On a tensor-based finite element model for the analysis of shell structures

摘要

In the present study, we propose a computational model for the linear and nonlinearanalysis of shell structures. We consider a tensor-based finite element formulation whichdescribes the mathematical shell model in a natural and simple way by using curvilinearcoordinates. To avoid membrane and shear locking we develop a family of high-orderelements with Lagrangian interpolations.The approach is first applied to linear deformations based on a novel and consistentthird-order shear deformation shell theory for bending of composite shells. Nosimplification other than the assumption of linear elastic material is made in thecomputation of stress resultants and material stiffness coefficients. They are integratednumerically without any approximation in the shifter. Therefore, the formulation is validfor thin and thick shells. A conforming high-order element was derived with 0 Ccontinuity across the element boundaries.Next, we extend the formulation for the geometrically nonlinear analysis ofmultilayered composites and functionally graded shells. Again, Lagrangian elementswith high-order interpolation polynomials are employed. The flexibility of theseelements mitigates any locking problems. A first-order shell theory with sevenparameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and,therefore, 3D constitutive equations are utilized. Finally, extensive numericalsimulations and comparisons of the present results with those found in the literature fortypical benchmark problems involving isotropic and laminated composites, as well asfunctionally graded shells, are found to be excellent and show the validity of thedeveloped finite element model. Moreover, the simplicity of this approach makes itattractive for future applications in different topics of research, such as contactmechanics, damage propagation and viscoelastic behavior of shells.