An isostatic assumed stress triangular element for the Reissner–Mindlin plate‐bending problem

Abstract

SUMMARYThe paper describes a new assumed stress triangular element for Reissner-Mindlin plates, called TIP3, with three nodes and three degrees of freedom per node. The kinematics is constructed by means of the so-called linked interpolation ruled by technically significant degrees of freedom (i.e. one transversal displacement and two rotations per node) without using additional bubble modes. The static representation starts from a moment-shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number. The resulting element is locking free, presents correct rank and passes the bending patch test even for very thin plates. The good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature.

An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

“…Unfortunately, the reduced integration often causes the instability due to rank deficiency and results in zero-energy modes. It is therefore many various improvements of formulations as well as numerical techniques have been developed to overcome the shear locking phenomenon and to increase the accuracy and stability of the solution such as mixed formulation/hybrid elements [13][14][15][16][17][18][19][20][21][22][23], Enhanced Assumed Strain (EAS) methods [24][25][26][27][28] and Assumed Natural Strain (ANS) methods [29][30][31][32][33][34][35][36][37][38]. Recently, the discrete shear gap (DSG) method [39] which avoids shear locking was proposed.…”

A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

“…This kind of approach based on hybrid stress element method became very useful in recent years [31][32][33][34][35][36]. A good number of effective elements which are free from shear locking have been developed by authors such as Tong [37], Bathe and Dvorkin [38], Ayad et al [39], Brasile [40], and Li et al [22,23]. The higher-order hybrid stress quadrilateral Mindlin plate bending element QH8 is based on complementary energy principle.…”

A Simple High-Order Shear Deformation Triangular Plate Element with Incompatible Polynomial Approximation

“…The 16 × 16 regular mesh similar to Section 4.1 is employed for computation. Tables 10 and 11 list the normalized defection W 0 of the FG plate for different aspect ratios h/L and different exponents n in Equation (15), where W 0 = W c / qL 4 E m h 3 and W c is the central deflection of the plate. In Ferreira et al [45], the FG plate is solved by the meshless collocation method with multiquadric radial basis functions and a third-order shear deformation theory.…”

“…In Ferreira et al [45], the FG plate is solved by the meshless collocation method with multiquadric radial basis functions and a third-order shear deformation theory. The problem is also solved by Talha and Singh [70] using the C 0 isoparametric finite element with 13 degrees of freedom per node, and the power-law similar to Equations (15) and (16) is used to describe the through-the-thickness distribution of FG materials in the HSDT model. The results obtained by the present TrSDTPE, FfSDTPE, and FiSDTPE are in good agreement with the meshless solutions of Ferreira et al [45], which compute the effective elastic moduli by the rule of mixture.…”

“…Unfortunately, the FSDT elements suffer from the shear-locking problem when the thickness to length ration of the plate becomes very small, due to inadequate dependence among transverse deflection and rotations using an ordinary low-order finite element [4]. Quite a large number of techniques have been developed to overcome this problem, such as the assumed shear strain approach, the discrete Kirchhoff/Mindlin representation, the mixed/hybrid formulation, and the reduced/selected integration [5][6][7][8][9][10][11][12][13][14][15]. These formulations are free from shear locking and are applicable to a wide range of practical engineering problems, but in general, it is rather complex and time consuming to include the transverse shear effects for thick plates, which would also lead to complexity and difficulty in the programming.…”