Session: 02-01-01: Dynamic Loads, Response, Vibration and Alleviation of Aerospace Structures - I

Paper Number: 108345

108345 - Dynamic Analysis of Variable Thickness Shells in Aerospace Applications via Cuf Adaptive Finite Elements 

The aerospace sector is always seeking in new tool to lighten structures without a reduction in the mechanical properties of the system. In last decades significant improvements have been achieved by new optimization tools or concepts. A very powerful method is the topology optimization, which can lead to a reduction in the system weight through the remotion and the addition of material in the less and the most loaded areas respectively. The results are usually unconventional geometries which require new production tools as additive manufacturing. For thin structures, such as plates and shells, the topology optimization can lead to a local variation of the thickness with a general reduction in the weight. This is especially true for local out-of-plane loads as those generated by an impact (e.g., ballistic, debris, etc.) and for vibrations absorption (e.g., those generated in the launch phase or inside the launcher). Nevertheless, there is a lack of reliable, flexible, and computationally cheap numerical tools for studying the dynamic behaviour of variable thickness plates and shells. In the Finite Element Method (FEM) framework these structures are traditionally studied through solid elements costing in terms of Degrees of Freedom (DoF).

The aim of this work is to develop a reliable finite element model for vibrational analysis of variable thickness shells. The structural kinematic is described according to the Carrera’s Unified Formulation (CUF), to enhance a wide class of powerful refined two-dimensional plate theories with a unique formulation, suitable for multi-layer structures. The classical Node-Dependent-Kinematic (NDK) in CUF is extended to take in account variable thickness plates or edges not orthogonal to the midsurface. In the framework of NDK approach, it is possible to extend the models of CUF to the modelling of this kind of geometries by incorporating the CUF kinematic assumption, the thickness functions, and the FEM discretization, the shape functions, in a unique 3D approximation. The new functions are developed in curvilinear coordinates and represent a non-conventional 3D shape function in which the order of expansion can be different along one of the spatial directions. Therefore, the Jacobian matrix in global coordinates is computed in 3D form. The choice of the thickness functions, and subsequently of the kinematic approach, is the core of the CUF, Taylor’s expansions lead to an Equivalent Single Layer (ESL), while Lagrange’s polynomials to a Layer Wise (LW) approach, which depends on the expansion order and on the number of nodes along the thickness (LWn where n is the number of the through-the-thickness nodes). The creation of the unconventional 3D function allows to use different kinematic approaches in the same shell, in particular for LWn models, increasing the number of nodes through-the-thickness in the same element according to the local thickness or to the number of layers of the plate. This new function and the whole formulation do not add DoF with respect to the traditional CUF. The formulation is exploited to evaluate the natural frequencies of two cases:

·       a topology optimized plate for impact applications. In this case the plate has different thicknesses according to the load condition;

·       a vibration control on a semi-cylinder with different thicknesses on the shell. A wave-shaped thickness is applied on a cylindrical midsurface.

These two examples aim to demonstrate the possible applications of the CUF enhanced for variable thickness shells, which allows to study advanced structures with 2D model and several kinematic approaches, as different LWn expansions. In this way, there is a significant saving in DoF compared to a solid model, without decreasing the accuracy of the solutions.

Finally, the proposed formulation wants to be a significant tool in the optimization of the vibration control or in the impact applications in the aerospace sector. In fact, it provides an accurate method for calculating the dynamic response of plates with unconventional designs, such as those usually obtained by topological optimisation methods.

 

Presenting Author: Martino Carlo Moruzzi Università di Bologna

Presenting Author Biography: Martino Moruzzi is a research fellow at Università di Bologna. He achieved his Phd in Mechanics and Advanced Engineering Sciences (curriculum in Aerospace engineering) at the Università di Bologna and the Master's Degree at Politecnico di Torino in Aerospace Engineering. In the last years he is working on vibro-acoustics for internal noise control in aircraft and on the extension of the Carrera's Unified Formulation in the vibro-acoustic fields.

Authors:

Maria Cinefra Politecnico di Bari
Martino Carlo Moruzzi Università di Bologna