Development of computational efficient shell formulation for analysis of multilayered structures subjected to mechanical, thermal, and electrical loadings

The aim of this work is the development of robust finite shell model suitable for numerical applications in solid mechanics with a remarkable reduction in computational cost. Two-dimensional (2D) structural models, commonly known as plates/shells, are for instance used in many applications to analyze the structural behavior of thin and slender bodies such as panels, domes, pressure vessels, and wing stiffened panels amongst others. These models reduce the three-dimensional 3D problem into a two-dimensional 2D problem, where variables depend on the in-plane axis coordinates. Two-dimensional elements are simpler and computationally more efficient than 3D (solid) models. This feature makes plate/shell theories still very attractive for the static, dynamic response, free vibration, thermo-mechanical and electro-mechanical analysis, despite the approximations which they introduce in the simulation. Nevertheless, analytical solutions for three-dimensional elastic bodies are generally available only for a few particular cases which represent rather coarse simplifications of reality. In most of the practical problems, the solution demands applications of approximated computational methods. The Finite Element Method (FEM) has a predominant role among the computational techniques implemented for the analysis of layered structures. The majority of FEM theories available in the literature are formulated by axiomatic-type theories. In this thesis, attention is focused on weak-form solutions of refined plate/shell theories. In particular, higher-order plate/shell models are developed within the framework of the Unified Formulation by Carrera, according to which the three-dimensional displacement field can be expressed as an arbitrary expansion of the generalized displacements. A robust finite shell element for the analysis of plate and shell structures subjected to mechanical, thermal, and/or electrical loadings is developed. A wide range of problems are considered, including static analysis, free vibration analysis, different boundary conditions and different laminations schemes, distributed pressure loads, localized pressure loads or concentrated loads are taken into account. The high computational costs represent the drawback of refined plate/shell theories or three-dimensional analyses. In recent years considerable improvements have been obtained towards the implementation of innovative solutions for improving the analysis efficiency for a global/local scenario. In this manner, the limited computational resources can be distributed in an optimal manner to study in detail only those parts of the structure that require an accurate analysis. In the second part of the thesis two different methodology are presented to improve the analysis efficiency, and at the same time keeping the finite higher-order plate/shell element accuracy. The two approaches can be collocated in the simultaneous multi-model methodologies. The first is the Mixed ESL/LW variable kinematic method, where the primary variables are described along the shell thickness selecting some plies with an ESL description and others with a LW behaviour by using the Legendre polynomials for both the assembling approaches. The second approach is a new simultaneous multi-model, here presented as Node-Dependent Variable Kinematic method. The shell element with node-dependent capabilities enables one to vary the kinematic assumptions within the same finite element. The expansion order ( along the shell thickness ) of the shell element is, in fact, a property of the FE node in the present approach. Different kinematics can be coupled without the use of any mathematical artifice. The theories developed in this thesis are validated by using some selected results from the literature. The analyses suggest that Unified Formulation furnishes a reliable method to implement refined theories capable of providing almost three-dimensional elasticity solution, and that the two simultaneous multi-theories methods are extremely powerful and versatile when applied to composite or sandwich structures subjected to various mutlifield loadings.