Dynamical Analysis of Shell Structures by Means of B-Spline Shape Functions

This paper presents a free vibration analysis of double curvature free form shaped shell structures using the B-spline shape functions approximation method. It is based on the Ritz method. The shell formulation is developed following the well known Ahmad degenerate approach including the effect of shear deformation. The assumed displacement field is described through non-uniform B-spline functions of any degree. The effect of locking is investigated and both reduced and modified quadrature integration rules are considered with the purpose of increasing the solution accuracy and diminishing the computational cost. Numerical simulation is reported for the evaluation of the eigensolution of plates, and of single and double curvature shells to test the effectiveness and the efficiency of the approach. The presence of spurious zero energy modes both at local and global level was investigated. The solutions are compared with other available analytical and numerical solutions, and discussed in detail