A Triangular Plate Bending Element Based on Discrete Kirchhoff Theory with Simple Explicit Expression

A simple locking-free discrete shear triangular plate element

A new three node triangular plate element, labeled here as DST-S6 (Discrete Shear Triangular element with 6 extra Shear degrees of freedom), is proposed for the analyses of plate/shell structures comprising of thin or thick members. The formulation is based on the DKT (Discrete Kirchhoff Technique) and an appropriate use of the independent shear DOF(Degrees Of Freedom). The shear locking is com...

A Pseudospectral Approach for Kirchhoff Plate Bending Problems with Uncertainties

This paper proposes a pseudospectral approach for the Kirchhoff plate bending problem with uncertainties. The Karhunen-Loève expansion is used to transform the original problem to a stochastic fourth-order PDE depending only on a finite number of random variables. For the latter problem, its exact solution is approximated by a gPC expansion, with the coefficients obtained by the sparse grid met...

Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems

and Applied Analysis 3 Let {T h } h>0 be a regular family of triangulations ofΩ (cf. [1, 20]); h := max K∈Th h K and h K := diam(K). Let E h be the union of all edges of the triangulation T h and E h the union of all interior edges of the triangulationT h . For any e ∈ E h , denote by h e its length. Based on the triangulationT h , let the finite element spaces be given by Σ h := {τ ∈ Σ : τ| K ...

Approximation of Large Bending Isometries with Discrete Kirchhoff Triangles

We devise and analyze a simple numerical method for the approximation of large bending isometries. The discretization employs a discrete Kirchhoff triangle to deal with second order derivatives and convergence of discrete solutions to minimizers of the continuous formulation is proved. Unconditional stability and convergence of an iterative scheme for the computation of discrete minimizers that...

Superconvergent eigenvalue bending plate element