Four-node ‘flat’ shell element: Drilling degrees of freedom, membrane-bending coupling, warped geometry, and behavior

Abstract A very simple way to obtain a quadrilateral shell element is to write membrane and bending stiffness matrices for a flat geometry and add them. This basic membrane-plus-bending element can be modified to incorporate membrane-bending coupling and to accommodate a geometry in which the four nodes are not coplanar. The present paper develops a 24 degree of freedom quadrilateral shell element and concurrently provides a status report on the formulation method by pointing out what works and what does not. Numerical results are good: the element is not the best available four-node shell element in all test cases but is far from the worst.

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