Keywords: refined beam theories, finite elements, unified formulation, composites, reinforced shell structures, civil engineering structures, component-wise.

Many engineering structures can be seen as multicomponent structures since they are composed of different parts which, most of the time, can have very different mechanical properties. Typical examples of such structures are aircraft wings and fiber-reinforced composites. The former are typically composed of skins, spars, stringers and ribs. The latter are composed of plies made of fibers and matrices.

Many critical issues have to be dealt with in the structural analysis of multicomponent structures. For instance, as far as aircraft wings are concerned, the proper structural modeling of longitudinal slender elements connected to transversal thin-walled structures can be problematic. In the analysis of composite structures, the proper detection of multiscale effects represents an open issue for structural scientists. All these problems often are solved by exploiting very burdensome finite element models with some 10⁵-10⁶ degrees of freedom.

The present work presents an innovative component-wise (CW) approach which can be employed for the structural analysis of multicomponent structures in mechanical and civil engineering. CW is based on the Carrera unified formulation (CUF) for structural models. In particular, the one-dimensional CUF models were exploited in this work. In the CUF framework, refined models are hierarchically obtained by considering arbitrary expansion orders of the problem unknowns. The one-dimensional CUF models, for instance, are based on higher-order displacement fields above the structure cross-section. The one-dimensional CUF has been recently developed, different classes of models are available and, in this work, Taylor-like (TE) [1] and Lagrange-like (LE) [2] elements were adopted. The main features of one-dimensional CUF can be summarized as follows: (1.) Results from the one-dimensional CUF have the same accuracy as those from shell and solid finite elements for many structural problems such as thin-walled structures and composites; (2.) The computational costs of the one-dimensional CUF are considerably lower than those of shell and solid finite element models.

The CW approach represents the last extension of the CUF models. In a CW model, each structural component is modeled by means of a unique structural formulation. In other words, only one-dimensional CUF models are exploited to model different structural components such as ribs and spars or fibers, matrix and plies. In a finite element model, this means that the stiffness matrices of different components are formally the same and can be assembled straightforwardly. CW models provide high accuracy with very low computational effort.

Different numerical examples were carried out in this work. Particular attention was given to aircraft wings, fiber-reinforced composites and typical structures from civil engineering. Comparisons with results from solid finite elements were given. It is concluded that the present CW approach represents a reliable and computationally cheap tool which can be exploited for many types of structural analyses.

[1]

E. Carrera, G. Giunta, M. Petrolo, "Beam Structures: Classical and Advanced Theories", John Wiley & Sons, 2011. doi:10.1002/9781119978565

[2]

E. Carrera, M. Petrolo, "Refined beam elements with only displacement variables and plate/shell capabilities", Meccanica, 47(3), 537--556, 2012. doi:10.1007/s11012-011-9466-5

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