Sorne Current Trends In Finite Elernent Research

In the 1960's the fini te clement method was under rapid development in the field of structural mechanics. The essen­ tial features of the methodology had been identified and it was clear to the research community what additional exten­ sions were needed to achieve general capabilities for the bulk of structural mechanics problems which had traditionally faced an alysts . The main thrusts of research at the time were directed towards the development of curved twoand three­ dimensional higher-order continuum elements, and the development of effective shell clements. Straight edged higher-order triangular and tetrahedral continuum elements were available early on, but were in­ convenient in Illany situations, and did not permit accurate gcometricalll odeling of curved domains. The import ance of elements of general shape, particularly curvilinear triangles, quadrilaterals, wedges and brick-shaped elements, was ac­ knowledged by researchers as a key step in the development of the finite clement method for it would enable convenient modeling of intricately shaped, realworld engineering designs. All classical an alytic al techniques, and even com­ peting numerical techniques of the time, were severely limited due to the inability to handle complex geometries. One may view the "geometry problem" as one which has beleaguered the history of analysis. Essentially with the development of curved "isoparametric" elements [EI-E3, 11, 12, 1'1, Z2] the problem was solved once and for all for most practical purposes. The ability to solve general s!Jell configurations was of considerable interest to the developers of finite element meth ods in the 1960's due to its obvious im portance through­ out structural analysis, and particularly because most re­ searchers were actively engaged in aerospace proje cts , a focal poillt of engineering en deavors at the time. By the latter part of the decade a wide variety of shell elemen ts had been developed which were adequate for most linear analy ses [A7, B24, C2, C7, C8, G17, P7, S6, Z8]. With the main problems of finite element/structural mechanics research (as perceived at the time) essentially