Alfonso Pagani

Linearized buckling analysis of isotropic and composite beam-columns by Carrera Unified Formulation and dynamic stiffness method.

Abstract This article introduces a one-dimensional (1D) higher-order exact formulation for linearized buckling analysis of beam-columns. The Carrera Unified Formulation (CUF) is utilized and the displacement field is expressed as a generic N-order expansion of the generalized unknown displacement field. The principle of virtual displacements is invoked along with CUF to derive the governing equations and the associated natural boundary conditions in terms of fundamental nuclei, which can be systematically expanded according to N by exploiting an extensive index notation. After the closed form solution of the N-order beam-column element is sought, an exact dynamic stiffness (DS) matrix is derived by relating the amplitudes of the loads to those of the responses. The global DS matrix is finally processed through the application of the Wittrick-Williams algorithm to extract the buckling loads of the structure. Isotropic solid and thin-walled cross-section beams as well as laminated composite structures are analyzed in this article. The validity of the formulation and its broad range of applicability are demonstrated through comparisons of results from the literature and by using commercial finite element codes.

Micromechanics Modeling of Unit Cells Using CUF Beam Models and the Mechanics of Structure Genome

A novel approach for the micromechanics analysis of composite structures is developed using refined beam models and the mechanics of structure genome (MSG). The MSG provides a tool to obtain the complete stiffness matrix of general composite materials by asymptotically minimizing the loss of information between the original heterogeneous body and the sought homogenized body. The constitutive information is in this manner extracted from the representative volume without the need of ad-hoc assumptions and in one single loading step. The local fields are then straightforwardly recovered using the same unknowns of the original homogenization problem, with no need of additional analyses. This work proposes the use of higher-order beam models based on the Carrera unified formulation (CUF) to solve the micromechanics problem by means of MSG. The fibers, or equivalent constituents, are discretized along the longitudinal direction with beam elements and the unknown variables are expanded over the remaining two local coordinates making use of Legendre-class polynomial sets, denoted to as Hierarchical Legendre Expansions (HLE). In addition, non-local expansion domains with curved boundaries are defined to capture the exact shape of the constituents independently of the refinement of the model. In this sense, the quality of the approximation is controlled by the polynomial order of the beam model, which is introduced in the analysis as a user input, and the size of the computational problem can be reduced for many typical microstructures with no loss of accuracy.