In this paper, a new rectangular flat shell element denoted 'ACM_RSBE5' is presented. The new element is obtained by superposition of the new strain-based membrane element 'RSBE5' and the well-known plate bending element 'ACM'. The element can be used for the analysis of any type of thin shell structures; even if the geometry is irregular. Comparison with other types of shell elements is performed using a series of standard test problems. A correlation study with an experimentally tested aluminum shell is also conducted. The new shell element proved to have a fast rate of convergence and to provide accurate results.
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A New Strain-Based Finite Element for Plane Elasticity Problems
ABSTRACTIn this paper, a new quadrilateral strain-based element is developed. The element has five nodes, four at the corners as well as an internal node. Through the introduction of the internal node, the numerical performance of the element proved to be superior to existing elements, even though a static condensation is required. From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The proposed element can be used to solve general plane elasticity problems resulting in excellent results. The results obtained are comparable with those given by the robust element Q8.
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.
In this paper, we present a comparative study of the transverse shear effect on the plate bending. The element used is a rectangular finite element called SBRPK (Strain Based Rectangular Plate-Kirchhoff Theory-), it used for the numerical analysis of thin plate bending, and it based on the strain approach. This element has four nodes and three degrees of freedom per node (w, θx, θy). Through the numerical applications with different loading cases and boundary conditions; the numerical results obtained are in close agreement with the analytical solution.
The effect of boundary conditions is very important in the analysis of cylindrical shells, and is rarely studied in the literature due to its difficult experimental simulation. For large structures such as shell roofs, the type of boundary supports is among the major factors that can minimize the stresses and deflections. In this study, experimental and numerical investigations of the effect of different boundary supports for stiffened and un-stiffened cylindrical shells were conducted. Two different models of the stiffened and un-stiffened cylindrical shells with different boundary conditions, "pinned and with rigid diaphragms", were studied. It was shown that by using rigid diaphragms for cylindrical shells, the deflections are minimized by 80%, and by (45-50) % for the stiffened cylindrical shells. From the experimental investigations and the numerical results obtained, the efficiency of the proposed boundary support types for cylindrical shells is confirmed, which can result in economic benefits.
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