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.

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.

scholarly journals Generalized finite element formulation for efficient first-order plastic hinge analysis

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983636
Author(s):  
Dae-Jin Kim ◽  
Hong-Jun Son ◽  
Yousun Yi ◽  
Sung-Gul Hong
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Plastic Hinge ◽  
Computational Cost ◽  
Finite Element Formulation ◽  
Solution Technique ◽  
Element Formulation ◽  
Plastic Hinges ◽  
First Order ◽  
Generalized Finite Element

This article presents generalized finite element formulation for plastic hinge modeling based on lumped plasticity in the classical Euler–Bernoulli beam. In this approach, the plastic hinges are modeled using a special enrichment function, which can describe the weak discontinuity of the solution at the location of the plastic hinge. Furthermore, it is also possible to insert a plastic hinge at an arbitrary location of the element without modifying its connectivity or adding more elements. Instead, the formations of the plastic hinges are achieved by hierarchically adding more degrees of freedom to existing elements. Due to these features, the proposed methodology can efficiently perform the first-order plastic hinge analysis of large-frame structures. A generalized finite element solution technique based on the static condensation scheme is also proposed in order to reduce the computational cost of a series of linear elastic problems, which is in general the most time-consuming portion of the first-order plastic hinge analysis. The effectiveness and accuracy of the proposed method are verified by analyzing several representative numerical examples.

scholarly journals Free vibration of bidirectional functionally graded sandwich beams using a first-order shear deformation finite element formulation

2020 ◽  
Vol 14 (3) ◽  
pp. 136-150
Author(s):  
Le Thi Ngoc Anh ◽  
Vu Thi An Ninh ◽  
Tran Van Lang ◽  
Nguyen Dinh Kien
Keyword(s):  
Finite Element ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
First Order ◽  
Various Boundary Conditions

Free vibration of bidirectional functionally graded sandwich (BFGSW) beams is studied by using a first-order shear deformation finite element formulation. The beams consist of three layers, a homogeneous core and two functionally graded skin layers with material properties varying in both the longitudinal and thickness directions by power gradation laws. The finite element formulation with the stiffness and mass matrices evaluated explicitly is efficient, and it is capable of giving accurate frequencies by using a small number of elements. Vibration characteristics are evaluated for the beams with various boundary conditions. The effects of the power-law indexes, the layer thickness ratio, and the aspect ratio on the frequencies are investigated in detail and highlighted. The influence of the aspect ratio on the frequencies is also examined and discussed. Keywords: BFGSW beam; first-order shear deformation theory; free vibration; finite element method.

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