Advances in swift analysis of structures: Near-regular structures, and optimal analysis and design

• A review of optimal analysis of structures is presented.
• Different methods for swift analysis are employed for various problems.
• Analysis of near-regular structures is performed using graph products and sub-structuring methods.
• Boundary-value and initial-value differential equations are solved using finite difference method and graph products.

In this paper a review of optimal analysis of structures is presented. Different methods of swift analyses are employed for various problem formulations. Depending on the problem at hand, a proper combination of graph products, sub-structuring methods, finite difference method and manipulating the stiffness matrix manipulation is selected to achieve the most efficient design. Design problems can be classified as three types. The first type includes the solution of near-regular structures using graph products and sub-structuring methods. These structures consist of two groups. In the first group, the main structure contains some additional members with respect to its corresponding regular structure while the structures in the second group contain some additional nodes with respect to the corresponding regular structures. The second type of problems includes the simultaneous optimal analysis and optimal design of structures. The presented method is applicable to an arbitrary structure and the optimal solution is obtained by manipulating the stiffness matrices and taking advantages of the iterations during design process. The third type of problems includes the efficient modal analysis of structures using a combined finite difference method and graph products. Boundary-value and initial-value differential equations are solved using finite difference method and graph products, and then the method is applied to the dynamic equations of modal analysis.