University of Illinois Urbana-Champaign

Finite element weighted residual methods for static analysis of reinforced axisymmetric shells

Sharma, S.K.; Boresi, A.P.

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https://hdl.handle.net/2142/112148

Description

Title
Finite element weighted residual methods for static analysis of reinforced axisymmetric shells
Author(s)
  • Sharma, S.K.
  • Boresi, A.P.
Issue Date
1977-04
Keyword(s)
  • Reinfroced Axisymmetric Shells
  • Finite Element Weighted Residual Methods
  • Love-kirchhoff Assumption
Abstract
This report presents finite element weighted residual methods for static analysis of reinforced axisymmetric shells. The shells may have variable thickness and reinforcement along the meridian. The reinforcing material is assumed to have an orthotropic distribution along the meridional and circumferential coordinate lines. External forces on the shells may include both pressure and thermal loads which need not be axisymmetric. The derivation of the required partial differential equations of equilibrium is based on thin elastic shell theory and utilizes the Love-Kirchhoff assumption. These partial differential equations are reduced to ordinary differential equations by Fourier expansions in the circumferential variable. Numerical solutions to the ordinary differential equations are then obtained for each Fourier harmonic by finite element weighted residual methods. Piecewise cubic Hermite polynomials are used for the construction of a finite element model of the displacement field along the meridian. The element stiffness matrices and load vectors are formulated by four different weighted residual methods, namely, subdomain collocation, Galerkin, moments and least squares. Appropriate continuity requirements are derived for the coefficients of the differential equations, interpolation functions, weighting functions and external loads. A finite element computer program is developed using the axisymmetric shell elements formulated in this report. The accuracy of these shell elements is studied by considering various example problems with different shell geometries, material properties, boundary conditions and prescribed forces.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 414
  • 1977-6001
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112148
Copyright and License Information
Copyright 1977 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.