Singular finite elements for the fracture analysis of V‐notched plate

Lin, K. Y.; Tong, Penger

doi:10.1002/nme.1620150907

Cited by 128 publications

(46 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another option is the use of tailormade finite elements. Lin and Tong [2] chose an assumed-stress hybrid formulation for the setup in Figure 2. Up to sixteen Williams basis functions were used, at the notch only, in combination with bilinear and quadratic basis functions.…”

Section: Finite Element Methods Calculationsmentioning

confidence: 99%

See 1 more Smart Citation

On the computation of stress fields on polygonal domains with V‐notches

Helsing

Jönsson

2001

Numerical Meth Engineering

View full text Add to dashboard Cite

The interior stress problem is solved numerically for a single edge notched specimen under uniaxial load. The algorithm is based on a modification of a Fredholm second kind integral equation with compact operators due to Muskhelishvili. Several singular basis functions for each of the seven corners in the geometry enable high uniform resolution of the stress field with a modest number of discretization points. As a consequence, notch stress intensity factors can be computed directly from the solution. This is an improvement over other procedures where the stress field is not resolved in the corners and where notch stress intensity factors are computed in a roundabout way via a pathindependent integral. Numerical examples illustrate the superior stability and economy of the new scheme.

show abstract

Section: Finite Element Methods Calculationsmentioning

confidence: 99%

“…Accuracy control is essential in such a simulation. The finite element method, which is the most versatile computational tool today, often give mesh-dependent results in this and other difficult settings [2,3,4].…”

Section: Introductionmentioning

confidence: 99%

On the computation of stress fields on polygonal domains with V‐notches

Helsing

Jönsson

2001

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Numerical predictions in terms of nondimensional SIF I ( / ), when / = 0.4, are shown in Table 2 as the V-notch angle varies from 0 ∘ to 90 ∘ . Also, the nondimensional SIFs with respect to depth of V-notch are shown in Table 3 [10,12,13] is good in both cases.…”

Section: V-notched Platesmentioning

confidence: 97%

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

Woo

Ahn

2015

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

A higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for singleedge-crack aluminum plates with patch repairs. The present method is based on -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 of -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 on ℎ-refinement.

show abstract

“…The decomposition into a homogeneous and a particular part is done not only with regard to the satisfaction of the homogeneous and inhomogeneous differential equation, but also in view of the exact fulfilment of homogeneous and inhomogeneous boundary conditions on some portions of the element boundary, for example on the surface of a circular hole. For the special elements, we assume that displacement boundary conditions u = U on 8 In these cases and if the boundary portions aA1 and aA;, respectively, do not belong to the element boundary, one needs only to integrate on the inter-element boundary aAI;.…”

Section: Variational Formulationsmentioning

confidence: 99%

Special finite elements with holes and internal cracks

Piltner

1985

Numerical Meth Engineering

136

View full text Add to dashboard Cite

SUMMARYFor the numerical treatment of stress concentration problems in plane elasticity, special finite elements with circular and elliptic holes and internal cracks have been developed. Two different variational formulations have been used to construct elements, which may be combined with conventional displacement elements. Using complex functions and conformal mapping techniques the systematic construction of trial functions is shown which not only satisfy a priori the governing differential equations but also the boundary conditions on such influential boundary portions as hole or crack surfaces. For the evaluation of the stiffness matrices of the special elements, only boundary integral computations are necessary. The numerical results of various examples are very accurate for both functionals.

show abstract

Singular finite elements for the fracture analysis of V‐notched plate

Cited by 128 publications

References 5 publications

On the computation of stress fields on polygonal domains with V‐notches

On the computation of stress fields on polygonal domains with V‐notches

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

Special finite elements with holes and internal cracks

Contact Info

Product

Resources

About