By E. Stein, W. Wendland

Traditional FEM and the more moderen BEM underlie many engineering computational equipment and corresponding software program. either equipment have their benefits and in addition their boundaries. the combo of either tools will offer a better numerical instrument sooner or later. the purpose of this publication is to offer major easy formulations of FEM and BEM and to teach their universal sensible and mathematical foundations, their adjustments and probabilities for his or her blend. those comprise variational foundations, FEM and BEM for linear and non-linear elasticity and power difficulties, the mix of FEM-BEM asymptotic errors research, ameliorations as a result of nook and crack singularities and corresponding development of convergence, plastic research, numerical algorithms and engineering applications.

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O Prof. Dr. Drs. c. H. Argyris on the occasion of his 70th birthday E. Stein ct al. 34 1 SURVEY OF NONLINEAR CONTINUUM MECHANICS In this chapter a short summary of the continuum mechanics of solids is given. Since only the basic ideas of continnum mechanics can be considered here we restrict ourselves to a theory with small strains but large rotations which will be the basis of the finite element formulation in chapter 2. g. buckling of shells or elasto-plastic limit analysis of folded plates. Problems which exhibit large strains like recasting processes or the analysis of rubber bearings are not considered here.

Stein et al. 58 which then includes shear deformations. From a numerical point of view the latter one has advantages because the shape functions have to fulfil only C 0 - continuity. In this paper we discuss only some selected theoretical and numerical aspects out of the wide field of shell problems. Especially we will describe the main ideas of a shear elastic shell theory, finite element formulations for associated shallow shell and axisymmetric shell elements and some examples dealing with the postbuckling behaviour of shallow shells.

1977) 20')-216. : Variational inequalities, complementary problems and duality theorems. J. f. Math. Anal. and Appl. 58 (1977) 1-10. : Complementary variational principles. Oxford Math. Monographs, Oxford 1970. : Variational Inequalities and Complementary Problems. Theory and Applications. (Internat. -30. Juni 1978 in Erice Sicily) John Wiley and Sons 1980 ยท FRAEIJS de VEUBEKE, B. : Displacement and e9uilibrium models in the finite element method. S. C. S. ) Stress Analysis, 'John Wiley 1965.

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