Search results for "Airy function"
showing 6 items of 6 documents
New indefinite integrals from a method using Riccati equations
2018
ABSTRACTAn earlier method for obtaining indefinite integrals of special function from the second-order linear equations which define them has been reformulated in terms of Riccati equations, which ...
Painlevé analysis and exact solutions for the coupled Burgers system
2006
We perform the Painleve test to a system of two coupled Burgers-type equations which fails to satisfy the Painleve test. In order to obtain a class of solutions, we use a slightly modified version of the test. These solutions are expressed in terms of the Airy functions. We also give the travelling wave solutions, expressed in terms of the trigonometric and hyperbolic functions.
Use of Automated Photoelasticity to Determine Stress Intensity Factors of Bimaterial Joints
2005
A new systematic experimental procedure has been developed to obtain the stress intensity factors governing the singular stress field that occurs near the intersection between the interface and free edges of bimaterial joints. A preliminary theoretical study of the singular stress field is carried out by the well-known Airy stress function method. The obtained stress laws are properly combined with the basic law of photoelasticity in order to define a procedure that permits the zone dominated by the singularity to be located and the stress intensity factors (SIFs) to be computed on the basis of full field data provided from automated photoelasticity. In particular, a systematic error analys…
Monotonicity properties of zeros of generalized Airy functions
1988
We show, among other things, that the positive zeros of a solution ofy ″+x α y=0,y(0)=0 decrease to 1 asα increases, 0〈α〈∞.
A novel boundary element formulation for anisotropic fracture mechanics
2019
Abstract A novel boundary element formulation for two-dimensional fracture mechanics is presented in this work. The formulation is based on the derivation of a supplementary boundary integral equation to be used in combination with the classic displacement boundary integral equation to solve anisotropic fracture mechanics problems via a single-region approach. The formulation is built starting from the observation that the displacement field for an anisotropic domain can be represented as the superposition of a vector field, whose components satisfy a suitably defined anisotropic Laplace equation, and the gradient of the Airy stress function. The supplementary boundary integral equation is …
Indefinite integrals of quotients of special functions
2018
ABSTRACTA new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica.