Application of the ps−Version of the Finite Element Method to the Analysis of Laminated Shells

Abstract

The development of accurate and efficient numerical methods is of crucial importance for the analysis and design of composite structures. This is even more true in the presence of variable stiffness (VS) configurations, where intricate load paths can be responsible for complex and localized stress profiles. In this work, we present the ps−version of the finite elements method (ps−FEM), a novel FE approach which can perform global/local analysis through different refinement strategies efficiently and easily. Within this framework, the global behavior is captured through a p−refinement by increasing the polynomial order of the elements. For the local one, a mesh−superposition technique, called s−refinement, is used to improve locally the solution by defining a local/fine mesh overlaid to the global/coarse one. The combination of p− and s−refinements enables us to achieve excellent accuracy−to−cost ratios. This paper aims to present the numerical formulation and the implementation aspects of this novel approach to VS composite shell analysis. Numerical tests are reported to illustrate the potential of the method. The results provide a clear insight of its potential to guarantee fast convergence and easy mesh refinement where needed.