HOURGLASS AND LOCKING CONTROL FOR RIGID PLASTIC FINITE ELEMENT ANALYSIS BASED ON MIXED FORMULATION

Abstract

 A conventional rigid plastic finite element method based on mixed formulation sometimes shows false collapse mechanisms containing hourglass modes and locking modes. These false mechanisms are mainly due to the spacial discretization of stresses within an element; a constant stress state is assumed within an element. To overcome these difficulties, a new spacial discretization of stresses is proposed in this paper; two additional variables per element are introduced to express stress distribution in an element. The validity of a newly proposed method is numerically scrutinized by solving the following four typical examples whose analytical solutions have been available; 1) Limit load of a rigid flat punching, 2) Limit load of a hollow cylinder subject to inner pressure, 3) Limit bending of a cantilever beam and 4) Limit load of a plate with a hole subject to biaxial stress. Numerical solutions show good agreement to analytical solutions for all the examples. It can be concluded that the proposed method is able to control both hourglass and locking modes successfully. It is also able to obtain rational plastic solutions with respect to both limit loads and collapse mechanisms.