Premium
3D‐FEM formulations of limit analysis methods for porous pressure‐sensitive materials
Author(s) -
Pastor Franck,
Kondo Djimedo,
Pastor Joseph
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4527
Subject(s) - finite element method , limit analysis , von mises yield criterion , kinematics , mathematics , limit (mathematics) , hydrostatic pressure , quadratic programming , numerical analysis , matrix (chemical analysis) , sequential quadratic programming , mathematical optimization , mathematical analysis , structural engineering , mechanics , engineering , materials science , classical mechanics , physics , composite material
SUMMARY The first purpose of this paper is the numerical formulation of the three general limit analysis methods for problems involving pressure‐sensitive materials, that is, the static, classic, and mixed kinematic methods applied to problems with Drucker–Prager, Mises–Schleicher, or Green materials. In each case, quadratic or rotated quadratic cone programming is considered to solve the final optimization problems, leading to original and efficient numerical formulations. As a second purpose, the resulting codes are applied to non‐classic 3D problems, that is, the Gurson‐like hollow sphere problem with these materials as matrices. To this end are first presented the 3D finite element implementations of the static and kinematic classic methods of limit analysis together with a mixed method formulated to give also a purely kinematic result. Discontinuous stress and velocity fields are included in the analysis. The static and the two kinematic approaches are compared afterwards in the hydrostatic loading case whose exact solution is known for the three cases of matrix. Then, the static and the mixed approaches are used to assess the available approximate criteria for porous Drucker–Prager, Mises–Schleicher, and Green materials. Copyright © 2013 John Wiley & Sons, Ltd.