The paper extends recent work of the authors to include transverse shear effects on rotation-free triangular element for plates (Oñate and Zárate in Int J Numer Methods Eng 83(2):196–227, 2010). Two new shell triangular elements are presented, the EBST+ and the EBST+1. Transverse shear deformation effects are important for thick shells, as well when the shell is laminated or formed by composite material. The ingredients for the element formulation are: a Hu-Washizu type mixed functional and linear interpolation for the displacement field. In both elements presented a finite volume approach is used for computing the bending moments and the curvatures over a patch of elements. The nodal translational degrees of freedom of the original enhanced basic shell triangle (EBST) are extended with the two shear deformation angles via two different approaches. The first one uses a linear interpolation of the rotation angles inside the element (EBST+) and the second one assumes a constant field for the rotation angles (EBST+1). For the thin shell case the shear angles vanish and the new elements reproduce the good behaviour of the original thin EBST element. As a consequence the elements can reproduce the solutions for thick to thin shells situations without exhibiting shear locking. The numerical solution for the thick shell case can be found iteratively starting from the deflection values for the Kirchhoff theory using the original thin EBST element. Examples of the good performance of the new rotation-free shell triangles are given.
Abstract
The paper extends recent work of the authors to include transverse shear effects on rotation-free triangular element for plates (Oñate and Zárate [...]
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective integration techniques are used to ensure the good behaviour of the elements when dealing with thin plates. Numerical results showing the convergence and accuracy of the elements for the analysis of plates of a wide range of thicknesses are given. The general performance of the three elements is discussed in detail. In particular, the linear element with a single integration point seems to be the best value strip element for practical purposes.
Abstract
The behaviour of the linear, quadratic and cubic elements of the Mindlin plate strip family for thick and very thin plate analysis is investigated in this paper. Selective integration techniques [...]