INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng. 47, 557–603 (2000) Rotation-free triangular plate and shell elements Eugenio O˜ nate ∗ and Francisco Z arate International Centre for Numerical Methods in Engineering; Universidad Polit ecnica de Catalu˜ na; Gran Capit an s=n; 08034 Barcelona; Spain SUMMARY The paper describes how the nite element method and the nite volume method can be successfully combined to derive two new families of thin plate and shell triangles with translational degrees of freedom as the only nodal variables. The simplest elements of the two families based on combining a linear interpolation of displacements with cell centred and cell vertex nite volume schemes are presented in detail. Examples of the good performance of the new rotation-free plate and shell triangles are given. Copyright ? 2000 John Wiley & Sons, Ltd. KEY WORDS: rotation-free; thin plate and shell triangles; nite elements; nite volumes INTRODUCTION The need for ecient plate and shell elements is essential for solving large-scale industrial prob- lems such as the analysis of shell structures in civil, mechanical, naval and airspace engineering, the study of vehicle dynamics and crash-worthiness situations and the design of sheet metal form- ing processes among others. Despite recent advances in the eld [1–3], the derivation of simple triangles capable of accurately representing the deformation of a plate or a shell structure under complex loading conditions is still nowadays a challenging topic of intensive research. The development of plate (and shell) nite elements was initially based on the so called thin plate theory following Kirchho ’s main assumption of preserving orthogonality of the normals to the mid-plane [1; 4]. Indeed, most plates and shells can be classed as ‘thin’ structures and there- fore Kirchho ’s theory can reproduce the essential features of the deformation in many practical cases. The well known problems to derive conforming C 1 continuous thin plate and shell elements motivated a number of authors to explore the possibilities of Reissner–Mindlin theory. This theory relaxes the normal orthogonality condition, thereby introducing the eect of shear deformation which can be of practical importance in thick situations, such as the analysis of some bridge slabs and, more important, it requires only C 0 continuity for the deection and rotation elds. Unfortu- nately Reissner–Mindlin plate and shell elements suer from the so called ‘shear locking’ deect which pollutes the numerical solution in the thin limit. This deciency has jeopardized the full success of Reissner–Mindlin plate= shell elements for practical engineering analysis, an exception ∗ Correspondence to: Eugenio O˜ nate, International Centre for Numerical methods in Engineering, Universidad Polit ecnica de Catalu˜ na, edicio C1, Campus Norte UPC, Gran Capit an s=n, 08034 Barcelona, Spain. E-mail: onate@cimne.upc.es CCC 0029-5981/2000/030557–47$17.50 Received 10 March 1999 Copyright ? 2000 John Wiley & Sons, Ltd.