Numerical analysis of structures of revolution using universal matrices approach

Stress and displacement analysis of structures of revolution under axisymmetric loading is of considerable interest in engineering. Many practical problems can be idealized as an axisymmetric case, which simplifies the analysis and reduces the computational work. The axisymmetric triangular element is commonly used for modeling these cases. This paper proposes a method of generating stiffness matrix for the axisymmetric triangular element using universal matrices instead of numerical integration. The computation time of the proposed method was compared against the Gaussian numerical integration. The CPU time ratio for the 3-node element was 1:1.56, 1:1.79, and 1:1.89 for the proposed method against 1-point, 3-points, and 4-points Gaussian numerical integration respectively. The accuracy of the proposed method was 0.012% against the exact integration method. The 1-point, 3-points, and 4-points Gaussian numerical integration have an error of 0.059%, 0.001%, and 0.0006% respectively. Nodal displacements from this method were compared against the results of some commercially available finite element packages. The proposed method has a deviation of 0.44% from the theoretical values, while ABAQUS, ANSYS, and Optistruct has a deviation of 1.26%, 1.29%, and 1.44% respectively using the default number of integration points provided by the packages.Keywords: Stiffness matrix; explicit formulation; closed-form; universal matrix; axisymmetric triangular element