LEFM Analysis of V-Notched Aluminum Plates Using Higher-Order Layerwise Model

2014 ◽  
Vol 898 ◽  
pp. 355-358
Author(s):  
Kwang Sung Woo ◽  
Yoo Mi Kwon ◽  
Dong Woo Lee ◽  
Hee Joong Kim
Keyword(s):  
Legendre Polynomials ◽  
Present Method ◽  
Higher Order ◽  
Virtual Crack Closure Technique ◽  
Shape Functions ◽  
Intensity Factors ◽  
Displacement Fields ◽  
Closure Technique ◽  
Aluminum Plates ◽  
Convergent Approach

Higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for V-notched plates. Present method is based on p-convergent approach and adopts the concept of subparametric element. In assumed displacement field, strain-displacement relations and 3-D constitutive equations of a layer are obtained by combination of 2-D and 1-D higher-order shape functions. Thus, it allows independent implementation of p-refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively.

scholarly journals Implementation of Virtual Crack Closure Technique for Damaged Composite Plates Using Higher-Order Layerwise Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Kwang S. Woo ◽  
Jae S. Ahn
Keyword(s):  
Crack Closure ◽  
Edge Crack ◽  
Present Model ◽  
Three Dimensional ◽  
Higher Order ◽  
Virtual Crack Closure Technique ◽  
Single Edge ◽  
Displacement Fields ◽  
Closure Technique ◽  
Aluminum Plates

A higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for single-edge-crack aluminum plates with patch repairs. The present method is based onp-convergent approach and adopts the concept of subparametric elements. In assumed displacement fields, strain-displacement relations and three-dimensional constitutive equations of layers are obtained by combination of two- and one-dimensional shape functions. Thus, it allows independent implementation ofp-refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively. For verification of the present model, not only single-edge-crack plates but also V-notch aluminum plates are first analyzed. For patched aluminum plate with behavior of complexity, the accuracy and simplicity of the present model are shown with comparison of the results with previously published papers using the conventional three-dimensional finite elements based onh-refinement.

Higher order TN approximation for the neutron diffusion problem in a slab reactor

Kerntechnik ◽  
2021 ◽  
Vol 86 (4) ◽  
pp. 294-301
Author(s):  
H. Öztürk ◽  
B. Durmaz
Keyword(s):  
Chebyshev Polynomials ◽  
Legendre Polynomials ◽  
Present Method ◽  
Diffusion Problem ◽  
Higher Order ◽  
Neutron Diffusion ◽  
Good Accordance ◽  
First Time ◽  
Secondary Neutrons ◽  
Better Than

Abstract Higher order approximations of the Chebyshev polynomials of first kind (TN) are used for the first time in calculation of the diffusion lengths of monoenergetic neutrons in a homogeneous slab. In the method, the diffusion lengths of the neutrons are calculated using various values of the c, the number of secondary neutrons per collision. First, the traditional Legendre polynomials (PN) approximation and then the present TN method are used separately. The numerical results for the diffusion lengths are tabulated in the tables up to an order of N = 9. A brief comparison is also done between the results obtained from the present method and the ones in literature. The advantages of the present method can easily be observed from the good accordance between results given in the tables for comparison and its easily executable equations. For many of the c values, the results obtained from TN method are better than the results obtained from PN method.

Quarter-Point Elements Are Unnecessary for the VCCT

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Elad Farkash ◽  
Leslie Banks-Sills
Keyword(s):  
Stress Intensity ◽  
Energy Release ◽  
Crack Closure ◽  
Stress Intensity Factors ◽  
Virtual Crack Closure Technique ◽  
Intensity Factors ◽  
Release Rates ◽  
Closure Technique ◽  
Established Method ◽  
Energy Release Rates

Abstract The virtual crack closure technique (VCCT) is a well-established method for determining energy release rates and stress intensity factors in homogeneous, isotropic materials. It has been implemented with four-noded, eight-noded, quarter-point, and other higher order elements. It is most convenient and accurate when used with eight-noded, isoparametric elements. VCCT produces less accurate results when used with quarter-point elements. Yet, this method continues to be employed with quarter-point elements. It is strongly recommended to use VCCT with regular eight-noded elements. Three examples will be presented to illustrate the inaccuracy when using quarter-point elements with VCCT.

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