THE SOLUTION OF BOUNDARY-VALUE PROBLEMS IN THE THEORY OF ELASTICITY FOR PIECEWISE-INHOMOGENEOUS MEDIA BY THE METHOD OF GENERALIZED FOURIER SERIES,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
Pagination or Media Count:
In an infinite elastic plane is built a finite elastic insert from another material, restricted by a closed boundary, with a constant curvature as regards H. The discontinuities in dislocations and stresses at the interface of the media are given. It is sought to determine the deformed state of the system. The boundary value problem of the elasticity theory for a piecewise inhomogeneous body is quite general despite of its seemingly particular nature and the solution of many boundary value problems in statics and oscillation of piecewise inhomogeneous bodies is advanced towards its solution. After making some general suppositions concerning the given data in the problem, the existence of a solution to the problem is proven and presented by Greens formula and an effective method of calculating the approximate values is given. This is accomplished by presenting the solution in the form of generalized Fourier series by a certain complete system of functions.