On a method of solving problems of bending of rods and plates of piecewise-constant stiffness (Q579024)

By using an effective procedure expansions were constructed by \textit{Ya. Uflyand} [On certain new integral transformations and their applications to mathematical physics (1976)] of an arbitrary function in the eigenfunction integral of a boundary value problem for second-order differential equations given in an interval with different sections of stepwise-changing physical characteristics. This procedure is applied to construct the expansion of an arbitrary function in an eigenfunction series for fourth-order equations given in a finite interval with an arbitrary quantity of stepwise-varying characteristics. The finite integral transforms obtained in such a manner can be utilized in solving different bending problems for rods or plates with piecewise-varying stiffness, which enables us to formalize the procedure for solving specific problems. The need to solve differential equations given in a composite interval also arises in a study of the state of stress of layered elastic media. A general approach to the solution of problems of mechanics for layered media is proposed by \textit{G. Ya. Popov} [Izv. Akad. Nauk Arm. SSR, Mekh. 31, No.2, 34-47 (1978; Zbl 0435.73019)], and is based on extending the method of initial parameters and results in an effective calculational procedure.