Free vibration analysis of thin plates by using a NURBS-based isogeometric approach

• Published in: Finite elements in analysis and design 2012-11, Vol.61, p.23-34
• Main Authors: Shojaee, S., Izadpanah, E., Valizadeh, N., Kiendl, J.
• Format: Article
• Language: English
• Subjects: Approximation; Exact sciences and technology; Finite element method; Free vibration; Fundamental areas of phenomenology (including applications); Galerkin methods; Isogeometric analysis; Kirchhoff plate; Mathematical analysis; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; NURBS; Physics; Plate; Robustness; Sciences and techniques of general use; Solid mechanics; Structural and continuum mechanics; Thin plates; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2012.06.005

An isogeometric finite element method is presented for natural frequencies analysis of thin plate problems of various geometries. Non-Uniform Rational B-Splines (NURBS) basis function is applied for approximation of the thin plate deflection field, as for description of the geometry. The governing and discretized equation for the free vibration of the Kirchhoff thin plates is obtained using the standard Galerkin method. Several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of proposed method and compared with the theoretical solutions and other numerical methods. ► The NURBS-based isogeometric method is developed for eigen-value analysis of plates. ► Several numerical simulations of thin plates with various shapes are examined. ► For such eigen-value problems considering various aspect ratios. ► Proposed approach can yield highly accurate solutions of the eigenvalue problems. ► The proposed method is potential and applicable to practical problems of engineering