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COBEM 2021
26th International Congress of Mechanical Engineering
A Hierarchical Finite Element Model for Modal Analysis of Aircraft Structures
Submission Author:
Eduardo Westphal da Cunha , SP
Co-Authors:
Eduardo Westphal da Cunha, Mauricio Donadon, Antônio Bernardo Guimarães Neto, Fernando José de Oliveira Moreira
Presenter: Eduardo Westphal da Cunha
doi://10.26678/ABCM.COBEM2021.COB2021-1534
Abstract
Conventional (or h-version) finite element method has been widely used in structural analysis for at least a few decades. It is a very robust method with many applications that allowed more complex and higher fidelity analysis and, consequently, more accurate results. Its convergence analysis is based on increasing the number of elements in each component domain by decreasing their size. When new elements are added in the model, it is necessary to perform a completely new solution, which means that the computer repeats all the computations and does not use the previously generated solution. The same occurs when any change of the geometric properties and/or material properties is made. In this work, a hierarchical p-version finite element model is proposed to analyze the free vibration behavior of a simplified aircraft structure. This method is based on the domain discretization by using a hierarchical series of shape functions that describes the displacement field within the element domain complying with essential boundary conditions. Alternatively, the convergence analysis in the p-version of the finite element method is carried out by increasing the degree p of the hierarchical shape functions instead of decreasing the size h of the elements. In this way, it is possible to optimize the convergence analysis by storing the previous calculations and just computing the terms corresponding to the newly added equations. Moreover, a parametrization of the beam properties in the form of polynomials, for instance, enables a quick and easy modification as it avoids the need of performing the entire computation again when the properties are changed. Study cases are presented for a typical aircraft configuration in which the aircraft structure is modeled by using only eight beam elements at first and in a second analysis, concentrated masses are attached to each element. The proposed p-version method-based model is implemented into a MATLAB script and an equivalent model is built up in FEMAP with the conventional h-version method. Finally, the modal frequencies obtained using both modeling methodologies are compared and conclusions are drawn.
Keywords
finite element, Aircraft structures, free vibration analysis, Hierarchical Finite Element
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