Static and dynamic analysis of arbitrary quadrilateral flexural plates by B3-spline functions

Abstract This paper presents static and free vibration analysis of arbitrary quadrilateral flexural plates by B3-spline functions. An actual arbitrary quadrilateral thin flat plate is mapped onto a square basic plate and a superelement is constructed for the whole plate. The present numerical analysis is based on a spline net with finite spline points on the square basic plate. Combination of B3-spline functions gives an easy way to satisfy various boundary conditions. The displacement function constructed by B3-spline functions in two directions has been formed to possess more flexibility to model the deflection shape efficiently. The main features of the present method are: minimal input preparation, easier programming and higher accuracy achieved by a system with fewer degrees of freedom. Compared with analytical solutions and other numerical methods, the method proposed yields excellent results for the test cases considered.