A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

A new 3-node triangular hybrid displacement function Mindlin- Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses

A mixed formulation for the stress analysis of curved pipes with tangent terminations under in-plane forces

Curved pipes connected to tangent terminations play an important role in process equipment design where there is fluid transport. They allow change in flow direction and simultaneously contribute to increase flexibility of the whole structure. The stress analysis of curved pipes (or pipe elbows) is an essential step in the project of piping systems. The method of hybrid formulation of the shell parameters (internal forces and displacements), is an alternative to the irreducible formulation, this last dealing with a totally assumed displacement field for the unknowns. The main advantage has incidence in the use of lower order formulations in the differential equations to set-up the solution compared with the irreducible formulation. The hybrid solution here proposed is based on a semi-analytic formulation, where the definition of the shell forces and displacements combines analytic and trigonometric functions. Tests for most usual loading cases are analysed and results for stress distribution are discussed