Application of the R-Functions Theory to Problems of Nonlinear Dynamics of Laminated Composite Shallow Shells and Plates: Review

A review of studies performed using the R-functions theory to solve problems of nonlinear dynamics of plates and shallow shells is presented. The systematization of results and studies for the problems of free and parametric vibrations and for problems of static and dynamic stability is fulfilled. Expansion of the developed original method of discretization for nonlinear movement equations on new classes of nonlinear problems is shown. These problems include researches of vibrations of antisymmetric laminated cylindrical and spherical panels; laminated composite shallow shells with variable thicknesss of the layers; functionally graded (FG) shallow shells and others. The basic issues that arise when using RFM are described. The future prospects of using the theory of R-functions for solving problems of nonlinear dynamics of plates and shallow shells with complex form are formulated. First of all this is an algorithms development and creation of the associated software to apply multi-modes approximations; improvement of approximation tools for nonlinear problems; investigation of the cracked functionally graded shallow shells; FG panels under thermal environments; parametric vibrations, static and dynamical stability of the multilayered and FG plates and shells