An isogeometric finite element method for the in-plane vibration analysis of orthotropic quadrilateral plates with general boundary restraints

Abstract

In this investigation, an isogeometric finite element method on the basis of non-uniform rational B-spline (NURBS) basis functions is developed for the in-plane vibration problems of various orthotropic shaped plates with general boundary restraints, which include rectangular plate with hole, rhombic, trapezoidal and quadrilateral plates. Under the framework, the gap between the designs of geometry with the analysis of variable field is bridged though applying NURBS basis functions to construct the displacement field and geometry of various orthotropic shaped plates. By the use of the virtual work principle, the differential equations of these orthotropic plates can be derived in detail. The current method can maintain exact geometry unchanged and flexibly elevate order of functions to obtain the desired accuracy. Arbitrarily restrained edges are realized by introducing the artificial boundary spring. In numerical results, refinement schemes are used to demonstrate the convergence of this method. Then the effectiveness and accuracy are validated through comparisons with results from open available literature. In addition, some new results of frequency parameter of various orthotropic shaped plates may serve as benchmark solution in future work. Finally, comprehensive studies on the effects of geometric proprieties, material parameters and boundary conditions on the frequencies are fully reported.