A simple triangular facet shell element with applications to linear and non-linear equilibrium and elastic stability problems

Abstract

This paper has two main objectives. First to describe a very simple facet triangular plate and shell finite element called TRUMP which includes, if required, transverse shear deformation and is based on physical lumping ideas with a simple mechanical interpretation [ 1,2,4,5 ]. Second to give an account of some non-trivial numerical examples of large deflection and post-buckling of shells. There are two types of non-linear structural problems which give rise to particularly delicate numerical experimentation. They are those involving deflections of the order of the structural dimensions, such as three-dimensional elastica, and the instability phenomena of the type leading to dynamic snapthrough, e.g. in cylindrical panels. To tackle such problems using a highly sophisticated shell element such as SHEBA is neither easy nor inexpensive. It is shown that the TRUMP element with only 18 displacement and rotation degrees of freedom is relatively economical to use and yet capable of engineering accuracy. The paper makes use of the theory of simplified geometrical stiffness based on the natural mode method which has been described fully in previous publications [1,2].