Similitude Theory: Plates and Shells Analysis

Any structural model must be designed, loaded, and interpreted according to a set of similitude requirements that relate the model to the prototype structure. These similitude requirements are based on the theory of modeling, which in turn is derived from a dimensional analysis of the physical phenomena involved in the behavior of the structure. To accomplish modeling, general similitude theory should be followed properly. This similitude theory is derived from the behavior of the structure using proper boundary conditions. Three theorems exist, of which only the Pi theorem is commonly known to engineers. With the particular problem of plates and shells, the other two theorems are important to derive behaviors of two similar systems at large and at the boundary conditions. Modifications to these theorems are presented in order to simplify the problem of designing the shell model. Methods are presented, with cylindrical shell as a special application, and the accuracy of these methods is verified. Conclusions can be reached in terms of using the theory to model shells and to enhance the results from scaled models by relaxing few conditions.