Geometry and classification of carved Monge surfaces

There are more and more needs of new forms in the world architecture. The thin shells theory and the surfaces theory give enough materials to scientifics and designers. This article is devoted to the geometric investigation of carved Monge surfaces. The geometry of these surfaces is inner and outer. For this, the coefficients of their fundamental forms are found and allow the classification of these surfaces. The kinetic method is used for their geometric investigation and classification. The parametric definitions of these multitude forms of carved Monge surfaces allow the 3D plotting of these surfaces by mean of the software MathCAD. The results obtained by this investigation are their vector, implicite, explicite and parametric definitions, the mathematic modelling of their inner and outer geometry, their 3D plotting and their classification. This variety of carved Monge surfaces can be used as the median surface of thin elastic shells design from them. The geometry these elastic shells, because their thin is the one of the carved Monge surfaces. The multitude of the designed thin elastic shells are expressive, durable and cover large spans. The multitude of their forms can find applications in the architecture of civil and industrial buildings and also in mechanical engineering. © Published under licence by IOP Publishing Ltd.