Geometric modelling and materially nonlinear numerical analysis of shells in the shape of one-sheet hyperboloid of revolution

A surface of revolution is generated by rotation of a plane curve z = f(x) about an axis Oz called the axis of rotation. This paper provides information on hyper-boloids of revolution surfaces and their classification. Their geometric modeling, linear and materially nonlinear analyses are worked out. Their middle surface are plotted using the software MathCAD. The Linear and materially nonlinear numerical analyses of thin shells of the shape of an hyperboloid of revolution surfaces on stress-strain state is given in this paper, using the finite elements method in a computer software R-FEM, the material which we use in our model is concrete with isotopic nonlinear 2D/3D stress-strain curve for materially nonlinear analysis and linear stress-strain curve for linear analyses. Comparison is done with the result of the finite elements linear analysis of their strain-stress results. That displacements in the investigated shells subject to self-weight, wind load with materially nonlinear analysis are bigger than which done by linear analysis, in the other side the displacements is similarity subjected to free vibration load case. Based on these results, conclusions are made for the whole paper. © 2021, Univelt Inc. All rights reserved.