A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures

L. Angela Mihai, Mark Ainsworth

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

A rigorous finite element numerical procedure is proposed for the computation of guaranteed lower and upper bounds for the limit load of failure in a system of linear-elastic blocks in mutual non-penetrative contact with given friction. First the static and kinematic principles are formulated as continuous optimization problems and existence of a solution to the corresponding limit load problems at the infinite dimensional level is established. Two numerical approaches are devised, one for each limit load problem, to obtain actual numerical bounds on the unique critical load. The first approach uses the static limit load problem involving stresses in conjunction with a non-standard conforming finite element method to obtain a linear program from which one can derive a lower (safe) bound for the limit load and an expression for the corresponding stress field. The second approach uses the kinematic limit load problem to obtain a linear optimization problem from which one can determine an upper (unsafe) bound for the limit load and an expression for the failure mode. Together, these procedures give rise to rigorous numerical enclosures on the limit load.
LanguageEnglish
Pages48-60
Number of pages12
JournalComputer Methods in Applied Mechanics and Engineering
Volume199
Issue number1-4
DOIs
Publication statusPublished - Dec 2009

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Load limits
enclosure
Enclosures
Kinematics
kinematics
optimization
failure modes
Failure modes
stress distribution
finite element method
friction
Friction
Finite element method

Keywords

  • Finite elements
  • Limit load
  • Contact problems
  • Linear elasticity
  • Mathematical programming
  • Masonry structures Finite elements
  • Masonry structures

Cite this

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abstract = "A rigorous finite element numerical procedure is proposed for the computation of guaranteed lower and upper bounds for the limit load of failure in a system of linear-elastic blocks in mutual non-penetrative contact with given friction. First the static and kinematic principles are formulated as continuous optimization problems and existence of a solution to the corresponding limit load problems at the infinite dimensional level is established. Two numerical approaches are devised, one for each limit load problem, to obtain actual numerical bounds on the unique critical load. The first approach uses the static limit load problem involving stresses in conjunction with a non-standard conforming finite element method to obtain a linear program from which one can derive a lower (safe) bound for the limit load and an expression for the corresponding stress field. The second approach uses the kinematic limit load problem to obtain a linear optimization problem from which one can determine an upper (unsafe) bound for the limit load and an expression for the failure mode. Together, these procedures give rise to rigorous numerical enclosures on the limit load.",
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A finite element procedure for rigorous numerical enclosures on the limit load in the analysis of multibody structures. / Mihai, L. Angela; Ainsworth, Mark.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 199, No. 1-4, 12.2009, p. 48-60.

Research output: Contribution to journalArticle

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AU - Mihai, L. Angela

AU - Ainsworth, Mark

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N2 - A rigorous finite element numerical procedure is proposed for the computation of guaranteed lower and upper bounds for the limit load of failure in a system of linear-elastic blocks in mutual non-penetrative contact with given friction. First the static and kinematic principles are formulated as continuous optimization problems and existence of a solution to the corresponding limit load problems at the infinite dimensional level is established. Two numerical approaches are devised, one for each limit load problem, to obtain actual numerical bounds on the unique critical load. The first approach uses the static limit load problem involving stresses in conjunction with a non-standard conforming finite element method to obtain a linear program from which one can derive a lower (safe) bound for the limit load and an expression for the corresponding stress field. The second approach uses the kinematic limit load problem to obtain a linear optimization problem from which one can determine an upper (unsafe) bound for the limit load and an expression for the failure mode. Together, these procedures give rise to rigorous numerical enclosures on the limit load.

AB - A rigorous finite element numerical procedure is proposed for the computation of guaranteed lower and upper bounds for the limit load of failure in a system of linear-elastic blocks in mutual non-penetrative contact with given friction. First the static and kinematic principles are formulated as continuous optimization problems and existence of a solution to the corresponding limit load problems at the infinite dimensional level is established. Two numerical approaches are devised, one for each limit load problem, to obtain actual numerical bounds on the unique critical load. The first approach uses the static limit load problem involving stresses in conjunction with a non-standard conforming finite element method to obtain a linear program from which one can derive a lower (safe) bound for the limit load and an expression for the corresponding stress field. The second approach uses the kinematic limit load problem to obtain a linear optimization problem from which one can determine an upper (unsafe) bound for the limit load and an expression for the failure mode. Together, these procedures give rise to rigorous numerical enclosures on the limit load.

KW - Finite elements

KW - Limit load

KW - Contact problems

KW - Linear elasticity

KW - Mathematical programming

KW - Masonry structures Finite elements

KW - Masonry structures

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