Title of article :
A nonlinear programming approach to kinematic shakedown analysis of frictional materials
Author/Authors :
H.X. Li، نويسنده , , H.S. Yu، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2006
Abstract :
This paper develops a novel nonlinear numerical method to perform shakedown analysis of structures subjected to variable
loads by means of nonlinear programming techniques and the displacement-based finite element method. The analysis
is based on a general yield function which can take the form of most soil yield criteria (e.g. the Mohr–Coulomb or
Drucker–Prager criterion). Using an associated flow rule, a general yield criterion can be directly introduced into the kinematic
theorem of shakedown analysis without linearization. The plastic dissipation power can then be expressed in terms of
the kinematically admissible velocity and a nonlinear formulation is obtained. By means of nonlinear mathematical programming
techniques and the finite element method, a numerical model for kinematic shakedown analysis is developed as
a nonlinear mathematical programming problem subject to only a small number of equality constraints. The objective
function corresponds to the plastic dissipation power which is to be minimized and an upper bound to the shakedown load
can be calculated. An effective, direct iterative algorithm is then proposed to solve the resulting nonlinear programming
problem. The calculation is based on the kinematically admissible velocity with one-step calculation of the elastic stress
field. Only a small number of equality constraints are introduced and the computational effort is very modest. The effectiveness
and efficiency of the proposed numerical method have been validated by several numerical examples.
Keywords :
shakedown analysis , Frictional materials , nonlinear programming , Finite element method , Kinematic theorem
Journal title :
International Journal of Solids and Structures
Journal title :
International Journal of Solids and Structures