Fracture Mechanics of Thin Plates and Shells Under Combined Membrane, Bending, and Twisting Loads

2005 ◽  
Vol 58 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Alan T. Zehnder ◽  
Mark J. Viz
Keyword(s):  
Fracture Mechanics ◽  
Plate Theory ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Crack Tip ◽  
Thin Plates ◽  
Element Analysis ◽  
Crack Tip Fields ◽  
Plates And Shells ◽  
Membrane Bending

The fracture mechanics of plates and shells under membrane, bending, twisting, and shearing loads are reviewed, starting with the crack tip fields for plane stress, Kirchhoff, and Reissner theories. The energy release rate for each of these theories is calculated and is used to determine the relation between the Kirchhoff and Reissner theories for thin plates. For thicker plates, this relationship is explored using three-dimensional finite element analysis. The validity of the application of two-dimensional (plate theory) solutions to actual three-dimensional objects is analyzed and discussed. Crack tip fields in plates undergoing large deflection are analyzed using von Ka´rma´n theory. Solutions for cracked shells are discussed as well. A number of computational methods for determining stress intensity factors in plates and shells are discussed. Applications of these computational approaches to aircraft structures are examined. The relatively few experimental studies of fracture in plates under bending and twisting loads are also reviewed. There are 101 references cited in this article.

Computational Models for Sandwich Panels and Shells

1996 ◽  
Vol 49 (3) ◽  
pp. 155-199 ◽  
Author(s):  
Ahmed K. Noor ◽  
W. Scott Burton ◽  
Charles W. Bert
Keyword(s):  
Computational Models ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Local Buckling ◽  
Sandwich Panels ◽  
Free Vibrations ◽  
Sandwich Plates ◽  
Material Parameters ◽  
Sandwich Plates And Shells ◽  
Plates And Shells

The focus of this review is on the hierarchy of computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters. The literature reviewed is devoted to the following application areas: heat transfer problems; thermal and mechanical stresses (including boundary layer and edge stresses); free vibrations and damping; transient dynamic response; bifurcation buckling, local buckling, face-sheet wrinkling and core crimping; large deflection and postbuckling problems; effects of discontinuities (eg, cutouts and stiffeners), and geometric changes (eg, tapered thickness); damage and failure of sandwich structures; experimental studies; optimization and design studies. Over 800 relevant references are cited in this review, and another 559 references are included in a supplemental bibliography for completeness. Extensive numerical results are presented for thermally stressed sandwich panels with composite face sheets showing the effects of variation in their geometric and material parameters on the accuracy of the free vibration response, and the sensitivity coefficients predicted by eight different modeling approaches (based on two-dimensional theories). The standard of comparison is taken to be the analytic three-dimensional thermoelasticity solutions. Some future directions for research on the modeling of sandwich plates and shells are outlined.

The Inelastic Line-Spring: Estimates of Elastic-Plastic Fracture Mechanics Parameters for Surface-Cracked Plates and Shells

1981 ◽  
Vol 103 (3) ◽  
pp. 246-254 ◽  
Author(s):  
D. M. Parks
Keyword(s):  
Fracture Mechanics ◽  
Crack Growth ◽  
Computing Time ◽  
Crack Tip ◽  
J Integral ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Elastic Plastic ◽  
Plates And Shells ◽  
Crack Tip Opening

Recent studies of the mechanics of elastic-plastic and fully plastic crack growth suggest that such parameters as the J-integral and the crack tip opening displacement can, under certain conditions, be used to correlate the initiation and early increments of the ductile tearing mode of crack growth. To date, elastic-plastic fracture mechanics has been applied mainly to test specimen geometries, but there is a clear need for developing practical analysis capabilities in structures. In principle, three-dimensional elastic-plastic finite element analysis could be performed, but, in fact, such analyses would be prohibitively expensive for routine application. In the present work, the line-spring model of Rice and Levy [1-3] is extended to estimate the J-integral and crack tip opening displacement for some surface crack geometries in plates and shells. Good agreement with related solutions is obtained while using orders of magnitude less computing time.

The Crack-Tip Fields of Reissner’s Plates of Radial Functionally Graded Materials

2011 ◽  
Vol 217-218 ◽  
pp. 1319-1323
Author(s):  
Yao Dai ◽  
Jun Feng Liu ◽  
Peng Zhang
Keyword(s):  
Functionally Graded Materials ◽  
Plate Theory ◽  
Crack Tip ◽  
Variable Coefficients ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Governing Equations ◽  
Crack Tip Field ◽  
Graded Materials ◽  
Crack Tip Fields

For homogeneous material plates and non-homogeneous material plates, the crack-tip field plays an important role in the research of fracture mechanics. However, the governing equations become the system of the sixth order partial differential ones with the variable coefficients when the material gradient is perpendicular to the thickness direction of plates. In this paper, they are derived first. Then, the crack-tip fields of the plates of radial functionally graded materials (FGMs) are studied and the higher order crack-tip fields are obtained based on the Reissner’s plate theory. The results show the effect of the non-homogeneity on the crack-tip fields explicitly and become the same as solutions of the homogeneous material plates as the non-homogeneous parameter approaches zero.

Efficient Analysis of 3-D Plates via Algebraic Reduction

2009 ◽  
Author(s):  
Vikalp Mishra ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Reduction Process ◽  
Thin Plates ◽  
Computationally Efficient ◽  
Design Environment ◽  
Element Analysis ◽  
Plates And Shells ◽  
Algebraic Reduction ◽  
Lower Dimensional Space

3-D finite element analysis (3-D FEA) is not generally recommended for analyzing thin structures such as plates and shells. Instead, a variety of highly efficient and specialized 2-D numerical methods have been developed for analyzing such structures. However, 2-D methods pose serious automation challenges in today’s 3-D design environment. In this paper, we propose an efficient yet easily automatable 3-D algebraic reduction method for analyzing thin plates. The proposed method exploits standard off-the-shelf finite element packages, and it achieves high computational efficiency through an algebraic reduction process. In the reduction process, a 3-D plate bending stiffness matrix is constructed from a 3-D mesh, and then projected onto a lower-dimensional space by appealing to standard 2-D plate-theories. Algebraic reduction offers the best of both worlds in that it is computationally efficient, and yet easy to automate. The proposed methodology is substantiated through numerical experiments.

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