Shakedown reduced kinematic formulation, separated collapse modes, and numerical implementation

• Published in: International journal of solids and structures Vol. 51; no. 15-16; pp. 2893 - 2899
• Main Authors: Tran, T.D., Le, C.V., Pham, D.C., Nguyen-Xuan, H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2014
• Subjects: Alternating plasticity; Collapse; Cyclic loading; Elastic–plastic material; Incremental plasticity; Kinematics; Loads (forces); Mathematical analysis; Mathematical models; Plane stress; Plastic collapse; Plasticity; Programming; Reduced kinematic formulation; Second-order cone programming; Shakedown; Cyclic loading; Plastic collapse; Shakedown; Elastic–plastic material; Reduced kinematic formulation; Alternating plasticity; Second-order cone programming; Incremental plasticity
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2014.04.016

Our shakedown reduced kinematic formulation is developed to solve some typical plane stress problems, using finite element method. Whenever the comparisons are available, our results agree with the available ones in the literature. The advantage of our approach is its simplicity, computational effectiveness, and the separation of collapse modes for possible different treatments. Second-order cone programming developed for kinematic plastic limit analysis is effectively implemented to study the incremental plasticity collapse mode. The approach is ready to be used to solve general shakedown problems, including those for elastic–plastic kinematic hardening materials and under dynamic loading.