SYMMETRICAL LOADING OF AN INFINITE PLATE WEAKENED BY THREE CIRCULAR HOLES (SIMMETRICHNOE NAGRUZHENIE BESKONECHNOI PLASTINKI, OSLABLENNOI TREMYA KRUGOVYMI OTVERSTIYAMI),
Abstract
A solution is given of the problem of the elastic equilibrium of an infinite plate with three identical circular holes (arranged in line and equally spaced) which is subjected to uniform pressure applied to the edges of the holes. Complex representation of stress functions is used in solving the problem. A method developed by N. I. Muskhelishvili is applied in setting up functional equations for the complex-variable stress functions. By introducing auxiliary functions describing the stress-strain relations in the hole-weakened domain, a general expression with unknown coefficients which represents the solution of the problem is written. After performing certain transformations and using the boundary conditions for the middle hole and side holes, expressions for determining the unknown coefficients are obtained. The solution obtained in this way can be easily extended to other types of symmetrical plate loading. Calculation procedures in cases when a uniform pressure is applied only to the edges of the side holes (the edge of the middle hole is free of external loads), and vice versa, are indicated. The values of coefficients calculated by means of three approximations are given in a table. It is noted that the third approximation does not introduce any essential corrections and thus can be omitted even under the most unfavorable conditions (when the edges of neighboring holes are close to each other). A diagram showing the stress distribution is given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 19, 1967
- Accession Number
- AD0673694
Entities
People
- M. Z. Narodetskii
Organizations
- National Air and Space Intelligence Center