Ritz Solution for Transient Analysis of Variable-Stiffness Shell Structures

Abstract

The dynamic response of thin-walled structures is driven by mass and stiffness distribution. As such, variable-stiffness (VS) composites offer opportunities to tune structural dynamic responses. To this extent, efficient analysis tools become increasingly important for structural analysis and design purposes. In this work, an efficient and versatile Ritz method for free vibrations and linear transient analysis of VS doubly curved shell structures is presented. VS shell structures are modeled as an assembly of shell-like domains. The shell kinematics is based on the first-order shear deformation theory, and no further assumption is made on the shallowness or on the thinness of the structure. The description of the shell is provided by a rational Bézier surface representation, and general surface geometries can be represented. Legendre polynomials are employed to approximate the displacement field, and penalty techniques are used to enforce displacement continuity and kinematical boundary conditions. Classical Rayleigh damping is considered, and solutions are obtained through the Newmark integration. The resulting model allows a wide range of configurations and load cases for multicomponent, VS composite structures to be solved, providing the same levels of accuracy as finite element analysis, yet with a reduced number of variables and simpler data preparation.