NURBS-Based Isogeometric Analysis of Beams and Plates Using High Order Shear Deformation Theory

Abstract

Isogeometric analysis (IGA) based on nonuniform rational B-splines (NURBS) is developed for static analysis of beams and plates using the third-order shear deformation theory (TSDT). TSDT requires C 1 -continuity of generalized displacements; quadratic, cubic, and quartic NURBS basis functions are utilized to satisfy this requirement. Due to the noninterpolatory nature of NURBS basis functions, a penalty method is presented to enforce the essential boundary conditions. A series of numerical examples of thick and thin beams and plates with different boundary conditions are presented. Results are compared with analytical solutions and other numerical methods. First-order shear deformation theory (FSDT) is also employed and compared with TSDT in the stress analysis. The effects of aspect ratios and boundary conditions are discussed as well.