Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

Anomalous Scaling in the Kinematic Magnetohydrodynamic Turbulence

The problem of the anomalous scaling in the kinematic magnetohydrodynamic turbulence is investigated using the field theoretic renormalization group method and the operator product expansion technique. The anomalous dimensions of all leading composite operators, which drive the anomalous scaling of the correlation functions of a weak passive magnetic field, are determined up to the second order of the perturbation theory (i.e., in the two-loop approximation in the field theoretic terminology) in the presence of a large scale anisotropy for physically the most interesting three-dimensional case. It is shown that the leading role in the anomalous scaling properties of the model is played by the anomalous dimensions of the composite operators near the isotropic shell, in accordance with the Kolmogorov’s local isotropy restoration hypothesis. The importance of the two-loop corrections to the anomalous dimensions of the leading composite operators is demonstrated.

Improvement of Continuity Between Industrial Software and Research One by Object-Oriented Finite Element Formulation of Shell and Plate Element

This chapter shows, through the example of the addition of a plate and shell element to freeware FEM-object, an object-oriented (C++) finite element program, how object-oriented approaches, as opposed to procedural approaches, make finite element codes more compact, more modular, and versatile but mainly more easily expandable, in order to improve the continuity and the compatibility between software of research and industrial software. The fundamental traits of object-oriented programming are first briefly reviewed, and it is shown how such an approach simplifies the coding process. Then, the isotropic shell and orthotropic plate formulations used are given and the discretized equations developed. Finally, the necessary additions to the FEM-object code are reviewed. Numerical examples using the newly created plate membrane plate element are shown.

Flow behavior analysis of confined fluid in a flexible tube: application of asymptotic approach

In this paper, we asymptotically investigate a confined fluid flow in a flexible tube with a variable section. The fluid is considered to be newtonian, incompressible and it elapses in elastic and isotropic shell. This study provides a review of recent analysing the effects of the elastic wall tube properties over the fluid behaviour. The unsteady fluid flow will be analysed following the singular perturbations theory according to a large Reynolds number and a small aspect radio. The wall is assumed to be a thin shell that generate a small axisymmetric vibration. This model is mathematically developed by using the thin shell linear theory that is governed by a geodesic curvature parameter.

Inflatable Octet-Truss Structures

The development of variable-stiffness systems is key to the advance of compact engineering solutions in a number of fields. Rigidizable structures exhibit variable-stiffness based on external stimuli. This function is necessary for deployable structures, such as inflatable space antennas, where the deployed structure is semi-permanent. Rigidization is also useful for a wide range of applications, such as prosthetics and exoskeletons, to help support external loads. In general, variable-stiffness designs suffer from a tradeoff between the magnitude of stiffness change and the ability of the structure to resist mechanical failure at any stiffness state. This paper presents the design, analysis, and fabrication of a rigidizable structure based on inflatable octet-truss cells. An octet-truss is a lattice-like configuration of elements, traditionally beams, arranged in a geometry reminiscent of that of the FCC lattice found in many metals; namely, the truss elements are arranged to form a single interior octahedral cell surrounded by eight tetrahedral cells. The interior octahedral cell is the core of the octet-truss unit cell, and is used as the main structure for examining the mechanics of the unit as a whole. In this work, the elements of the inflatable octet truss are pneumatic air muscles, also called McKibben actuators. Generalized McKibben actuators are a type of tubular pneumatic actuator that possess the ability to either contract or expand axially due to an applied pressure. Their unique kinematics are achieved by using a fiber wrap around an isotropic elastomeric shell. Under normal conditions, pressurizing the isotropic shell causes expansion in all directions, like a balloon. The fiber wrap constrains the ability of the shell to freely expand, due to the fiber stiffness. The wrap geometry thus guides the extensile/contractile motion of the actuator by controlling its kinematics. It is their ability to contract under pressure that makes McKibben actuators unique, and consequently they are of great interest presently to the robotics community due to their similitude to organic muscles. Kinematic analysis from constrained maximization of the shell volume during pressurization is used to obtain relations between the input work due to applied pressure and the resulting shape change due to strain energy. Analytical results are presented to describe the truss stiffness as a function of the McKibben geometry at varying pressures.