Abstract
Aims of research. 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 hyperboloids of revolution surfaces and their classification. Their geometric modeling, linear and materially nonlinear analysis are worked out. Methods. Hyperboloids of revolution middle surface is 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. 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.
Highlights
Geometric ModelingOne-sheet hyperboloid of revolution is generated by the rotation of hyperbola about the z-axis (Figure 2, a)
This paper provides information on hyperboloids of revolution surfaces and their classification
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
Summary
One-sheet hyperboloid of revolution is generated by the rotation of hyperbola about the z-axis (Figure 2, a). Thorough every point of the surface, two straight lines, lying on the hyperboloid, pass (Figure 2, b). A hyperboloid can be constructed by rotation of a generatrix straight line about the z-axis but the straight generatrix and the axis are skew lines (Figure 2, c and d). All of the rest of the geodesic lines besides the equator go from infinity coming. One of them intersects the equator and goes to other half of the surface but others do not reach the equator and touching the some parallel, turn back; the third geodesic lines come nearer asymptotically to the equator. Structural Mechanics of Engineering Constructions and Buildings, 2019, 15(3), 210–218 a b c d
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