Finite element method project dr. Ing. Adrian Dogariu
Finite element method project
Determination of membrane stress resultants for a hemispherical
shell under own weight Goal of the project
The goal of this project was to obtain the membrane stress
resultants of a hemispherical shell under vertical load (own
weight).
The two stresses are:the circumferential hoop stress -n the
meridional stress -n
The shell has the following geometry:Span: 25000 mmRadius of
curvature: 12500 mmThickness: 20 mm R/t 625 Material used:
Steel
Software used: Abaqus 6.13-1
Geometry: Part module
The three-dimensional shell model consists of curved shell
elements. The model is generated by constructing several meridional
and circumferential ribs whichenclose rectangular and triangular
surface areas
Material: Property Module
Analysis
Step module:Static analysisLoad and boundary conditionsLoad
considered:Self weight
Boundary conditions:
Continous fixed support at the baseMeshingElement type:
membrane
4 node quadrilateral elements, reduced integration points,
M3D4RThe top part was meshed separately using the sweep
technique
Results
FEM vs. TheoryTop (=00)Base (=900)
n-0.5 N/mm2-1.0 N/mm2
n-0.5 N/mm2
+1.0N/mm2
The meridional stress resultants are compression stresses. The
circumferential stresses, however, change from compression to
tension.Top (=00)
Base (=900)
n-0.496 N/mm2-0.961 N/mm2
n-0.496 N/mm2
+0.900 N/mm2Theory resultsFEM results9ConclusionThe stresses at
the top of the dome, obtained with FEM, are very close to the ones
obtained with theory.
However, at the stresses at the base of the dome, some
discrepancies are observed.
