Linear and non-linear dynamic analyses of sandwich panels with face sheet-tocore debonding

А survey of recent developments in the dynamic analysis of sandwich panels with face sheet-to-core debonding is presented. The finite element method within the ABAQUSTM code is utilized. The emphasis is directed to the procedures used to elaborate linear and non-linear models and to predict dynamic response of the sandwich panels. Recently developed models are presented, which can be applied for structural health monitoring algorithms of real-scale sandwich panels. First, various popular theories of intact sandwich panels are briefly mentioned and a model is proposed to effectively analyse the modal dynamics of debonded and damaged (due to impact) sandwich panels. The influence of debonding size, form and location, and number of such damage on the modal characteristics of sandwich panels are shown. For nonlinear analysis, models based on implicit and explicit time integration schemes are presented and dynamic response gained with those models are discussed. Finally, questions related to debonding progression at the face sheet-core interface when dynamic loading continues with time are briefly highlighted

Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements

A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUSTM code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction

Three-dimensional free vibration analysis of thermally loaded fgm sandwich plates

Using the finite element code ABAQUS and the user-defined material utilities UMAT and UMATHT, a solid brick graded finite element is developed for three-dimensional (3D) modeling of free vibrations of thermally loaded functionally gradient material (FGM) sandwich plates. The mechanical and thermal material properties of the FGM sandwich plates are assumed to vary gradually in the thickness direction, according to a power-law fraction distribution. Benchmark problems are firstly considered to assess the performance and accuracy of the proposed 3D graded finite element. Comparisons with the reference solutions revealed high efficiency and good capabilities of the developed element for the 3D simulations of thermomechanical and vibration responses of FGM sandwich plates. Some parametric studies are carried out for the frequency analysis by varying the volume fraction profile and the temperature distribution across the plate thickness

Influence of geometry, elasticity properties and boundary conditions on the Mode I purity in sandwich composites

The present work addresses the problem of skin/core debonding in sandwich materials. The main goal is to carry out parametric analyses for studying the influence of various materials, geometrical parameters and boundary conditions of sandwich fracture specimens such as a Single Cantilever Beam and a Double Cantilever Beam on the skin/core opening (KI ) and shearing (KII ) modes. The analyses have been performed by means of fracture mechanics tools implemented into the commercial finite element code ABAQUS™. A two-dimensional model of the fracture specimens has been developed with plane strain finite elements. The dependence of the stress intensity factors in the sandwich specimens on the skin thickness, ratio between the Young’s moduli of the skin and core materials and boundary conditions imposed on the specimens has been examined under quasi-static loading by using the interaction integral method

On the regularity of Lagrangian trajectories corresponding to suitable weak solutions of the Navier-Stokes equations

The putative singular set S in space-time of a suitable weak solution u of the 3D Navier–Stokes equations has box-counting dimension no greater than 5/3. This allows one to prove that almost all trajectories avoid S. Moreover, for each point x that does not belong to S, one can find a neighbourhood U of x such that the function u is continuous on U and space derivatives of u are bounded on every compact subset of U. It follows that almost all Lagrangian trajectories corresponding to u are C^{1} functions of time (Robinson & Sadowski, Nonlinearity 2009). We recall the main idea of the proof, give examples that clarify in what sense the uniqueness of trajectories is considered, and make some comments on how this result might be improved

Analysis of recreational land using Skylab data

The author has identified the following significant results. S192 data collected on 5 August 1973 were processed by computer to produce a classification map of a part of the Gratiot-Saginaw State Game Area in south central Michigan. A 10-category map was prepared of an area consisting of diverse terrain types, including forests, wetlands, brush, and herbaceous vegetation. An accuracy check indicated that 54% of the pixels were correctly recognized. When these ten scene classes were consolidated to a 5-category map, the accuracy increased to 72%. S190 A, S190 B, and S192 data can be used for regional surveys of existing and potential recreation sites, for delineation of open space, and for preliminary evaluation of geographically extensive sites

Nonlinear fracture dynamics of double cantilever beam sandwich specimens

A virtual testing of double cantilever beam interlaminar fracture toughness sandwich specimens under different types of dynamic loads and loading rates is considered. The nonlinear dynamic response of those sandwich specimens being fractured during the test is numerically examined using the two-dimensional finite element model within the ABAQUSTM code. The interaction integral method is exploited to extract the dynamic stress intensity factor. Cohesive elements allocated along the face/core interface are used to simulate the dynamic fracturing of the specimens

Чисельний аналіз полів в околі вершини тріщини у двоконсольному балочному тришаровому зразку, що навантажений згинальними моментами

The paper presents an interfacial crack problem adopted for studying fracture toughness and debonding tolerance of sandwich composite materials. A specific example of the fracture sandwich specimens such as a double cantilever sandwich beam subjected to uneven bending moments (DCB-UBM) is considered. A finite element modelling of this test method is carried out using the ABAQUS™ code. Atwo-dimensional (2-D) model has been developed to highlight the distribution of stress and displacement fields and to calculate the energy release rate (ERR) and the phase angle at the interface crack between two dissimilar orthotropic materials. The J − integral approach built-in ABAQUS code and the crack surface displacement method programmed as an add-on subroutine within the Matlab® environment are used for computing those fracture parameters. The influence of different moment ratios on the near crack tip stress state, the ERR, and phase angle fracture parameters is estimated.Представлено проблему міжфазної тріщини, за допомогою якої вивчаються в’язкість руйнування та стійкість до відшарування у тришарових композиційних матеріалах. Розглянуто конкретний приклад тришарового зразка на руйнування – двохконсольна тришарова балка, яка навантажена згинальними моментами. Скінчено елементне моделювання цього тесту здійснюється за допомогою програми ABAQUS™. Двовимірна модель була розроблена для виявлення розподілу полів напружень та переміщень, а також для розрахунку швидкості вивільнення енергії руйнування та фазового кута міжфазної тріщини поміж двома різними ортотропними матеріалами. J − інтеграл підхід, який є вбудованою опцією у ABAQUS, та метод відносних зміщень на поверхнях тріщини, який запрограмований у середовищі Matlab® окремою програмою, використовуються для обчислення цих параметрів руйнування. Оцінюється вплив різних співвідношень згинальних моментів на напружений стан в околі вершини тріщини, швидкості вивільнення енергії руйнування і фазовий кут

High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy

We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However, at higher energies (>500 meV) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is 40 meV. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.Comment: 4 pages,3 figure