Structural analysis of axisymmetric shells with axisymmetric loads can be solved in closed form for simple cases, and need help of numerical methods, such as finite difference or finite element, for more complex cases. In this study, finite element method is used to compute displacements and stresses. The displacements and stresses will be used as constraints in the optimization problem.
Straight (conic) element is the simplest element in formulation, programming and data input, but its results are still needed to increase their accuracy. Curve element is used to overcome lack of straight element, but choosing of the displacement function assumption must consider rigid body motion. This is in order curve element does not become so stiff that the result is less accurate. Therefore the displacement function assumption of straight (conic) element, standard curve element, one term surplus curve element, two terms surplus element and Cantin element are developed in this study. According to formulation of each assumption of the displacement function, the computer programs are written in Fortran language. The computer programs are validated toward the cases that have been completed solving theoretically or have been solved by other researchers, and with software SAP 90.
The result of this study found rigid body motion must be included implicitly or explicitly in the displacement assumption function of the finite element method. And the displacement assumption with two terms surplus curve element gives the best result, but it needs additional process to condensed the surplus terms before assembly. Also, curve element with two terms surplus and straight element are the main candidate as axisymmetric shells analysis in the shape optimization, and one of them will be used in second year research.