Static and modal analyses of structures with different repeated patterns

The aim of this paper is two fold. In the first part, static analysis of structures with repeated patterns is presented. These structures are comprised of submodels each having different repeated pattern. As an example, considering a structure with two different repeated patterns, the nodal numbering is performed in such a manner that the resulting stiffness matrix of the structure contains two block diagonal matrices. Thus their inversion can easily be performed using regular matrices requiring smaller amount of computational time. In the second part, the modal analysis, free vibration and eigen-frequencies of such structures are studied. Here as well the stiffness and mass matrices are transformed into two block matrices forms and using dynamic condensation and the matrix inversion which is involved in this condensation, the eigensolution is performed on matrices of lower dimensions.The presented examples consist of 2D and 3D structures in which in some stories the stiffnesses are changed due to the addition of some members taking the structures out of regularity. Apart from these, the power transition towers often having additional bracings in some levels are investigated. Other applications correspond to calculating the buckling loads and natural frequencies of regular plates driven to irregular forms by having different support conditions and some added parts.

► Static analysis of structures with repeated patterns is presented. ► Nodal numbering is performed to obtain stiffness matrices with two block diagonal matrices. ► The inversion is obtained for regular matrices with small computational time. ► Modal analysis and eigensolution of these structures are performed efficiently.