Geometric nonlinear analyses of functionally graded beams using a tailored Lagrangian formulation

This paper presents a geometric nonlinear analysis formulation for beams of functionally graded cross-sections by means of a Total Lagrangian formulation. The influence of material gradation on the numerical response is investigated in detail. Two examples are given that illustrate the main features of the formulation, in which the behavior of beams of graded cross-sections is compared with homogeneous material beams. A motivation for this work is the potential development of functionally graded risers for the offshore oil exploration industry.     

Large deflection of flexible tapered functionally graded beam

In this paper the semi-analytical analyses of the flexible cantilever tapered functionally graded beam under combined inclined end loading and intermediate loading are studied.In order to derive the fully non-linear equations governing the non-linear deformation,a curvilinear coordinate system is introduced.A general non-linear second order differential equation that governs the shape of a deflected beam is derived based on the geometric nonlinearities,infinitesimal local displacements and local rotation concepts with remarkable physical properties of functionally graded materials.The solutions obtained from semi-analytical methods are numerically compared with the existing elliptic integral solution for the case of a flexible uniform cantilever functionally graded beam.The effects of taper ratio,inclined end load angle and material property gradient on large deflection of the beam are evaluated.The Adomian decomposition method will be useful toward the design of tapered functionally graded compliant mechanisms driven by smart actuators.     

THREE-DIMENSIONAL THERMOELASTIC ANALYSIS OF FUNCTIONALLY GRADED PLATE

Three-dimensional thermoelastic analysis is presented for an orthotropic functionally graded rectangular plate,which is simply supported and isothermal on its four lateral edges.With the assumption that material properties have arbitrary dependence on the thickness-coordinate,a Peano-Baker series solution is obtained for the thermoelastic fields of the functionally graded plate subjected to mechanical and thermal loads on its upper and lower surfaces by means of state space method.The correctness of the obtained series solution is validated through numerical examples.The influence of different material properties distributions on the structural response of the plate is also studied.     

Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects

This paper presents an analytical approach to investigate the non-linear axisymmetric response of functionally graded shallow spherical shells subjected to uniform external pressure incorporating the effects of temperature. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for shallow spherical shells are derived by using the classical shell theory and specialized for axisymmetric deformation with both geometrical non-linearity and initial geometrical imperfection are taken into consideration. One-term deflection mode is assumed and explicit expressions of buckling loads and load-deflection curves are determined due to Galerkin method. Stability analysis for a clamped spherical shell shows the effects of material and geometric parameters, edge restraint and temperature conditions, and imperfection on the behavior of the shells.     

An analytical study of the non-linear vibrations of cylindrical shells

The primary resonance response of simply supported circular cylindrical shells is investigated using the perturbation method. Donnell's non-linear shallow-shell theory is used to derive the governing partial differential equations of motion. The Galerkin technique is then employed to transform the equations of motion into a set of temporal ordinary differential equations. Considering only the primary resonance case, the method of multiple scales is used to study the periodic solutions and their stability. The necessary and sufficient conditions for appearance of the so-called companion mode are also discussed. To this end, a range of the possible multi-mode solution is obtained for response and excitation amplitudes and also excitation frequency as a function of damping, geometry and material properties of the shell. Parametric studies are performed to illustrate the effect of different values of thickness, length and material composition on the possibility of the companion mode participation in primary resonance response.     

Morita contexts and Galois theory for weak Hopf comodulelike algebras

We investigate the Morita context and graded cases for weak group corings and derive some equivalent conditions for μ to be surjective. Furthermore, we develop Galois theory for weak group corings. As an application, we give Galois theory for comodulelike algebras over a weak Hopf group coalgebra.     

A novel simulation method to evaluate the collection performance of a monolithic active pixel sensor

A novel simulation method is presented in this paper to evaluate the collection performance of monolithic active pixel sensor (MAPS) devices for minimum ionizing particle tracking. A simplified 3D matrix pixel structure is built using the computer aided design software Sentaurus. The virtual device is then divided into hundreds of parts and an independent customized X photon model is involved in each part to simulate the conditions under ⁵⁵Fe radiation. After data processing and analysis, charge collection efficiency, collection time and diffusion conditions can be estimated in detail. In order to verify the reliability of the method, comparisons are made between the simulations and experiments. Although there are some defects, it can be concluded that the proposed idea is a feasible method for the evaluation of the MAPS collection performance.     

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为了获取HL-2A等离子体的离子温度、旋转速度及其分布等重要参数,首次在HL-2A装置上开展了CXRS诊断。通过利用能有效探测微弱光的EMCCD和特殊设计的光学采集系统,获得了具有足够信噪比的诊断信号。实验得到的测量信号分析表明,设计是切实可行的。     

Synthesis, spectroscopic characterization, DFT studies and biological assays of a novel gold(I) complex with 2-mercaptothiazoline

A new gold(I) complex with 2-mercaptothiazoline (MTZ) with the coordination formula [AuCN(C₃H₅NS₂)] was synthesized and characterized by chemical and spectroscopic measurements, DFT studies and biological assays. Infrared (IR) and ¹H, ¹³C and ¹⁵N nuclear magnetic resonance (NMR) spectroscopic measurements indicate coordination of the ligand to gold(I) through the nitrogen atom. Studies based on DFT confirmed nitrogen coordination to gold(I) as a minimum of the potential energy surface with calculations of the hessians showing no imaginary frequencies. Thermal decomposition starts at temperatures near 160 °C, leading to the formation of Au⁰ as the final residue at 1000 °C. The gold(I) complex with 2-mercaptothiazoline (Au-MTZ) is soluble in dimethyl sulfoxide (DMSO), and is insoluble in water, methanol, ethanol, acetonitrile and hexane. The antibacterial activities of the Au-MTZ complex were evaluated by an antibiogram assay using the disc diffusion method. The compound showed an effective antibacterial activity against Staphylococcus aureus (Gram-positive) and Escherichia coli and Pseudomonas aeruginosa (Gram-negative) bacterial cells. Biological analysis for evaluation of the cytotoxic effect of the Au-MTZ complex was performed using HeLa cells derived from human cervical adenocarcinoma. The complex presented a potent cytotoxic activity, inducing 85% of cell death at a concentration of 2.0 μmol L⁻¹.     

The superhydrophobicity of polymer surfaces: Recent developments

Superhydrophobicity is the extreme water repellence of highly textured surfaces. The field of superhydrophobicity research has reached a stage where huge numbers of candidate treatments have been proposed and jumps have been made in theoretically describing them. There now seems to be a move to more practical concerns and to considering the demands of individual applications instead of more general cases. With these developments, polymeric surfaces with their huge variety of properties have come to the fore and are fast becoming the material of choice for designing, developing, and producing superhydrophobic surfaces. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1203–1217, 2011