On the automation of the force method in the optimal plastic design of frames
(EN)
Spiliopoulos, KV
(EN)
It is well known that linear programming provides, computationally, the only solution to the optimal plastic design of plane frames. It is also known that the formulation of the problem by the force method, using kinematic variables, requires for its solution, by the simplex method, much less computation than the corresponding program which uses for its formulation the displacement method. However, the force method is not easily automated. This problem is circumvented in the paper by presenting a new algorithm which automatically selects a subminimal cycle base in any planar graph. Based on a shortest path technique between two points of a connected graph, the algorithm forms cycles by finding the shortest paths between the end nodes of members of the graph. The check for independence is done by fictitiously increasing the lengths of the members that form the cycle. This leads to an easy computer implementation of the algorithm. The algorithm is then used to provide a statical basis for any plane frame. Equilibrium with applied loads is satisfied by the use of cantilevers that follow the shortest load path of each load to the ground. The whole process automates the data generation of the force method and makes possible to use, in a computer program, the same input data as in the displacement method. A few examples of applications are given.
(EN)
