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The present paper is concerned with the stability problems of a thin solid circular plate and some annular plates, each stiffened by a cylindrical shell on the external boundary. Assuming an axisymmetric dead load and non-axisymmetric deformations we determine the critical load in order to clarify what effect the stiffening shell has on the critical load. Using Kirchhoff's theory of thin shells and plates the paper presents the governing equations both for the circular plate and for the cylindrical shell, where the displacement field of the shell is obtained from a Galerkin function. The deflection of the plate and the Galerkin function are expanded into Fourier series and consequently all physical quantities in the structural elements as well. The boundary-and continuity conditions and last but not least numerical results are also presented.Mathematical Subject Classification: 74K20, 65L15

A new, general hp-version axisymmetric finite element is derived for the boundary value problems of thin linearly elastic shells of revolution, applying a complementary strain energy-based three-field dual-mixed variational principle. For the interpolation of the mid-surface geometry, non-uniform rational B-splines-NURBS-is used. The independent field variables of the weak formulation are the a priori non-symmetric stress tensor, the displacement vector, and the infinitesimal skew-symmetric rotation tensor. The theoretical model of the shell formulation is based on a consistent dimensional reduction process and a systematic variablenumber reduction procedure. The inverse of the unvaried three-dimensional constitutive equation is employed since neither the classical kinematical assumptions nor the stress hypotheses are built in the mathematical model; namely, both the through-the-thickness variation and the normal stress to the shell mid-surface are not excluded. The new hp axisymmetric shell finite element is tested by a representative model problem for extremely thin and moderately thick, singly and doubly curved shells of negative and positive Gaussian curvature. Following from the numerical experiments, the constructed hp-shell finite element gives locking-free results not only for the displacement but also for the stresses.

Jelen cikk egy négytagú síkbeli RRRP mechanizmus analitikus szintézisével és helyzetanalízisével foglalkozik. A vizsgálat tárgyát képező mechanizmus két kívánt helyzetéhez tartozó szintézise során vektorhurkok kerülnek felírásra, melyek skaláregyenletei egy nemlineáris egyenletrendszert alkotnak. A nemlineáris egyenletrendszer ismeretlenjei közül vannak szabadon választhatók, míg a többit numerikus eljárással határozzuk meg. A szabadon választott és ismeretlen változók megoldásai adják a mechanizmus tagjainak fő méreteit. A mechanizmus helyzetanalízise során szintén vektorhurkok skaláregyenletei szolgáltatnak nemlineáris egyenletrendszert, melyek segítségével meghatározhatók a mechanizmus másodlagos koordinátái az elsődleges koordináta függvényében.