Symmetries of Differential Equations Describing Beams and Plates on Elastic Foundations

Symmetries of differential equations play very important role in understanding of their properties. In principle, the only systematic general method for finding solutions of differential equations is based on the theory of Lie group symmetries of differential equations. Despite of this fact, the underlying theory is relatively unknown in community of engineers. The paper describes some important questions concerning Lie groups in the context of differential equations that describe beams and plates on elastic foundations.