Nine-Node Resultant-Stress Shell Element for Free Vibration and Large Deflection of Composite Laminates

The newly constructed formulation of an element-based resultant-stress nine-node composite shell element is presented for the solution of free vibration and large deflection problems of isotropic and composite laminates. In this paper, the effectiveness of this new formulation is investigated in the static and free vibration analysis. The strain–displacement relationship of the shell could be explained from the point of the new element-based Lagrangian finite element formulation. The newly added terms between bending strain and displacement reflect the contributions of displacements to the curvature. Natural coordinate-based strains, stresses, and constitutive equations are used throughout the element-based Lagrangian formulation of the present shell element which offers significant implementation advantages compared with the traditional Lagrangian formulation. Using the assumed natural strain method the present shell element generates neither membrane nor shear locking behavior, and such an element performs very well as much as shells become thin. The arc-length control method is used to trace complex load–displacement paths and the Lanczos method is employed in the calculation of the eigenvalues of shells. A number of numerical analyses are presented and discussed in order to explore the capabilities of the present shell element. The test results showed very good agreement.