We present an extragradient-type algorithm for solving bilevel pseudomonone variational inequalities. The proposed algorithm uses simple projection sequences. Under mild conditions, the convergence of the iteration sequences generated by the algorithm is obtained.

A B S T R A C TThe effect of a second non-singular term of mode I in the vicinity of the tip of a V-notched crack is discussed. The undetermined eigenvector coefficients of singular and non-singular terms of eigenfunction expansion were calculated by the numerical analysis method using the reciprocal work contour integral method (RWCIM) based on Betti's reciprocal work theorem and finite-element analysis. This study demonstrates that the second non-singular term of mode I can have a significant effect on the size and shape of plastic zones as an additional fracture mechanics parameter along with the conventional parameter K.Keywords RWCIM; T-stress; V-notched crack; V-stress. N O M E N C L A T U R Ea = half crack length or half V-notched crack length A R , A I = eigenvector coefficients related to mode I and mode II C = closed contour C i = inner contour C o = outer contour F I , F II = dimensionless stress intensity factors F V = dimensionless V-stress K n I , K n II = notch stress intensity factors for the mode I and mode II r, θ = polar coordinate of general point P T = T-stress V = V-stress α = half-wedge angle β = half-notch angle γ = bisector angle of notch μ, ν = shear modulus and Poisson's ratio ϕ, η = eigenvalues related to mode I and mode II σ o = tensile yield stress I N T R O D U C T I O NIt is well known that a linear elastic body with a sharp notch shape has stress singularities at the tip of the Vnotched crack. The crack propagation may commence from the tip of V-notched crack due to these singular stresses. Therefore, researchers aimed at establishing methods for evaluating the stress intensity factors representing the singular fields near the tip of the V-notched crack as a fracture mechanics parameter have made rapid progress.For a V-notched crack, Williams 1 presented an eigenvalue formulation based on the notch angle by using eigenfunction expansion. The stress intensity factors related to the orders of stress singularity were investigated by Gross and Mendelson 2 using a boundary collocation method and by Lin and Tong 3 who employed special hybrid elements. For a homogeneous material and two dissimilar isotropic materials with a notch shape, the reciprocal work contour integral method (RWCIM) used by Stern et al. 4 was employed by Carpenter 5-7 to calculate the undetermined eigenvector coefficients associated with each eigenvalue. Zhao and Hahn 8 and Chen 9 also obtained the stress intensity factors under mixed mode 346

In this paper, we introduce an iterative method for solving the multiple-set split feasibility problems for asymptotically strict pseudocontractions in infinite-dimensional Hilbert spaces, and, by using the proposed iterative method, we improve and extend some recent results given by some authors.

This paper deals with the problems of blunt V‐notch with various notch shapes. The purpose is to develop a new method capable of obtaining more accurate solutions for the stress fields around a blunt V‐notch tip under opening and sliding modes. The key method is to use the principle of superposition for linear elastic materials. On the basis of the superposition method and the conventional stress fields for a sharp V‐notch, the stress fields useful for any shapes of blunt V‐notch is proposed. The notch stress intensity factors are estimated by the numerical analysis with finite element analysis, and then the effectiveness and validation of the proposed superposition approach are discussed by comparison with the results from the literature.

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