Non Uniform Rational B Spline (NURBS) Based Non-Linear Analysis of Straight Beams with Mixed Formulations

Journal of Solid Mechanics

مقاله 3، دوره 10، شماره 1، خرداد 2018، صفحه 38-56   

نوع مقاله: Research Paper

نویسندگان

R Ranjan^{* 1}؛ J.N Reddy²

¹School of Aerospace and Mechanical Engineering, 865 Asp Avenue, Norman, OK, 73019, USA

²Department of Mechanical Engineering, 3123 TAMU, College Station, TX, USA

چکیده

Displacement finite element models of various beam theories have been developed traditionally using conventional finite element basis functions (i.e., cubic Hermite, equi-spaced Lagrange interpolation functions, or spectral/hp Legendre functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation , and/or shear strain , as well as the variational method used (e.g., collocation, weak form Galerkin, or least-squares). When nonlinear shear deformation theories are used, the displacement finite element models experience membrane and shear locking. The present study is concerned with development of alternative beam finite elements using both uniform and non-uniform rational b-splines (NURBS) to eliminate shear and membrane locking in an hpk finite element setting for both the Euler-Bernoulli beam and Timoshenko beam theories. Both linear and non-linear analysis are performed using mixed finite element models of the beam theories studied. Results obtained are compared with analytical (series) solutions and non-linear finite element and spectral/hp solutions available in the literature, and excellent agreement is found for all cases.

کلیدواژه‌ها

NURBS basis؛ Euler-Bernoulli beam theory؛ Timoshenko Beam Theory؛ B-splines؛ Mixed formulation

مراجع

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