A hybrid stress-assumed transition element for solid to beam and plate to beam connections

This paper presents a new transition element for modelling solid-to-beam and plate-to-beam connections. The approach is based upon the hybrid stress method and the resulting transition element is hypostatic, i.e. the number of independent stress parameters is less than the number of independent displacements. As a consequence, there are further displacement modes called spurious kinematic modes which are eliminated by means of a suitable “penalty” method. The numerical performance of the proposed element is assessed by a number of relevant tests

An unsymmetric stress formulation for Reissner-Mindlin plates: a simple and locking free four node element

In the present paper a simple mixed-hybrid element for the linear analysis of Reissner-Mindlin plates is discussed. The element is derived from a modified Reissner functional and standard bilinear (isoparametric) interpolation for displacement and rotations is assumed whereas local stresses (rather than stress resultants and moments) are explicitly modelled. It is assumed that in plane shear stresses are not a priori symmetric. This choice allows to decouple the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling degrees of freedom. Out-of-plane shear stresses are then obtained such that equilibrium equations are exactly satisfied. The proposed element does not exhibit locking effects at all: i.e. the shear deformation energy is zero in the thin plate limit. Details of the formulation are provided, and the performances of the element are assessed with reference to well-established benchmark problems

Mixed finite elements for plate analysis with unsymmetric stresses

A mixed-hybrid model similar to one already presented for the case of beams is developed: for a Reissner-Mindlin-type plate local stresses (rather than stress resultants and moments) are explicitly modelled. By following the ideas previously used for membranes, it is assumed that in plane shear stresses are not a priori symmetric. This choice allows the decoupling of the equilibrium equations, and involves introducing an in-plane infinitesimal rotation field, corresponding to drilling dofs. Out-of plane shear stresses are then chosen such that equilibrium equation are exactly satisfied. Details of the formulation are provided, and the performances of the new element are assessed with reference to well-established benchmark problems

A 4-noded mixed-hybrid finite element, using unsymmetric stresses, for linear analysis of plates

Shells in general, and flat shells (i.e. plates) in particular have received a lot of attention in the finite element research world: as a matter of fact in a recent survey [1], spanning the last 15 years, more than 350 contribution are enlisted, and in another one [2], covering only papers about plates appeared in the years 1992-94 a list of 250 titles is presented. Such a research effort is justified by the quest of plate models which may both deal with general thickness/shape and provide a higher accuracy in evaluating shear stress distributions, especially when laminated structures are considered. In order to achieve better performances mixed models [3] have been often exploited. In the present paper a mixed-hybrid model for a Reissner-Mindlin-type plate is presented where local stresses (rather than stress resultants and moments) are explicitly modelled. Moreover, by following the ideas already used for membranes in [4], it is assumed that in plane shear stresses are not a priori symmetric [5]. This choice allows the decoupling of the equilibrium equations, and involves introducing an in plane infinitesimal rotation field, corresponding to drilling dofs. Out-of plane shear stresses are then chosen such that equilibrium equation are exactly satisfied. Details of the formulation are provided, and the performances of the new element are assessed with reference to well-established benchmark problems. The analysis of laminated plates appears possible [6]