Análise isogeométrica de cascas cilíndricas de material com gradação funcional

Abstract

Shells are structures of great interest in engineering and present a wide range of applications, among which we can mention civil, aeronautical, mechanical, automotive and naval applications. Associated with composite materials, these structures offer improved properties, such as increased stiffness and specific strength. Among the composite materials, fiber-reinforced laminated materials and functionally graded materials deserve particular attention. From the engineering point of view, it is essential to determine the behaviour of structures, such as the composite shells, in order to provide safe and economical design. For this purpose, several theories have been proposed, being the theories of cylindrical shells considered good starting models for more complex formulations. Among them, due to its efficiency and simplicity, Donnell’s nonlinear theory stands out, being the object of several studies. The method chosen to carry out the study was the isogeometric analysis, since this is a recent and open field to many possibilities with great advantages such as the exact representation of the geometry of the problem and the easy refinement, especially when compared to the MEF. The present work aims to contribute to the advancement of the analysis of FGMs cylindrical shells subjected to mechanical loading using an isogeometric approach. To that end, an isoparametric finite element formulation based on Donnell’s nonlinear theory was adapted by adding transversal shear terms and implemented in a program named FAST. Thereafter, this formulation was extended to an isogeometric element. The effective properties of the materials were evaluated using an external routine to FAST and later read as input to the program. To validate the implementation, numerical examples found in the literature and results obtained by commercial software were compared to the ones found here use of refinements and different integration schemes. In all tests, the element presented excellent results, validating the implementation of the proposed formulation and the external routine for the effective properties determination. An analysis of the FGMs cylindrical panels subjected to transverse load and uniaxial compression was proposed. The postbuckling response was studied. The results confirm the behaviour predicted in the literature, where the response of the FGM structure is between the responses of its isolated constituents.