Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman＇s plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material （FGM） circular plates with in- plane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.

Thermal buckling analysis of functionally graded cylindrical shells

Thermal buckling behavior of cylindrical shell made of functionally graded material（FGM） is studied. The material constituents are composed of ceramic and metal.The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations（ODEs）. A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail.

Free vibration analysis of functionally graded material beams based on Levinson beam theory

Free vibration response of functionally graded material （FGM） beams is studied based on the Levinson beam theory （LBT）. Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.

Homogenized and classical expressions for static bending solutions for functionally graded material Levinson beams

The exact relationship between the bending solutions of functionally graded material （FGM） beams based on the Levinson beam theory and those of the correspond- ing homogenous beams based on the classical beam theory is presented for the material properties of the FGM beams changing continuously in the thickness direction. The de- flection, the rotational angle, the bending moment, and the shear force of FGM Levinson beams （FGMLBs） are given analytically in terms of the deflection of the reference ho- mogenous Euler-Bernoulli beams （HEBBs） with the same loading, geometry, and end supports. Consequently, the solution of the bending of non-homogenous Levinson beams can be simplified to the calculation of transition coefficients, which can be easily deter- mined by variation of the gradient of material properties and the geometry of beams. This is because the classical beam theory solutions of homogenous beams can be eas- ily determined or are available in the textbook of material strength under a variety of boundary conditions. As examples, for different end constraints, particular solutions are given for the FGMLBs under specified loadings to illustrate validity of this approach. These analytical solutions can be used as benchmarks to check numerical results in the investigation of static bending of FGM beams based on higher-order shear deformation theories.

Clinical validation of serum immunosignatures in early diagnosis of Crohn's disease

Background:The search for biomarkers suitable for early diagnosis of Crohn's disease(CD)is challenging.This study investigated the efficacy of serological markers for the early diagnosis of CD.Methods:This was a retrospective nested cohort study.Indirect immuno-fluorescence and enzyme‐linked immunosorbent assay were used to detect ASCA IgG,ASCA IgA,AYMA IgG,AYCA IgG,FI2Y IgG,p‐ANCA IgG,GAB IgG and PAB IgG in patient serum samples.Results:The positive rates of ASCA IgG,ASCA IgA,AYMA IgG,AYCA IgG,FI2Y IgG,p‐ANCA IgG,GAB IgG and PAB IgG in patients with early CD,advanced CD and other intestinal diseases were 37.0%versus 56.8%versus 27.8%;3.7%versus 20.5%versus 19.4%;14.8%versus 2.3%versus 2.8%;25.9%versus 9.1%versus 8.3%;18.5%versus 15.9%versus 8.3%;0.0%versus 2.8%,18.5%;13.6%versus 18.2%versus 16.7%;and 7.4%versus 20.5%versus 0.0%,respectively.The positive rates of ASCA IgG,AYCA IgG and PAB IgG were significantly different among the three groups(p<0.05).In 85.2%of early CD patients,at least one antibody was detected 1 year before diagnosis.The sensitivity of the ASCA/AYMA/AYCA/FI2Y/GAB combination for early diagnosis was 85.2%.The sensitivity of the ASCA/AYMA/AYCA/FI2Y/GAB/PAB/PANCA combination for differentiating CD from other diseases was 87.3%.Conclusions:ASCA IgG and AYCA IgG have potential value in identifying the course of CD.AYCA IgG may be a potential marker for the early diagnosis of CD,and ASCA IgG indicates an advanced stage.The combination of ASCA,AYMA,AYCA,FI2Y,and GAB improves early diagnostic accuracy of CD.

CLASSICAL AND HOMOGENIZED EXPRESSIONS FOR BUCKLING SOLUTIONS OF FUNCTIONALLY GRADED MATERIAL LEVINSON BEAMS

The relationship between the critical buckling loads of functionally graded material （FGM） Levinson beams （LBs） and those of the corresponding homogeneous Euler-Bernoulli beams （HEBBs） is investigated. Properties of the beam are assumed to vary continuously in the depth direction. The governing equations of the FGM beam are derived based on the Levinson beam theory, in which a quadratic variation of the transverse shear strain through the depth is included. By eliminating the axial displacement as well as the rotational angle in the governing equations, an ordinary differential equation in terms of the deflection of the FGM LBs is derived, the form of which is the same as that of HEBBs except for the definition of the load parameter. By solving the eigenvalue problem of ordinary differential equations under different boundary conditions clamped （C）, simply-supported （S）, roller （R） and free （F） edges combined, a uniform analytical formulation of buckling loads of FGM LBs with S-S, C-C, C-F, C-R and S-R edges is presented for those of HEBBs with the same boundary conditions. For the C-S beam the above-mentioned equation does not hold. Instead, a transcendental equation is derived to find the critical buckling load for the FGM LB which is similar to that for HEBB with the same ends. The significance of this work lies in that the solution of the critical buckling load of a FGM LB can be reduced to that of the HEBB and calculation of three constants whose values only depend upon the through- the-depth gradient of the material properties and the geometry of the beam. So, a homogeneous and classical expression for the buckling solution of FGM LBs is accomplished.

Derived norms of finite groups

The intersection of particular subgroups is a kind of interesting substructure in group theory. Let G be a finite group and D(G) be the intersection of the normalizers of the derived subgroups of all the subgroups of G. A group G is called a D-group if G = D(G). In this paper, we determine the nilpotency class of the nilpotent residual G^(N) and investigate the structure of D(G) by a new concept called the IO-D-group. A non-D-group G is called an IO-D-group(inner-outer-D-group) if all of its proper subgroups and proper quotient groups are D-groups. The structure of IO-D-groups are described in detail in this paper. As an application of the classification of IO-D-groups, we prove that G is a D-group if and only if any subgroup of G generated by3 elements is a D-group.