Claudia Chinosi

Refined shell elements for the analysis of functionally graded structures

Abstract The present paper considers the static analysis of plates and shells made of Functionally Graded Material (FGM), subjected to mechanical loads. Refined models based on the Carrera’s Unified Formulation (CUF) are employed to account for grading material variation in the thickness direction. The governing equations are derived from the Principle of Virtual Displacement (PVD) in order to apply the Finite Element Method (FEM). A nine-nodes shell element with exact cylindrical geometry is considered. The shell can degenerate in the plate element by imposing an infinite radius of curvature. The Mixed Interpolation of Tensorial Components (MITC) technique is extended to the CUF in order to contrast the membrane and shear locking phenomenon. Different thickness ratios and orders of expansion for the displacement field are analyzed. The FEM results are compared with both benchmark solutions from literature and the results obtained using the Navier method that provides the analytical solution for simply-supported structures subjected to sinusoidal pressure loads. The shell element based on refined theories of the CUF turns out to be very efficient and its use is mandatory with respect to the classical models in the study of FGM structures.

MITC9 Shell Elements Based on Refined Theories for the Analysis of Isotropic Cylindrical Structures

In this work a nine-nodes shell finite element, formulated in the framework of Carrera’s Unified Formulation (CUF), is presented. The exact geometry of cylindrical shells is considered. The Mixed Interpolation of Tensorial Components (MITC) technique is applied to the element in order to overcome shear and membrane locking phenomenon. High-order equivalent single layer theories contained in the CUF are used to perform the analysis of shell structures. Benchmark solutions from the open literature are taken to validate the obtained results. The mixed-interpolated shell finite element shows good properties of convergence and robustness by increasing the number of used elements and the order of expansion of displacements in the thickness direction.

Mixed-interpolated elements for thin shells

The subject of this work is the construction of some special finite elements for the numerical solution of Naghdi cylindrical shell problems. The standard numerical approximation of the shell problem is subjected to the shear and membrane locking phenomenon, i.e. the numerical solution degenerates for low thickness. The most common way to avoid locking is the use of modified bilinear forms to describe the shear and membrane energy of the shell. In this paper we build a family of special finite elements that still follow the above strategy by introducing a linear operator that reduces the influence both of the shear and membrane energy terms. The main idea comes from the non-standard mixed interpolated tensorial components (MITC) formulation for Reissner-Mindlin plates. The performance of the new elements is then tested for solving benchmark problems involving very thin shells. The results show both the properties of convergence and robustness.

Hierarchic finite elements for thin Naghdi shell model

Abstract Two approaches have traditionally been used when general shell structures have been analysed. The first approach has been devised by Kirchhoff and Love and later the model has been improved by Koiter. A second class of models is based on the notion of surface introduced by Cosserat. Naghdi has developed this model, where the Reissner-Mindlin-type assumptions are taken into account. In this paper we consider the shell model arising from the Naghdi formulation. It is known that finite element schemes for this model suffer from both shear and membrane locking. Several solutions to avoid the numerical locking have been proposed. Here a displacement finite element scheme is developed using C0 finite elements of hierarchic type with degrees ranging from one to four. Two severe test problems are solved. The results show that good performances are achieved by using high-order finite elements to solve the shell problem in its displacement formulation. The numerical results indicate that high-order elements perform very well in both test problems and match all the available benchmark results.

Rotating Electromagnetic Waves In Toroid-Shaped Regions

Electromagnetic waves, solving the full set of Maxwell equations in vacuum, are numerically computed. These waves occupy a fixed bounded region of the three-dimensional space, topologically equivalent to a toroid. Thus, their fluid dynamics analogs are vortex rings. An analysis of the shape of the sections of the rings, depending on the angular speed of rotation and the major diameter, is carried out. Successively, spherical electromagnetic vortex rings of Hills type are taken into consideration. For some interesting peculiar configurations, explicit numerical solutions are exhibited.