Numerical results for mimetic discretization of Reissner-Mindlin plate problems

A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Full details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported

Approximation of the vibration modes of a plate by Reissner-Mindlin equations

This paper deals with the approximation of the vibration modes of a plate modelled by the Reissner-Mindlin equations. It is well known that, in order to avoid locking, some kind of reduced integration or mixed interpolation has to be used when solving these equations by finite element methods. In particular, one of the most widely used procedures is the mixed interpolation tensorial components, based on the family of elements called MITC. We use the lowest order method of this family. Applying a general approximation theory for spectral problems, we obtain optimal order error estimates for the eigenvectors and the eigenvalues. Under mild assumptions, these estimates are valid with constants independent of the plate thickness. The optimal double order for the eigenvalues is derived from a corresponding L 2 -estimate for a load problem which is proven here. This optimal order L 2 -estimate is of interest in itself. Finally, we present several numerical examples showing the very good behavior of the numerical procedure even in some cases not covered by our theory.Facultad de Ciencias ExactasConsejo Nacional de Investigaciones Científicas y Técnica

A novel 2.5D spectral approach for studying thin-walled waveguides with fluid-acoustic interaction

This paper presents a novel formulation of two spectral elements to study guided waves in coupled problems involving thin-walled structures and fluid-acoustic enclosures. The aim of the proposed work is the development of a new efficient computational method to study problems where geometry and properties are invariant in one direction, commonly found in the analysis of guided waves. This assumption allows using a two-and-a-half dimensional (2.5D) spectral formulation in the wavenumber-frequency domain. The novelty of the proposed work is the formulation of spectral plate and fluid elements with an arbitrary order in 2.5D. A plate element based on a Reissner-Mindlin/Kirchhoff-Love mixed formulation is proposed to represent the thin-walled structure. This element uses approximation functions to overcome the difficulties to formulate elements with an arbitrary order from functions. The proposed element uses a substitute transverse shear strain field to avoid shear locking effects. Three benchmark problems are studied to check the convergence and the computational effort for different strategies. Accurate results are found with an appropriate combination of element size and order of the approximation functions allowing at least six nodes per wavelength. The effectiveness of the proposed elements is demonstrated studying the wave propagation in a water duct with a flexible side and an acoustic cavity coupled to a Helmholtz resonator.Ministerio de Economía y Competitividad BIA2013-43085-P y BIA2016-75042-C2-1-RCentro Informático Científico de Andalucía (CICA

Finite element analysis of the vibration problem of a plate coupled with a fluid

We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindlin equations while the fluid is described in terms of displacement variables. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindlin equations are discretized by a mixed method, the equations for the fluid with Raviart-Thomas elements and a non conforming coupling is used on the interface. In order to prove that the method is locking free we consider a family of problems, one for each thickness t>0, and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t→0. We prove that spurious eigenvalues do not arise with this discretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t. Finally we present numerical results confirming the good performance of the method.Facultad de Ciencias Exacta

Free vibrations of laminated composite elliptic plates

The free vibrations are studied of laminated anisotropic elliptic plates with clamped edges. The analytical formulation is based on a Mindlin-Reissner type plate theory with the effects of transverse shear deformation, rotary inertia, and bending-extensional coupling included. The frequencies and mode shapes are obtained by using the Rayleigh-Ritz technique in conjunction with Hamilton's principle. A computerized symbolic integration approach is used to develop analytic expressions for the stiffness and mass coefficients and is shown to be particularly useful in evaluating the derivatives of the eigenvalues with respect to certain geometric and material parameters. Numerical results are presented for the case of angle-ply composite plates with skew-symmetric lamination

Laminated Beam Analysis by Polynomial, rigonometric, Exponential and Zig-Zag Theories

A number of refined beam theories are discussed in this paper. These theories were obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials, trigonometric series, exponential, hyperbolic and zig-zag functions. The Finite Element method is used to derive governing equations in weak form. By using the Unified Formulation introduced by the first author, these equations are written in terms of a small number of fundamental nuclei, whose forms do not depend on the expansions used. The results from the different models considered are compared in terms of displacements, stress and degrees of freedom (DOFs). Mechanical tests for thick laminated beams are presented in order to evaluate the capability of the finite elements. They show that the use of various different functions can improve the performance of the higher-order theories by yielding satisfactory results with a low computational cost

Structural study of a wind sensor for Mars under vibrations induced during launch

Arid, rocky, cold and ’apparently’ lifeless, Mars has captured humanity’s attention for the past few decades. "It’s such a fundamental question. ’Are we alone?’ " Hubbard said. Scientists are deeply interested in the Red Planet since it was found plenty of evidence that it was once far warmer and could potentially host life as we know it. NASA’s Mars Exploration Program has built up momentum, from the first flybys, followed by orbiters, then landers and rovers to a sample-return mission. Mars is seen as a prime target for future human colonization but, before sending any astronaut to the Red Planet, more knowledge is required. The characterization of surface weather in Mars is one of the main science objectives in NASA’s Mars Exploration Program, specially, the measurement of wind direction, as it is considered to be the dominant force shaping the Red Planet’s landscape. Currently, UPC is improving a 3D miniaturised wind sensor capable of collecting data samples of Mars’ atmospheric dynamics. The purpose of this paper is to do a structural study of the UPC’s wind sensor for Mars under vibrations induced during the launching phase. In order to do so, the sensor has been evaluated under a quasi-static test, a random vibration test and a pyroshock test. The first chapter will include detailed explanation of the state of the art. This section defines the characteristics of the three spatial certification tests performed to the sensor including different Finite Element Model satellite simulations already carried out by different research groups. In the second chapter, a detailed description of the wind sensor is elaborated. Then, it has been defined the mathematical formulation behind the different test using Reissner-Mindlin flat shell theory, a Vibrations analysis and a Shock analysis. The fourth chapter details the geometry, element type and boundary conditions used to perform each of the tests. Next, the different results have been analysed and finally some conclusions have been drawn