Automatic procedure for analysis and geometry definition of axisymmetric domes by the membrane theory with constant normal stress

F T Rabello,N A Marcellino,D D Loriggio

doi:10.1590/s1983-41952016000400005

F T Rabello, N A Marcellino + Show 1 more

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https://doi.org/10.1590/s1983-41952016000400005

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Abstract

Abstract This paper presents an automatic procedure using the membrane theory of shells to analyse and define geometries for axisymmetric domes subjected to its own weight, varying its thickness and bend radius, to obtain constant normal stresses along the structure. The procedure offers a great advantage over the analytic solution of the problem and usual shell numerical methods when one wants to determine the dome geometry with constant stresses, since the presented procedure has the goal stress as input value for obtaining the geometry, as opposed to the usual numerical methods, where the reverse occurs. An example clarifies the differences between a spherical dome with constant thickness and a dome subjected to constant stress. The convergence of the method for a specific material weight and stress for a dome are also presented.

Highlights

Thin shells are curved laminar structures, whose thickness is small when compared to its other dimensions
This paper presents an automatic procedure using the membrane theory of shells to analyse and define geometries for axisymmetric domes subjected to its own weight, varying its thickness and bend radius, to obtain constant normal stresses along the structure
This paper proposes an automatic process for the analysis and definition of thin shells segments revolution geometry submitted to its own weight by membrane theory with thickness and radii of curvature variation in order to obtain meridional and tangential stresses constant by a process of simple implementation and low computational cost

Summary

Introduction

Thin shells are curved laminar structures, whose thickness is small when compared to its other dimensions These elements may be subject to membrane and bending stresses, depending on its restraints and loadings. This paper proposes an automatic process for the analysis and definition of thin shells segments revolution geometry (domes) submitted to its own weight by membrane theory with thickness and radii of curvature variation in order to obtain meridional and tangential stresses constant by a process of simple implementation and low computational cost. According to the membrane theory, the stiffness to flexure and torsion in the shell should not be considered, which causes the bending and torsional moments to resulting null Under these conditions, only normal and tangential forces will request cancel each other out the shear forces and the shell. Using Lamé equations and the ones presented in this work , it can be seen by Figure 2, the variation in tangential stress σθ of revolution walls shells subjected to internal pressure p, when there are revolution shells with a thickness equal to 10 % of the inner radius and the thickness of the cylinder is equal to 400 % of the inner radius

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