Finite Rotation Geometrically Exact Four-Node Solid-Shell Element with Seven Displacement Degrees of Freedom

Abstract

This paper presents a robust non- linear four-node solid-shell element based on the first-order seven-parameter equivalent single-layer theory, which permits us to utilize the 3D constitutive equations. The term geometrically exact reflects the fact that geom- etry of the reference surface is described by ana- lyticallygiven functionsand displacementvectors are resolved in the reference surface frame. As fundamental shell unknownssix displacements of the outer surfaces and a transverse displacement of the midsurface are chosen. Such choice of dis- placements gives the possibility to derive strain- displacement relationships, which are invariant under arbitrarily large rigid-body shell motions in a convected curvilinear coordinate system. To avoid shear and membrane locking and have no spurious zero energy modes, the assumed strain and stress resultant fields are invoked. To im- prove a non-linear shell response, the modified ANS method is applied. Addi- tionally, analytical integration throughout the el- ement is employed to evaluate the tangent stiff- ness matrix. As a result, the present finite rota- tion solid-shell element formulation allows using coarse meshes and very large load increments. Keyword: solid-shell ele- ment, finite rotations, seven-parameter shell for- mulation