Abstract
An improved 8-node shell finite element applicable for the geometrically linear and nonlinear analyses of plates and shells is presented. Based on previous first-order shear deformation theory, the finite element model is further improved by the combined use of assumed natural strains and different sets of collocation points for the interpolation of the different strain components. The influence of the shell element with various conditions such as locations, number of enhanced membranes, and shear interpolation is also identified. By using assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, to characterize the efficiency of these modifications of the 8-node shell finite elements, numerical studies are carried out for the geometrically linear and non-linear analysis of plates and shells. In comparison to some other shell elements, numerical examples for the methodology indicate that the modified element described locking-free behavior and better performance. More specifically, the numerical examples of annular plate presented herein show good validity, efficiency, and accuracy to the developed nonlinear shell element.
Highlights
The 8-node isoparametric serendipity shell finite elements were suffering from locking effects due to smaller thickness
The primary goal of this paper is to propose an improvement of the most useful curved quadrilateral shell finite element, which is clearly, from a practical point of view, the 8-node element and in order to improve the 8-node ANS shell element, a new combination of sampling points and shaper functions are adopted for the analysis of plates and shells
The objective of this paper is to present some results using the 8-node shell element when the sampling points for the strain components are changed
Summary
The 8-node isoparametric serendipity shell finite elements were suffering from locking effects due to smaller thickness. To avoid this deficiency, reduced and selective integration techniques in the finite element method have been proposed; spurious zero-energy kinematic modes occur and may disturb the finite element response in a mesh. Bathe and Dvorkin [3] proposed an 8-node shell elementMITC8 to avoid membrane and shear locking problem. The strain tensor was expressed in terms of the covariant components and contravariant base vectors. The performance of this element was quite satisfying and suggested as the promising results in very complex shell structures. Bucalem and Bathe [4] had improved in previous publications the MITC8 shell elements [3], and the results provided conservative and unconservative performance in the finite element method
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