In this thesis, we consider the deformation of shell structures defined as thin threedimensional elastic bodies. These can be modelled using a lowerdimensional theory but the governing partial differential equation of thin shells contains fourthorder derivatives which require C1continuity in their solutions. Consequently, both the unknown and its first derivatives have to be continuous.Employing a finite element method in our study suggests that the C1finite element representation of the shell solution has to be employed. Therefore, appropriate interpolation functions defined on a typical finite element are studied on both straight and curvilinear boundary domains. Our study of C1finite element representations shows that the Bell triangular finite element which is derived from the quintic polynomials is more appropriate than the bicubic Hermite rectangular element as it converges faster and provides higher accuracy on domains with straight boundaries. However, when the physical boundary is curved, a straightline approximation is not exact and the performance of the Bell triangular element decreases in terms of both accuracy and convergence rate. To retain a convergence rate and accuracy of the solution of a C1problem on a curvilinear boundary domain, the C1curved triangular finite element is introduced. It is proved to show superiority in both convergence rate and accuracy when solving the C1problem on a curved boundary domain.Furthermore, numerical comparisons between the solutions obtained from the linear and nonlinear governing equations with the linear constitutive law are also reported here. These comparisons confirm that the solutions obtained from the linearised governing equation agree with those of the nonlinear when a loading is small and they start to disagree when the loading becomes larger.
Date of Award  31 Dec 2013 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Andrew Hazel (Supervisor) & Matthias Heil (Supervisor) 

 Thin Shell Theory
 Small Strain
 Finite Element Method
 Linear Elasticity
Finite element based solutions of thinshell problems with a small strain
Phusakulkajorn, W. (Author). 31 Dec 2013
Student thesis: Master of Philosophy