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An Explicit Quadrilateral Shell Element


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DOI: https://doi.org/10.15866/irece.v6i6.8202

Abstract


The present study introduces a 4-node quadrilateral shell element (which is called EQ7) for the analysis of plates and shells. The element is a flat element with 6 degrees of freedom at each node; three displacements and three rotations. It is based on the Explicit Finite Element Method. All quantities, matrices, etc., are explicitly derived. We apply to the shell element a number of modes and besides the Modal Stiffness Matrix we introduce the Modal Mass Matrix and the Modal Geometric Matrix. We employ also an iterative scheme for the solution of the linear system of equations. Numerical simulations are provided. Stress Wave Patterns are found in deforming plates and shells. Because all quantities are explicitly derived, the theory and method is suited for efficient computer implementation.
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Keywords


Shell Element; Modes; Modal Matrices; Stress Wave Patterns

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References


L. T. Tenek, Some Explicit Beam, Plate and Shell Finite Elements, (2007) International Review of Mechanical Engineering (IREME), 1 (3), pp. 225-231.

L. T. Tenek, On the Concepts of Action, Reaction, and Stress Wave Patterns in Structures, (2007) International Review of Mechanical Engineering (IREME), 1 (5), pp. 538-542.

L. T. Tenek, A Beam Finite Element Based on the Explicit Finite Element Method, (2008) International Review of Mechanical Engineering (IREME), 2 (1), pp. 122-131.

L. T. Tenek, The Explicit Finite Element Method in Structural Mechanics and Computing (Tziola Publications, 2007).

G. Nitsiotas, Theory of Elasticity, (Ziti Publications, 1985).

R.D. Cook, D.S. Malkus and M.E. Plesha, Concepts and Applications of Finite Element Analysis (3rd ed., John Wiley & Sons Inc., 1989).

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http://dx.doi.org/10.1002/nme.1620090322


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