Linear and Non-Linear Analysis of Plates and Shells by Use of Morley Finite Elements

Doctoral thesis, 1997

The thesis deals with plate bending analysis and shell analysis in static linear and dynamic non-linear situations. The thesis contains two parts. In common for them is the use of the Germain-Kirchhoff plate theory, constant strain, constant curvature triangular plate elements and adaptive improvement of original solution. In the first part a numerical plate bending solution according to the Germain-Kirchhoff plate theory is improved by adaptively adding the shear deformation. A mixed formulation is used in order to make the adaptive process simple. A high quality numerical approximation of the shear force along the boundaries are obtained by use of the reaction force. Numerical results for thin and moderately thick circular and rectangular plates and for thin skew plates are compared to analytical and other numerical solutions and found to have good accuracy. In the second part a dynamic explicit shell formulation with large displacements and large elastic-plastic deformations has been implemented. An adaptive mesh refinement has been installed. An impact load on a shell is simulated. It has been compared with experimental results and results obtained with a commercial code. The new code can be used as a basis for a sheet metal forming simulation.