Analysis of Embedded and Surface Elliptical Flaws in Transversely Isotropic Bodies by the Finite Element Alternating Method

1991 ◽  
Vol 58 (2) ◽  
pp. 435-443 ◽  
Author(s):  
H. Rajiyah ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Transversely Isotropic ◽  
Generalized Solution ◽  
Solution Procedure ◽  
Isotropic Case ◽  
The Finite Element Method ◽  
Crack Face ◽  
Elastic Symmetry ◽  
Alternating Method ◽  
Isotropic Bodies

The general analytical solution to the problem of a flat elliptical crack embedded in an infinite, transversely isotropic solid, oriented perpendicular to the axis of elastic symmetry, is derived along the lines of Vijayakumar and Atluri’s solution procedure for the isotropic case. The prior work of Kassir and Sih on this problem is limited to some constant and linear variations of normal and shear tractions on the crack face. The generalized solution is employed in the Schwarz-Neumann alternating method in conjunction with the finite element method. Such a method of analysis is shown to be an efficient way to evaluate the stress intensity factors along the flaw border.

Analysis of Surface Crack in Cylinder by Finite Element Alternating Method

2005 ◽  
Vol 127 (2) ◽  
pp. 165-172 ◽  
Author(s):  
Masayuki Kamaya ◽  
Toshihisa Nishioka
Keyword(s):  
Finite Element ◽  
Crack Growth ◽  
Surface Cracks ◽  
Inclined Crack ◽  
Element Analysis ◽  
Crack Face ◽  
Simple Method ◽  
Alternating Method ◽  
The Finite Element Analysis ◽  
Inclined Surface

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, is used for evaluating the stress intensity factor (SIF) of surface cracks in a cylinder. The major advantage of this method is that the SIF can be calculated by using the FEA results for an uncracked body. A newly developed system allows the FEAM to be performed by a simple method, which consists of the conventional FEA for an uncracked body and a subroutine for the FEAM alternating procedure. It is shown that the system can derive the precise SIF of circumferential, longitudinal, and inclined surface cracks in a cylinder. The crack growth predictions are performed for an inclined crack and projected longitudinal and circumferential crack in a cylinder. The results suggests that the crack characterizing procedure prescribed in Sec. XI may cause an unconservative evaluation in the crack growth prediction, and that the FEAM is valid for complex problems, to which the SIF evaluation by the FEA cannot be adopted easily.

An Introduction to the Finite Element Method Using MATLAB

2005 ◽  
Vol 33 (3) ◽  
pp. 260-277 ◽  
Author(s):  
Donald W. Mueller
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Engineering Students ◽  
Solid Mechanics ◽  
Solution Procedure ◽  
The Finite Element Method ◽  
Stepped Shaft ◽  
Systematic Solution ◽  
Force Equilibrium ◽  
Element Method

This paper outlines an efficient approach to introducing the finite element method to undergraduate mechanical engineering students. This approach requires that the students have prior experience with MATLAB and a fundamental understanding of solid mechanics. Only two-dimensional beam element problems are considered, to simplify the development. The approach emphasizes an orderly solution procedure and involves important finite element concepts, such as the stiffness matrix, element and global coordinates, force equilibrium, and constraints. Two important and challenging engineering problems — a statically indeterminate beam structure and a stepped shaft — are analyzed with the systematic solution procedure and a MATLAB program. The ability of MATLAB to manipulate matrices and solve matrix equations makes the computer solution concise and easy to follow. The flexibility associated with the computer implementation allows example problems to be easily modified into design projects.

Evaluation of Stress Intensity Factors by Finite Element Alternating Method

2004 ◽  
Author(s):  
Masayuki Kamaya ◽  
Toshihisa Nishioka
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Maximum Error ◽  
Surface Cracks ◽  
Element Analysis ◽  
Crack Face ◽  
Simple Method ◽  
Alternating Method ◽  
Fine Mesh ◽  
The Finite Element Analysis

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, is used for evaluating the stress intensity factor (SIF) of surface cracks. The major advantage of this method is that the SIF can be calculated by using the FEA results for an uncracked body. A newly developed system allows the FEAM to be performed by a simple method, which consists of the conventional FEA for an uncracked body and a subroutine for the FEAM alternating procedure. The SIFs are evaluated for semi-elliptical surface cracks on a plate and in a cylinder as well as interacting cracks on a plate. It is also shown that, by using fine mesh, the maximum error of the evaluation by the FEAM can be suppressed less than 2 percent.

Elasto-Plastic Analysis of 3-D Inner Cracks Using the Finite Element Alternating Method

2007 ◽  
Vol 345-346 ◽  
pp. 881-884
Author(s):  
Sang Yun Park ◽  
Jai Hak Park
Keyword(s):  
Finite Element ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Infinite Body ◽  
Alternating Method ◽  
Crack Problems ◽  
Finite Body ◽  
Initial Stress Method ◽  
Galerkin Boundary Element Method ◽  
Element Method

The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.

Finite Element Alternating Method for Solving Two-Dimensional Cracks Embedded in a Bimaterial Body

2006 ◽  
Vol 326-328 ◽  
pp. 945-948
Author(s):  
Sang Yun Park ◽  
Jai Hak Park
Keyword(s):  
Finite Element ◽  
Superposition Principle ◽  
Stress Singularity ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Infinite Body ◽  
Element Analysis ◽  
Alternating Method ◽  
Crack Problems ◽  
The Finite Element Analysis

The finite element alternating method based on the superposition principle has been known as an effective method to obtain the stress intensity factors for general multiple collinear or curvilinear cracks in an isotropic plate. In this paper the method is extended further to solve two-dimensional cracks embedded in a bimaterial plate. The main advantage of this method is that it is not necessary to make crack meshes considering the stress singularity at the crack tip. The solution of the developed code is obtained from an iteration procedure, which alternates independently between the finite element method solution for an uncracked body and the analytical solution for cracks in an infinite body. In order to check the validity of the method, several crack problems of a bimaterial body are solved and compared with the results obtained from the finite element analysis.

Finite Element Alternating Method for Interacting Surface Cracks

2007 ◽  
Vol 120 ◽  
pp. 147-153 ◽  
Author(s):  
Masayuki Kamaya ◽  
Toshihisa Nishioka
Keyword(s):  
Finite Element ◽  
Crack Size ◽  
Surface Cracks ◽  
Combination Rules ◽  
Element Analysis ◽  
Crack Face ◽  
Direct Evaluation ◽  
Alternating Method ◽  
The Finite Element Analysis ◽  
The Difference

The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, can derive the stress intensity factor (SIF) of surface cracks by using the FEA results for an uncracked body. In the present study, the FEAM was applied to evaluations of SIF for noncoplanar multiple surface cracks. The SIF was evaluated for two surface cracks of dissimilar size, and three crack of the same size. The results suggested that the interaction is greatly affected by the relative crack size and negligible when the difference in the crack size is large enough, and the interaction can be evaluated by taking into account the adjacent cracks even if there are many cracks around them. Finally, the crack growth simulations were conducted and a possibility of the direct evaluation of influence of interaction between adjacent crack without using the combination rules was revealed.

Three-Dimensional Elasticity Solution for the Buckling of Transversely Isotropic Rods: The Euler Load Revisited

1995 ◽  
Vol 62 (2) ◽  
pp. 346-355 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Critical Load ◽  
Transverse Shear ◽  
Isotropic Material ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Radius Ratio ◽  
Isotropic Case ◽  
Elasticity Solution ◽  
Three Dimensional Elasticity ◽  
Isotropic Bodies

The bifurcation of equilibrium of a compressed transversely isotropic bar is investigated by using a three-dimensional elasticity formulation. In this manner, an assessment of the thickness effects can be accurately performed. For isotropic rods of circular cross-section, the bifurcation value of the compressive force turns out to coincide with the Euler critical load for values of the length-over-radius ratio approximately greater than 15. The elasticity approach predicts always a lower (than the Euler value) critical load for isotropic bodies; the two examples of transversely isotropic bodies considered show also a lower critical load in comparison with the Euler value based on the axial modulus, and the reduction is larger than the one corresponding to isotropic rods with the same length over radius ratio. However, for the isotropic material, both Timoshenko’s formulas for transverse shear correction are conservative; i.e., they predict a lower critical load than the elasticity solution. For a generally transversely isotropic material only the first Timoshenko shear correction formula proved to be a conservative estimate in all cases considered. However, in all cases considered, the second estimate is always closer to the elasticity solution than the first one and therefore, a more precise estimate of the transverse shear effects. Furthermore, by performing a series expansion of the terms of the resulting characteristic equation from the elasticity formulation for the isotropic case, the Euler load is proven to be the solution in the first approximation; consideration of the second approximation gives a direct expression for the correction to the Euler load, therefore defining a new, revised, yet simple formula for column buckling. Finally, the examination of a rod with different end conditions, namely a pinned-pinned rod, shows that the thickness effects depend also on the end fixity.

Large Displacement Analysis of Viscoelastic Beams and Frames by the Finite-Element Method

1974 ◽  
Vol 41 (3) ◽  
pp. 635-640 ◽  
Author(s):  
T. Y. Yang ◽  
G. Lianis
Keyword(s):  
Finite Element ◽  
Geometrical Nonlinearity ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Large Displacement ◽  
Cantilever Beams ◽  
The Finite Element Method ◽  
Stress Strain Relation ◽  
Linear Viscoelastic ◽  
Hereditary Integral

A finite-element displacement formulation and solution procedure are developed for the analysis of large displacement problems of viscoelastic beams and frames. The displacements considered are of the same order as the length of the beam member. The geometrical nonlinearity is accounted for by a midpoint-tangent incremental approach together with coordinate transformation at every step. The linear viscoelastic stress-strain relation in the form of hereditary integral is accounted for by the numerical integration with trapezoidal rule. Results are given for the displacements of a variety of beam and frame problems. For the simple case of cantilever beams, some alternative approximate solutions are available for comparison and reasonable agreement is indicated.

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