Geometrically-exact sandwich shells: The static case

• Published in: Computer methods in applied mechanics and engineering Vol. 189; no. 1; pp. 167 - 203
• Main Authors: Vu-Quoc, L., Deng, H., Tan, X.G.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.08.2000; Elsevier
• Subjects: Computational techniques; Exact sciences and technology; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Solid mechanics; Static elasticity; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Viscoelasticity; Stiffness matrix; Variable thickness shell; High strain; Stratified material; Sandwich structure; Equilibrium equation; Modeling; Projection method; Finite element method; Shell; Weak solution; Symmetric matrix; Piezoelectricity; Galerkin method
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/S0045-7825(99)00294-7

The present formulation offers a general method for analyzing the static response of geometrically-exact sandwich shells undergoing large deformation. The layer directors at a point in the reference surface are connected to each other by universal joints, and form a chain of rigid links. Finite rotations of the directors in every layer are allowed, with shear deformation independently accounted for in each layer. The thickness and the length of each layer can be arbitrary, thus allowing the modeling of an important class of multilayer structures having ply drop-offs. The present formulation is thus suitable to model shell structures with patches of constrained viscoelastic materials or of piezoelectric materials. The nonlinear weak form of the governing equations of equilibrium is constructed here, and then the linearization of the weak form and the associated inextensible directors update are derived, leading to a symmetric tangent stiffness matrix. A Galerkin finite element projection of the linearized equilibrium equations results in a system of nonlinear algebraic equations, in which the interpolation accounts for the finite rotations of the directors. We present extensive numerical examples, including sandwich shells with three identical layers and ply drop-offs, to illustrate the applicability and versatility of the proposed formulation.