On smoothness of solutions to structural problems and physical interpretation of weak formulation

Abstract

Typical structural modelling solutions are classified and described in the paper based on an approach that is more interpretative than formal. A special emphasis is placed on weak formulation and its physical interpretation which, in the authors’ opinion, is lacking in the literature. The attention is also drawn to approximation mistakes, caused by insisting on excessive smoothness of solutions. These considerations are backed by examples. It is hoped that the paper will contribute to understanding the essence of approximation of practical models in civil engineering, while clearly pointing to the power of weak formulation - the foundation of approximation procedures.