Continuous/discontinuous finite element modelling of Kirchhoff plate structures in R3 using tangential differential calculus
نویسندگان
چکیده
We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations, we employ a finite element method based on elements that are continuous for the displacements and discontinuous for the rotations, using C0-elements for the discretisation of the plate as well as for the membrane deformations. Key to the formulation of themethod is a convenient definition of jumps and averages of forms that are d-linear in terms of the element edge normals.
منابع مشابه
A simple approach for finite element simulation of reinforced plates
We present a new approach for adding Bernoulli beam reinforcements to Kirchhoff plates. The plate is discretised using a continuous/discontinuous finite element method based on standard continuous piecewise polynomial finite element spaces. The beams are discretised by the CutFEM technique of letting the basis functions of the plate represent also the beams which are allowed to pass through the...
متن کاملTHESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Adaptive finite element methods for plate bending problems
The major theme of the thesis is the development of goal-oriented model adaptive continuous-discontinuous Galerkin (c/dG) finite element methods (FEM), for the numerical solution of the Kirchhoff and Mindlin-Reissner (MR) plate models. Hierarchical modeling for linear elasticity on thin domains (beam-like) in two spatial dimensions is also considered, as a natural extension of the Bernoulli and...
متن کاملNew DKFT Elements for the Finite Element Analysis of Thin Viscoelastic Plates
In this paper, finite element analysis of thin viscoelastic plates is performed by proposing new plate elements using complex Fourier shape functions. New discrete Kirchhoff Fourier Theory (DKFT) plate elements are constructed by the enrichment of quadratic function fields in a six-noded triangular plate element with complex Fourier radial basis functions. In order to illustrate the validity...
متن کاملAutomatically inf sup compliant diamond-mixed finite elements for Kirchhoff plates
We develop a mixed finite-element approximation scheme for Kirchhoff plate theory based on the reformulation of Kirchhoff plate theory of Ortiz and Morris [1]. In this reformulation the moment-equilibrium problem for the rotations is in direct analogy to the problem of incompressible two-dimensional elasticity. This analogy in turn opens the way for the application of diamond approximation sche...
متن کاملFinite Element Methods for Thin Structures with Applications in Solid Mechanics
Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the de...
متن کامل