A general methodology for deriving shear constrained Reissner‐Mindlin plate elements

Abstract

SUMMARYIn this paper the necessary requirements for the good behaviour of shear constrained Reissner-Mindlin plate elements for thick and thin plate situations are re-interpreted and a simple explicit form of the substitute shear strain matrix is obtained. This extends the previous work of the authors presented in References 18 and 31. The general methodology is applied to the re-formulation of some well known quadrilateral plate elements and some new triangular and quadrilateral plate elements which show promising features. Some examples of the good behaviour of these elements are given.

A stabilized one‐point integrated quadrilateral Reissner–Mindlin plate element

“…A further method uses substitute shear strain fields [11], subsequently extended and reformulated in [12,13] and [14,15,16]. In [17] the authors propose procedures to impose shear strain fields which satisfy a priori the conditions of vanishing transverse shear strains for the thin plate limit. A Taylor series expansion of the stiffness is derived using an assumed strain interpolation in [18].…”

An XFEM approach for modelling delamination in composite laminates

“…Another approach is to modify the formulation by linearly varying the transverse strain field in one direction which is assumed constant in the FSDT formulation [3]. The methodology was proposed by Oñate et al for the quadrilateral plate element in [22]. Here, it is applied for the XFEM-based topology.…”

Stability and accuracy of non-linear dynamic analysis using time integration algorithms

“…Consequently, the structure is modelled with 96 Mindlin triangular elements. The TQQQ element of Onate et al (1992) is used to construct the model. The material properties are: E ¼ 10 .…”