unconstrained) thin cylinders. In the direction of its axis, the shell is discretized by ÿnite strips which circumferentially use straight bar and beam displacement functions. It is proved that when the widths of the strips approach zero, the geometrical relationships used in this paper approach those of Koiter-Sanders cylindrical shell theory.

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A Mathematical Method for the Determination of the Critical Axial Loads of Continuous Beams with Unilateral Constraints for Various Initial Geometric Imperfections

Tzaros

Mistakidis

2013

Recent Advances in Contact Mechanics

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The calculation of critical buckling loads for externally constrained structures

Cited by 11 publications

References 7 publications

The unilateral contact buckling problem of geometrically perfect and imperfect beams

The unilateral contact buckling problem of geometrically perfect and imperfect beams

Calculation of critical buckling loads for finite length externally constrained thin circular cylinders

A Mathematical Method for the Determination of the Critical Axial Loads of Continuous Beams with Unilateral Constraints for Various Initial Geometric Imperfections

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