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.     

Design of novel bis-benzimidazole derivatives as DNA minor groove binding agents

A new series of bis-benzimidazole derivatives were designed and synthesized.In vitro cytotoxicity evaluation showed that these compounds exhibited high activity against the selected tumor cells.Among them,compound 9 owned the best potential,its IC_(50) values being 5.95 μmol/L(mononuclear tumor cell line(U937)) and 5.58 μmol/L(cervical cancer cell(HeLa)).Fluorescence and UV-vis studies showed that compound 9 could bind into the minor groove of DNA.     

Strain energy density of a circular cavity buried in semi-infinite functionally graded materials subjected to shear waves

In this paper, based on the theory of multiple scattering of elastic waves, employing wave functions expansion method, multiple scattering and strain energy density in semi-infinite functional graded materials with a circular cavity are investigated, the analytical solution of the problem is derived, and the numerical solution of the strain energy density factors around the cavity is also presented. The effects of the distance between the cavity and the edge of the materials, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. From analysis, it can be seen that when the non-homogeneous parameter of materials is less than zero, it has less influence on the maximum strain energy density factor around the cavity; however, it has greater influence on the distribution of strain energy density factors around the cavity. When the non-homogeneous parameter of materials is greater than zero, it has greater influence on both the maximum strain energy density factor and the distribution of strain energy density factor around the cavity, especially in the case that the distance between the cavity and the edge is comparatively little.     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论，考虑材料物性参数随坐标和温度变化的特性，研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题，基于一维DQ法和Galerkin技术，给出了一对边固支，另对边任意约束时板弯曲问题的半解析解，以Si3N4/SUS304板为例考察了材料组份，温度场，面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响。     

A novel class of graded cylinders neutral to host shafts of arbitrary cross-sections under torsion

A novel class of graded cylinders is proposed as neutral inclusions inside host shafts of arbitrary cross-section under Saint-Venant's torsion. The graded cylinder is made of cylindrically orthotropic materials with position varying quantities. The profiles of the two distinct shear moduli in the radial and tangential directions follow specific forms based on an arbitrarily selected function along the radial distance. We show that this type of graded cylinders can serve as universal neutral inclusions within host shafts of arbitrary cross-sections. In addition, we find that the associated warping fields can be exactly determined in terms of simple exponents of the selected function. This suggests that, by tuning the gradation parameter, one can manipulate the warping field of the inserted cylinder without disturbing the fields inside the host shaft. This finding is an original contribution to the existing solvable configurations of composite shafts under torsion.     

Free vibration of functionally graded sandwich plates using four-variable refined plate theory

This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates.Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-ordex theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.     

Exact solutions of functionally graded piezoelectric material sandwich cylinders by a modified Pagano method

The three-dimensional (3D) coupled analysis of simply-supported, functionally graded piezoelectric material (FGPM) circular hollow sandwich cylinders under electro-mechanical loads is presented. The material properties of each FGPM layer are regarded as heterogeneous through the thickness coordinate, and obey an exponent-law dependent on this. The Pagano method is modified to be feasible for the study of FGPM sandwich cylinders. The modifications are as follows: a displacement-based formulation is replaced by a mixed formulation; a set of the complex-valued solutions of the system equations is transferred to the corresponding set of real-valued solutions; a successive approximation method is adopted to approximately transform each FGPM layer into a multilayered piezoelectric one with an equal and small thickness for each layer in comparison with the mid-surface radius, and with the homogeneous material properties determined in an average thickness sense; and a transfer matrix method is developed, so that the general solutions of the system equations can be obtained layer-by-layer, which is significantly less time-consuming than the usual approach. A parametric study is undertaken of the influence of the aspect ratio, open- and closed-circuit surface conditions, and material-property gradient index on the assorted field variables induced in the FGPM sandwich cylinders.