A FORMULATION OF GENERAL SHELL OF TENSORIAL COMPONENTSt ELEMENTS - THE USE OF MIXED INTERPOLATION

SUMMARY We briefly discuss the requirements on general shell elements for linear and nonlinear analysis in practical engineering environments, and present our approach to meet these needs. We summarize and give further insight into our formulation of a 4-node shell element using a mixed interpolation of tensorial components, and present a new 8-node element using this approach. Specific attention is given to the general applicability of the elements and their efficient use in practice. 1. INTRODUCTION The development of analysis procedures for shell structures represents surely one of the most challenging tasks of finite element research. Over the last two decades much effort has been directed towards this task with impressive advances, but-measured on the desirable features for practical analyses-still not enough success. An important and large application area for shell analysis will be the CAD environment. In this area routine linear and nonlinear shell analysis will have to be conducted by relatively inexperienced analysts. The analysis capabilities must, therefore, be versatile, robust and above all reliable for all possible analysis conditions. Many shell elements are currently in use and have been re~earched.~' These elements have been largely developed for linear analysis, and frequently various assumptions restrict their use. However, it is mostly implied that 'an element can easily be extended to general non-linear analysis'. Our experiences are quite different, and our approach towards the development of general shell solution capabilities is consequently also different. We believe that the extension of a plate element to a general nonlinear shell element represents a major step (with the requirements we have laid down to be satisfied, see Section 2) and is most frequently not possible. It is, therefore, more appropriate to concentrate directly on the development of a general nonlinear shell analysis 'This is an extended version of the same title paper presented at the