scholarly journals Analysis of Elasto-plastic Thin-shell Structures using Layered Plastic Modeling and Absolute Nodal Coordinate Formulation

2021 ◽  
Author(s):  
Jiachen Li ◽  
Cheng Liu ◽  
Haiyan Hu ◽  
Shixiong Zhang
Keyword(s):  
Plane Stress ◽  
Thin Shell ◽  
Absolute Nodal Coordinate Formulation ◽  
Special Treatment ◽  
Stress Constraint ◽  
Isotropic Hardening ◽  
Thin Shells ◽  
Equilibrium Path ◽  
Absolute Nodal Coordinate ◽  
Tangent Moduli

Abstract A new elasto-plastic thin shell finite element of the absolute nodal coordinate formulation (ANCF) allowing for large deformation and finite rotation is proposed based on the Kirchhoff-Love theory and layered plastic model. The von Mises yield criterion of plane-stress with linear isotropic hardening is adopted in constitutive description of elasto-plastic material. Owing to the plane-stress constraint, special treatment should be given to the stress update algorithm for plasticity. To accommodate the plasticity formulation, the Gauss-point layered integration is inserted into the thickness of the element to produce the internal force. Then, the Jacobian of internal forces is deduced by deriving the consistent elasto-plastic tangent moduli. To accurately track the load-displacement equilibrium path in the buckling analysis of elasto-plastic thin shells, the arc-length method is used. The dynamics of the thin shells is also studied by using the generalized-alpha algorithm. Finally, several static and dynamic examples are presented to verify the accuracy of the proposed formulation.

In-plane nonlinear postbuckling analysis of circular arches using absolute nodal coordinate formulation with arc-length method

2020 ◽  
pp. 146441932097141
Author(s):  
Abdur Rahman Shaukat ◽  
Peng Lan ◽  
Jia Wang ◽  
Tengfei Wang
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Experimental Result ◽  
Equilibrium Path ◽  
Arc Length ◽  
Concentrated Load ◽  
Absolute Nodal Coordinate ◽  
Split Method ◽  
Geometric Configurations ◽  
General Continuum

In this study, Absolute Nodal Coordinate Formulation (ANCF) in conjunction with Crisfield’s arc-length method is utilized in order to predict the nonlinear postbuckling behaviour of circular arches. The whole primary equilibrium path in load-displacement space of circular arches under central concentrated load is obtained. Three ANCF based approaches, i.e., the conventional two-dimensional fully parameterized shear deformable ANCF beam element based on the General Continuum Mechanics (GCM) approach, the same element modified by the Strain Split Method (SSM) approach and the ANCF planar Higher Order Beam Element (HOBE) with GCM approach are used. Circular arches with various geometric configurations and boundary conditions such as clamped-clamped, hinged-hinged, clamped-hinged and three-hinged arches are studied which exhibit nonlinear response in the form of snap-through, snap-back and looping phenomenon. The obtained results are compared with the analytical solutions, experimental result (where available in the literature) and numerical approximations (by using the commercially available FEM package). In this paper, the recently proposed ANCF based approaches are successfully implemented which validate and verify the utility of ANCF in nonlinear postbuckling analysis. The characteristics of the three approaches with regard to the adoptability of arc-length method are compared and discussed.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Nonlinear Analysis of L-shaped Pipe Conveying Fluid with the Aid of Absolute Nodal Coordinate Formulation

2021 ◽  
Author(s):  
K. Zhou ◽  
H.R. Yi ◽  
Huliang Dai ◽  
H Yan ◽  
Z.L. Guo ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Flow Velocity ◽  
Absolute Nodal Coordinate Formulation ◽  
Strong Relationship ◽  
Excitation Amplitude ◽  
Pipe Conveying Fluid ◽  
Base Excitation ◽  
Absolute Nodal Coordinate ◽  
Nonlinear Behaviors ◽  
Conveying Fluid

Abstract By adopting the absolute nodal coordinate formulation, a novel and general nonlinear theoretical model, which can be applied to solve the dynamics of combined straight-curved fluid-conveying pipes with arbitrary initially configurations and any boundary conditions, is developed in the current study. Based on this established model, the nonlinear behaviors of the cantilevered L-shaped pipe conveying fluid with and without base excitations are systematically investigated. Before starting the research, the developed theoretical model is verified by performing three validation examples. Then, with the aid of this model, the static deformations, linear stability, and nonlinear self-excited vibrations of the L-shaped pipe without the base excitation are determined. It is found that the cantilevered L-shaped pipe suffers from the static deformations when the flow velocity is subcritical, and will undergo the limit-cycle motions as the flow velocity exceeds the critical value. Subsequently, the nonlinear forced vibrations of the pipe with a base excitation are explored. It is indicated that the period-n, quasi-periodic and chaotic responses can be detected for the L-shaped pipe, which has a strong relationship with the flow velocity, excitation amplitude and frequency.

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