CCOME2025

Special Guests

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Update Time: 2025-10-23 14:06:51 CST

Suliman Khan

Nanjing University of Aeronautics and Astronautics

On Numerical Computation of the Cauchy-type Singular Integrals

Abstract | Introduction

To approximate Cauchy-type singular integrals with a high-frequency Fourier kernel, we suggest two different kinds of splitting techniques. We suggest modified Levin collocation techniques using Chebyshev polynomials and a multi-quadric radial basis function to evaluate non-singular integrals. A multi-resolution quadrature is employed to address the singularity-ridden kernel in the interval splitting scenario. In contrast, the singular component integral is evaluated analytically in the case of integrand splitting. The novel algorithms convert logarithmic singular integrals with oscillatory kernels to Cauchy principal value integrals and compute them. Benchmark problems verify both the individual approaches and the component algorithms. We can easily extend the algorithms to other classes of oscillatory integrals, such as Hadamard finite part integrals and hypersingular oscillatory integrals.

Waseem Sarwar

合肥工业大学

Evaluation of stress singularity orders and generalized stress intensity factors for axisymmetric V-notches

Abstract | Introduction

A detailed linear elastic stress state analysis around the vertex of an axisymmetric V-notch depends on understanding stress singularities, eigen angular functions, and generalized stress intensity factors. This study introduces a numerical method for determining the stress singularity state at the singularity of the axisymmetric V-notches. The displacement field near the axisymmetric V-notch tip is expanded asymptotically and substituted into the equilibrium equations of the axisymmetric structure, yielding a system of nonlinear characteristic ordinary differential equations that govern the stress singularity orders. The nonlinear ones are linearized by introducing two variables, and then the interpolating matrix method is introduced for solving the established characteristic equations, which simultaneously determines the stress singularities and their associated eigen-angular functions under different radial boundary conditions for both single and bi-material axisymmetric V-notch configurations. The generalized stress intensity factors of axisymmetric V-notches are computed using the finite element method by postprocessing the stress results. The results show that there are two singularity orders for the single material axisymmetric V-notch, their values are the same with the ones of the plane V-notch, while their meaning are different. The singularity orders of the axisymmetric V-notch are with respect to displacement of ur and w, while they are corresponding to ur and uθ for the plane V-notch. There are only real singularity orders for axisymmetric V-notch under free-free and clamped-clamped radial boundary conditions, while there are complex singularity orders for the V-notch under free-clamped conditions. The singularities of single-material axisymmetric V-notches are significantly dependent on the notch opening angle, while the elastic modulus ratios have a significant influence on the stress singularity orders in bi-material configurations. It is found that the notch depth is the dominant factor, whereas the notch opening angle has a secondary influence on the generalized stress intensity factor values.