Efficient and Automated Analysis of Potentially Slender Structures

Computer-based engineering analysis is now a routine process in virtual product design. However, when an object becomes slender, i.e., beam, plate, or shell like, 3D computational analysis is known to slowdown, or even lead to erroneous results. Indeed, the recommended method for analyzing slender objects is to replace them with equivalent lower-dimensional entities. However, explicit geometric reduction and replacement is impractical during automated product design, and requires specialized software tools. In this paper, we therefore develop an implicit dimensional reduction method, where the reduction is achieved through an algebraic process. The proposed reduction method is computationally efficient, and numerically equivalent to explicit geometric reduction. Moreover, standard off-the-shelf 3D finite element packages can be used to implement the proposed methodology. The efficacy of the proposed method is demonstrated within the context of shape optimization. Finally, the related problem of “automatic slenderness-detection” is also addressed briefly.