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The evaluation of the stress intensity factors at the tips of a crack in a homogeneous isotropic and elastic medium may be achieved with higher accuracy and much less computation if the
Application of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity
SummaryA modification of the form of the singular integral equation for the problem of a plane crack of arbitrary shape in a three-dimensional isotropic elastic medium is proposed. This modification
The V-notched elastic half-plane problem
SummaryThe problem of a V-notched isotropic elastic half-plane under generalized plane stress or plane strain conditions can be reduced, by using the complex variable technique, to a complex Cauchy
Quadrature Methods for the Determination of Zeros of Transcendental Functions - A Review
A review of quadrature methods for the numerical determination of zeros of algebraic or transcendental functions is presented, finding the common point of these methods is the use of numerical integration rules for the determination of the aforementioned zeros.
An elementary noniterative quadrature-type method for the numerical solution of a nonlinear equation
The convergence of the method is proved under mild assumptions and numerical results for two classical transcendental equations are presented.
Derivation of feasibility conditions in engineering problems under parametric inequality constraints with classical Fourier elimination
Fourier (or Motzkin or even Fourier–Motzkin) elimination is the classical and equally old analogue of Gaussian elimination for the solution of linear equations to the case of linear inequalities.
A modification of the classical quadrature method for locating zeros of analytic functions
The classical method for determination of a simple zeroa of an analytic functionf(z) inside a closed contourC by using the formulaa=(2πi)−1 εC[zf'(z)/f(z)]dz is reconsidered and modified. The
Analytical solution of the Lagrange quintic equation in the three-body problem in celestial mechanics
SummaryThe Lagrange equation is a quintic (fifth-degree) equation appearing in a stationary solution of the three-body problem in celestial mechanics. This equation has one positive root, which is