A Novel Highly Accurate Finite-Element Family

作者：Bernardini Giovanni; Cetta Fabio; Morino Luigi

来源：International Journal of Aerospace Engineering, 2017, 2017: 7293682.

DOI：10.1155/2017/7293682

<jats:p>A novel <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>th order finite element for interior acoustics and structural dynamics is presented, with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math> arbitrarily large. The element is based upon a three-dimensional extension of the Coons patch technique, which combines high-order Lagrange and Hermite interpolation schemes. Numerical applications are presented, which include the evaluation of the natural frequencies and modes of vibration of (1) air inside a cavity (interior acoustics) and (2) finite-thickness beams and plates (structural dynamics). The numerical results presented are assessed through a comparison with analytical and numerical results. They show that the proposed methodology is highly accurate. The main advantages however are (1) its flexibility in obtaining different level of accuracy (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-convergence) simply by increasing the number of nodes, as one would do for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:math>-convergence, (2) the applicability to arbitrarily complex configurations, and (3) the ability to treat beam- and shell-like structures as three-dimensional small-thickness elements.</jats:p>

• 出版日期2017