Laminated Beam Analysis by Polynomial, rigonometric, Exponential and Zig-Zag Theories

A number of refined beam theories are discussed in this paper. These theories were obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials, trigonometric series, exponential, hyperbolic and zig-zag functions. The Finite Element method is used to derive governing equations in weak form. By using the Unified Formulation introduced by the first author, these equations are written in terms of a small number of fundamental nuclei, whose forms do not depend on the expansions used. The results from the different models considered are compared in terms of displacements, stress and degrees of freedom (DOFs). Mechanical tests for thick laminated beams are presented in order to evaluate the capability of the finite elements. They show that the use of various different functions can improve the performance of the higher-order theories by yielding satisfactory results with a low computational cost

Carrera Unified Formulation for Free-Vibration Analysis of Aircraft Structures

Advanced structural models, based on variable one-, two-, and three-dimensional kinematics, are proposed in this paper and applied to the analysis of the free vibration of reinforced aircraft shell structures. The used models go beyond classical structural theories, that is, Euler–Bernoulli (for one-dimensional beams) and Kirchhoff (for two-dimensional plates) type assumptions. The order of the expansion of the displacement fields over the cross section (one-dimensional case) and along the plate thickness (two-dimensional case) is, in fact, a free parameter of the problem. In this paper, Lagrange polynomials are used to build such expansions, and as a consequence, only displacements are used as the problem unknowns (no rotations or derivatives of displacements, which are typical of one-dimensional/two-dimensional classical theories, are introduced). The finite-element method is used to provide numerical solutions. The related arrays and the governing dynamical equations are written in terms of a few fundamental nuclei according to the Carrera unified formulation. Classical three-dimensional finite-element solid models are also considered. One-, two-, and three-dimensional finite elements are easily connected to each other to make the most appropriate computational model of the reinforced shell structures. The capability to use the same fundamental nucleus to derive finite-element matrices of one-, two-, and three-dimensional elements of the present model is unique because it is usually not available in other finite-element formulations, that is, no ad hoc techniques are required in the present case to couple finite elements with different kinematics. Three main benchmarks have been analyzed: a plate stiffened by means of bidirectional I-stiffeners, a simplified model of a complete aircraft, and a fuselage–wing connection. Comparison with commercial finite-element software (MSC Nastran) is provided for most of the quoted numerical investigations. The modal assurance criterion has been used to compare the free-vibration modes of the different models. The present mathematical models appear closer to reality and cheaper, from the computational point of view, than those of other existing formulations. Carrera unified-formulation-based finite elements do not require the definition of virtual lines (beam axes) or virtual surfaces (plate reference surfaces), and only physical lines/surfaces are therefore used

Advanced modeling of embedded piezo-electric transducers for the health-monitoring of layered structures

The present paper presents an innovative approach for the numerical modeling of piezo-electric transducers for the health-monitoring of layered structures. The numerical approach has been developed in the frameworks of the Carrera Unified Formulation. This computational tool allows refined numerical models to be derived in a unified and efficient fashion. The use of higher-order models and the capability to connect different kinematic models using the node-dependent kinematic approach has led to an efficient modeling technique for global-local analysis. This approach can refine the model only in those regions where it is required, e.g., the areas where piezo-electric transducers are placed. The model has been used to study embedded and surface-mounted sensors. The accuracy of the present model has been verified by comparing the current results with numerical and experimental data from the literature. Different modeling solutions have been developed, mixing one-, two- and three-dimensional finite elements. The results show that the use of the present modeling technique allows the computational cost to be reduced with respect to the classical approaches preserving the accuracy of the results in the critical areas

Thermo-piezo-elastic analysis of amplified piezoceramic actuators using a refined one-dimensional model

The thermo-piezo-elastic analysis of amplified piezoceramic actuators is presented in this article. A refined one-dimensional multi-field finite element model, based on the Carrera Unified Formulation, has been developed. Thermal and piezoelectric effects have been included in the structural model and a fully coupled thermo-piezo-elastic analysis has been performed. The finite element model has been assessed by comparing it with results from open literature The model has also been used to perform the analysis of complex amplified piezoceramic actuators. These actuators are able to amplify the displacements produced by piezoceramic material, but they suffer from high deformations when they undergo high thermal loads. An accurate thermal analysis has been performed to evaluate the strain/stress field. The results show the accuracy of the present model and its capabilities in multi-field analyses

Multidimensional Model for the Stress Analysis of Reinforced Shell Structures

The present paper proposes an approach that can be used to mix one-, two-, and three-dimensional refined models, derived using the Carrera Unified Formulation, to build a variable kinematic model that is able to deal with the static analysis of complex thin-walled structures. The adopted formulation, which only has displacements as degrees of freedom, allows these models to easily be connected to each other; that is, a variable kinematics model can be derived without ad hoc techniques. The refined models used in the present paper ensure high accuracy and low computational costs. The displacement continuity at the interface is guaranteed by the formulation, and no stress singularities appear in the kinematic model transition. The mixed interpolation tensorial component approach has been used, in a unified sense, for one-, two-, and three-dimensional models to avoid the shear locking effect. The accuracy of the present approach has been confirmed by comparing the results with those from the literature and with those obtained using commercial finite element codes. The static response of a reinforced panel and a section of an aircraft fuselage have been investigated to show the capabilities of the present approach. The use of refined structural models makes it possible to overcome the limits of classical structural models and, at the same time, to reduce the computational costs