Optimal structural topologies with transmissible loads

In optimal topological design of structures one obtains the configuration o f optimal structures when the design domain, the displacement boundary cond itions and the applied loads are specified. In the optimal structure one of ten notices a marked difference between the main bearing structure and the load transfer zones. The latter are composed of relatively light elements t he exact nature of which is not always very distinct. The main purpose of t his paper is to allow the main bearing part of the structure to emerge. Mor eover the actual location of the load along its line of action is not alway s a design requirement. In order to include this relaxed condition regardin g the loading position the concept of transmissible or sliding forces is in troduced in topological design of structures. A transmissible force is a fo rce of given magnitude and direction which can be applied at any point alon g the line of action of the force. The optimization formulation is similar to standard topological design procedure in addition to the condition of tr ansmissability of the forces. It is shown that this condition reduces to an equal displacement constraint along the line of action of the forces. The method is illustrated by typical structural examples. It is observed that t his numerical method produces indeed crisp images of the main structural co mponents, unblurred by the secondary load transfer elements. It is also ind icated that many results are often replicas of Prager structures which were previously obtained by analytical methods.