Lucia Della Croce

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.

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.

On the robustness of hierarchic finite elements for Reissner-Mindlin plates

The discretization of the Reissner-Mindlin model for plates requires finite elements of class only C0. This is perhaps the main advantage respect to the Kirchhoff formulation, where C1 finite elements need to be used for a conforming approximation. However, despite its simple approach, the numerical approximation of the Reissner-Mindlin plate is not straightforward. The inclusion of transverse shear strain effect in standard finite element models introduces undesirable numerical effects. Standard low order finite elements are not able to meet the Kirchhoff constraint enforced when the thickness becomes smaller and therefore are subject to the locking phenomenon. The approximate solution is very sensitive to the plate thickness and unsatisfactory results are obtained for small thickness. We have solved the Reissner-Mindlin plate problem in its plain formulation with the use of high order finite elements. We have developed a hierarchic family of finite elements and have performed several numerical tests to analyze the behavior with respect to the thickness. In this paper we are particularly interested in the investigation of the robustness properties of the family of finite elements. In this direction we analyse the performance of the elements when very small values of the thickness of the plate are considered. The numerical results indicate a large range of robustness for the higher order elements.

Combining hierarchic high order and mixed-interpolated finite elements for Reissner-Mindlin plate problems

Abstract The Reissner—Mindlin plate bending model describes the deformation of a plate subject to a transverse loading when transverse shear deformation is taken into account. Despite its simple approach, the discretization of the Reissner—Mindlin model is not straightforward. The inclusion of the transverse shear strain effect in standard finite element models introduces undesirable numerical effects. The approximate solution is very sensitive to the plate thickness and, for small thickness, it is very far from the true solution. The phenomenon is known as locking of the numerical solution. The most common way to avoiding the locking problem is to use non-standard finite elements and/or modify the variational formulation. Recently, numerical experiences with high order finite elements applied to the plain Reissner—Mindlin formulation have shown a consistent improvement in the quality of the results. Meanwhile some mixed-interpolated finite elements have been suggested and shown to be locking free. In this paper we propose the combination of the two classes of elements introducing a family of hierarchic high order mixed-interpolated finite elements.

Is BaF3 bioassay useful to identify patients with bioinactive growth hormone

ABSTRACT We analyzed the ability of the BaF3 cell line bioassay to select patients with biologically inactive GH. We first evaluated the biological response of the Ba/F3-hGHR cells to rhGH additional doses from 10 to 5000 pg/ml. The concentration points corresponding to the linear part of the curve were selected. We then analyzed a group of sera, diluted like the standard, including the entire range of GH concentrations that can be analyzed by bioassay. The serum/standard area below the curve ratio was calculated. Serum GH immunoactivity determined by IMMULITE/GH bioactivity ratios was calculated. Our experimental data showed that GH-bioactivity/GH-immunoactivity ratios below 0.303 are indicative of a bioinactive GH molecule. This bioassay would recognize only extreme cases of GH bioinactivity, and it would not be a useful tool in the search for patients with altered forms of GH.

On the implementation of an equilibrium finite element method for the numerical solution of plate bending problems

A finite element method of equilibrium type is used to solve plate bending problems. Continuity of displacemnts, bending moments and Kirchhoff shear forces at the interelement boundaries are required. Suitable choices for the approximation spaces allow the continuity requirements to be satisfied. The paper focuses on the implementation of the method. After recalling the main features of the equilibrium approximation we describe in details the numerical program. Finally the numerical results obtained solving a model problem are presented.