Curved Finite Elements in the Analysis of Solid, Shell and Plate Structures

• Main Author: Ahmad, S.
• Published: Swansea University 1969
• Subjects: 620.001
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.447036

The formulations of a number of curved finite elements for analysing solid, shell or plate structures are presented in this thesis. The hybrid method of derivation of element stiffness matrices based on the principle of minimum complementary energy using assumed stress distributions is developed for three dimensional stress analysis. A new process of curved thick shell finite elements based on the principle of minimum potential energy using assumed displacements is developed overcoming the previous approximations to the geometry of the structure and the neglect of shear deformations. A general formulation for a curved, arbitrary shape of shell is presented as well as a simplified form suitable for axisymmetric situations. Further modifications of the general thick shell element are presented in the form each membrane shell element and a thick plate clement. A computer program has been written and developed for each type of element. The method of computation is discussed in an appendix. A number of illustrated examples ranging from thin to thick shell applications are given to assess the versatility, accuracy and economy attainable with the new formulation&. These examples include a roof, a conduit, an idealised dam, an actual darn, tanks and a cooling tower for which many alternative solutions were used. The possible scope of further developments is suggested