On Improved Thin Plate Bending Rectangular Finite Element Based on the Strain Approach

Abstract

We propose in this paper the development of a new rectangular finite element for thin plate bending based on the strain approach with linear elastic behavior. An analytical integration is used to evaluate the element stiffness matrix. The present element possesses the three main degrees of freedom (d.o.f) per node, namely, one transverse displacement (w) and two normal rotations about x and y axis respectively (Ɵx, Ɵy). The proposed displacement field represents exactly the rigid body motion and satisfies the compatibility equations. The numerical results converges rapidly to the Kirchhoff solution for thin plates, this makes the present element robust, better suitable for computations, and particularly interesting in modeling this type of structures.

A four-node rectangular plate finite element using Airy functions with transverse shear

“…SBRPK: rectangular finite element for thin plate bending based on the strain approach with linear elastic behavior (Sifeddine et al ., 2016).…”

“…Also, another flat shell element is developed to analyze this shell structures with different geometrical shapes, and good results can be obtained (Djamal et al ., 2016b). For plates bending problems, more elements have also been formulated by Belarbi and Charif (1999), Belounar and Guenfoud (2005), Himeur and Guenfoud (2011) and Sifeddine et al . (2016) and Sifeddine et al .…”

A New Strain Based Sector Finite Element for Plate Bending Problems

“…Before considering the development of the present element, let us see the formulation of the robust finite sector element for the plane problems SBS4 [15] where; also, the first method is used. This element has three degrees of freedom at each corner node and the displacement field is: [16] have developed a new rectangular finite element for thin plate bending based on the strain approach with linear elastic behavior .This element is possesses the three main degrees of freedom (d.o.f) per node, namely, one transverse displacement (w) and two normal rotations (Ɵ x , Ɵ y ) about x and y axis respectively. The first method "direct approach" mentioned above is used to develop a new sector element based on the shape functions of SBRPK element [16].…”

The Transverse Shear Effect of a New Plate Bending Finite Element Based on the Strain Approach

“…It is not the first attempt to present solution based on this approach, a set of elements have been already developed [ (Belounar et al 2005), (Belarbi et al .1999), (Himeur et al 2011), [(Hamadi et al 2012)] which give a very good results. The purpose of this work is to study the transverse shear effect of a new plate bending finite element 'SBRPK' (Abderrahmani et al 2016) based on the strain approach. A comparative study with finite elements based on the strain approach is presented.…”