Isogeometric nonlinear bending and buckling analysis of   variable-thickness composite plate structures
  This paper investigates nonlinear bending and buckling behaviours of composite plates characterized by a thickness variation. Layer interfaces are described as functions of inplane coordinates. Top and bottom surfaces of the plate are symmetric about the midplane and the plate could be considered as a flat surface in analysis along with thickness parameters which vary over the plate. The variable thickness at a certain position in the midplane is modeled by a set of control points (or thickness-parameters) through NURBS (Non-Uniform Rational B-Spline) basic functions. The knot parameter space which is referred in modelling geometry and approximating displacement variables is employed for approximating thickness, simultaneously. The use of quadratic NURBS functions results in C^1 continuity of modeling variable thickness and analyzing solutions. Thin to moderately thick laminates in bound of first-order shear deformation theory (FSDT) are taken into account. Strain-displacement relations in sense of von-Karman theory are employed for large deformation. Riks method is used for geometrically nonlinear analysis. The weak form is approximated numerically by the isogeometric analysis (IGA), which has been found to be a robust, stable and realistic numerical tool. Numerical results confirm the reliability and capacity of the propose method. 
T. Le-Manh, Q. Huynh-Van, Thu D. Phan, Huan D. Phan, H. Nguyen-Xuan
cs.CE