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 C1-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.
Highlights
Various kinds of beams and plates have become the most significant applications in modern industries, which makes their analysis very important
The shear correction factor (SCF) depends on many factors, such as material coefficients, stacking scheme, plate geometry and boundary conditions; the evaluation of the SCF remains a subject of research [5]
Several methods including some mesh-free approaches have been used, for example, the moving least-squares (MLS) method [8] and the radial point interpolation method (RPIM) [9]. We demonstrate that such a C1-third-order shear deformation theory (TSDT) formulation can be conveniently achieved by using nonuniform rational B-splines (NURBS)-based isogeometric analysis
Summary
Various kinds of beams and plates have become the most significant applications in modern industries, which makes their analysis very important. Isogeometric analysis (IGA) was first proposed by Hughes and coworkers [10, 11]; the basic idea is that basis functions, usually NURBS basis functions, which accurately represent the geometry, are directly used as the interpolation functions of the unknown field variables. In IGA, NURBS basis functions are first chosen to exactly capture the geometry and be used to approximate the unknown field. The geometry can keep exact at the very beginning and during the mesh refinement process
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