Axisymmetric Free Vibration of Layered Cylindrical Shell Filled with Fluid

The aim of the study is to analyse the axisymmetric free vibration of layered cylindrical shells filled with a quiescent fluid. The fluid is assumed to be incompressible and inviscid. The equations of axisymmetric vibrations of layered cylindrical shell filled with fluid, on the longitudinal and transverse displacement components are obtained using Love’s first approximation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for a frequency parameter and an associated eigenvector of spline coefficients. Two layered shells with three different types of materials under clamped-clamped boundary conditions are considered. Parametric studies are made on the variation of the frequency parameter with respect to length-to-radius ratio and length-to-thickness ratio.

An Effective Method of Modeling the Deformation Behavior of Polymer Sandwich Structures with Adhesive Joints

Polymer sandwich structures have high bending stiffness and strength and also low weight. Therefore, they are widely used in the transportation industry. In the conceptual design phase, it is essential to have a method to model the mechanical behavior of the sandwich and its adhesive joints accurately in full-vehicle scale to investigate different structure partitioning strategies. In this paper, a novel approach using finite element modeling is introduced. The sandwich panels are modeled with layered shells and the joint lines with general stiffness matrices. Stiffness parameters of the face-sheets and the core material are obtained via mechanical tests. Stiffness parameters of the joints are determined by using the method of Design of Experiments, where detailed sub-models of the joints serve as a reference. These models are validated with experimental tests of glass-fiber reinforced vinyl ester matrix composite sandwich structure with a foam core. By using two joint designs and three reference geometries, it is shown that the method is suitable to describe the deformation behavior in a full-vehicle scale with sufficient accuracy.

The triangle grid, the evolution of layered shells since the beginning of the 19th century

This paper presents the evolution of and influence that the use of a triangular grid has had on the transformation of layered grid structures during the last two centuries. Historical facts, technological advances, economic and social crises among other factors influence the process of change and evolution of the grid systems in architecture to make construction processes more efficient by reducing the consumption of materials and qualified labor. Geometry and structure innovate styles and processes that are perfected over the years, achieving lighter and more stable structures. For the purpose of this paper historical data will be collected that allows the development of a theory that shows the influence of various periods based on technological advances. This research shows four historical periods in the evolution of layered grid structures. Being the triangular grid a widely used methodology in the construction of a diversity of geometric proposals and innovative construction systems for the solution of a diversity of buildings from the first domes built in the early 19th century to the free-form structures built from the late 20th century to the present day.

An advanced shell model for the analysis of geometrical and material nonlinear shells

In this paper layered shells subjected to static loading are considered. The displacements of the Reissner–Mindlin theory are enriched by a an additional part. These so-called fluctuation displacements include warping displacements and thickness changes. They lead to additional terms for the material deformation gradient and the Green–Lagrangian strain tensor. Within a nonlinear multi-field variational formulation the weak form of the boundary value problem accounts for the equilibrium of stress resultants and couple resultants, the local equilibrium of stresses, the geometrical field equations and the constitutive equations. For the independent shell strains an ansatz with quadratic shape functions is chosen. This leads to a significant improved convergence behaviour especially for distorted meshes. Elimination of a set of parameters on element level by static condensation yields an element stiffness matrix and residual vector of a quadrilateral shell element with the usual 5 or 6 nodal degrees of freedom. The developed model yields the complicated three-dimensional stress state in layered shells for elasticity and elasto-plasticity considering geometrical nonlinearity. In comparison with fully 3D solutions present 2D shell model requires only a fractional amount of computing time.

Acoustic scattering from a stiffened finite cylindrical shell with external rings

Studying the interaction of sound with cylindrical shells immersed in water is essential and helpful to improving underwater target detection and classification algorithms. Elastic cylindrical shells often occur as part of double-layered shell and have been widely used in marine and aerospace area. Acoustic waves are easy to be transmitted through the outer shell to the interior especially at low frequencies, thus directly being scattered by the inner shell and the rings in water between double-layered shells. Therefore, the externally ring-stiffened cylindrical shell is investigated in this paper. An experiment was conducted that measured the acoustic scattering. A hybrid 2-D/3-D finite-element modelling technique is employed to numerically calculate the scattering characteristics. Good qualitative agreement is found between numerical calculations and experimental measurement. An approximate analytical expression is given explicitly to identify the Bragg wave trajectories in the frequency-angle spectrum. It also has been shown that the rings not only affect the dynamic response of shell and indirectly influence the exterior scattered field, but also become direct acoustic scatterers in water and increase the target cross section especially at oblique incidence.