Finite element formulation by parametrized hybrid variational principles: Variable stiffness and removal of locking

1994 ◽  
Vol 37 (16) ◽  
pp. 2797-2818 ◽  
Author(s):  
K. Y. Sze
Keyword(s):  
Finite Element ◽  
Variational Principles ◽  
Variable Stiffness ◽  
Finite Element Formulation ◽  
Element Formulation

FEM Modeling of Beams Cyclic Loading Based on Ziegler-Prager and Armstrong-Frederick Kinematic Hardening Models

2011 ◽  
Vol 110-116 ◽  
pp. 2838-2846
Author(s):  
Ehsan Hashemi ◽  
Mani Sharifi ◽  
Behrooz Farshi
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Variable Stiffness ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Fem Modeling ◽  
Response Curves ◽  
Strain Behavior ◽  
Hardening Models ◽  
Incremental Step

In this investigation the behavior of classical beams are simulated by a finite element formulation of the plasticity problem under two major kinematic hardening models. Complete formulation is presented for both load and deformation controlled cases. The proposed finite element formulation uses a variable stiffness matrix in each incremental step reflecting the yield surface movement. Examples are worked out for both the Ziegler-Prager and the Armstrong-Frederick theories, to show the stress-strain behavior under cyclic symmetric and asymmetric flexural loading. The results have been graphically illustrated in plots of the response curves and are compared to the published and experimental ones. It was observed that Ziegler-Prager theory for anisotropic cases with symmetric loading predicts a ratcheting response. While the results show agreement with published ones; it was also observed that the two theories do not show similar responses of reverse plasticity or ratcheting for Euler-Bernoulli beams in all the example cases.

FINITE ELEMENT BASED ELASTO-PLASTIC ANALYSIS OF CLASSICAL AND FIRST ORDER BEAMS WITH ARMSTRONG–FREDERICK KINEMATIC HARDENING MODEL

2014 ◽  
Vol 38 (1) ◽  
pp. 1-14
Author(s):  
Ehsan Hashemi ◽  
Behrooz Farshi
Keyword(s):  
Finite Element ◽  
Kinematic Hardening ◽  
Variable Stiffness ◽  
Finite Element Formulation ◽  
Plastic Behavior ◽  
Element Formulation ◽  
Timoshenko Beams ◽  
First Order ◽  
Hardening Models ◽  
Symmetric Loading

This investigation is focused on the elasto-plastic behavior of classical and first order Timoshenko beams by a finite element formulation under two major kinematic hardening models. The approach consists of proposing a finite element formulation with variable stiffness matrix and optimized solution for the Armstrong–Frederick theory together with the Ziegler–Prager model under cyclic flexural and deformation controlled loading conditions. In symmetrical cyclic deformation and flexural controlled states of the first order beams, it was concluded that after several cycles, the total stress-strain curves tend to be coincident. It also corroborates that the anisotropic characteristic cases with symmetric loading exhibit a ratcheting response for both beam models.

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