Study of Elastic–Plastic Fracture Problem Using Finite Element Technique

1984 ◽  
Vol 106 (4) ◽  
pp. 476-482
Author(s):  
F. T. C. Loo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Graphical Form ◽  
The Finite Element Method ◽  
Finite Element Technique ◽  
Elastic Plastic ◽  
Center Crack ◽  
Initial Stress Method ◽  
Element Technique

Numerical methods for the analysis of the elastic-plastic fracture problem using a special finite element technique are presented. A brief description of some concepts in elastic-plastic fracture mechanics and of the finite element method is followed by the formulation procedure of the stiffness matrix using eight-noded quadrilateral isoparametric elements. After a terse discussion of the initial stress method, the procedure of computation is extended in the analysis by using an incremental load process. The size and the shape of the plastic zone of a center crack specimen is investigated. Results are presented in graphical form.

A Study of Wall Ironing by the Finite Element Technique

1978 ◽  
Vol 100 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. I. Odell
Keyword(s):  
Finite Element ◽  
Lower Bound ◽  
Cone Angle ◽  
Reduction Ratio ◽  
Operating Parameters ◽  
Finite Element Technique ◽  
Elastic Plastic ◽  
Maximum Reduction ◽  
Load Displacement ◽  
Element Technique

Wall ironing has been analyzed using an elastic-plastic finite element technique. The effects that the ironing ring semi-cone angle and friction have on the maximum reduction ratio are studied in detail. Stress contours are given for a typical set of operating parameters. Several ram load/displacement curves are provided and compared with upper and lower bound loads.

Development of Bifurcation Analysis Method for Rate Dependent Materials

2019 ◽  
Vol 794 ◽  
pp. 220-225
Author(s):  
Daiki Towata ◽  
Yuichi Tadano
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Bifurcation Analysis ◽  
Stiffness Matrix ◽  
Computational Method ◽  
Analysis Method ◽  
The Finite Element Method ◽  
Tangent Stiffness Matrix ◽  
Rate Dependent ◽  
Element Method

In this study, a novel numerical method to analyze the bifurcation problemof a rate dependent material using the finite element method is proposed. The consistent stiffness matrix, which is required for a bifurcation analysis using the finite element method, for a rate dependent material is generally hard to compute, therefore, a computational method to calculate the tangent stiffness matrix based on a numerical differential is introduced so that exact bifurcation analyses for the rate dependent material can be conducted. A numerical example of the proposed method is demonstrated, and the adequacy of the proposed method is discussed.

On the Unsymmetric Eigenproblem for the Buckling of Shells Under Pressure Loading

1983 ◽  
Vol 50 (1) ◽  
pp. 95-100 ◽  
Author(s):  
H. A. Mang ◽  
R. H. Gallagher
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Stiffness Matrix ◽  
Circular Cylindrical Shell ◽  
The Finite Element Method ◽  
Equilibrium Equations ◽  
Buckling Loads ◽  
Large Rotations ◽  
Element Method

Consideration of the dependence of hydrostatic pressure on the displacements may result in significant changes of calculated buckling loads of thin arches and shells in comparison with loads calculated without consideration of this effect. The finite element method has made it possible to quantify these changes. On the basis of a shell theory of small displacements but moderately large rotations, this paper derives consistent incremental equilibrium equations for tracing, via the finite element method, the load-displacement path for thin shells subjected to nonuniform hydrostatic pressure and establishes the buckling condition from the incremental equilibrium equations. Within the framework of the finite element method, the character of hydrostatic pressure as one of a follower load is represented in the so-called pressure-stiffness matrix. For shells with loaded free edges, this matrix is unsymmetric. The principal objective of the present paper is to demonstrate that symmetrization of the pressure stiffness matrix resulting from linearization of the buckling condition yields buckling loads that are identical to the eigenvalues resulting from first-order perturbation analysis of the unsymmetric eigenproblem. A circular cylindrical shell with a free and a hinged end, subjected to hydrostatic pressure, is used as an example of the admissibility of symmetrizing the pressure stiffness matrix and for assessing its effect.

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