“A new approach to formulate the general strength theories for anisotropic discontinuous materials” Part B General form of polynomial to describe the strength of anisotropic discontinuous materials

A new approach to describe the failure hypersurface on the basis of assumptions presented in Part A reveals the new form of failure stress polynomial. In the presented theory new terms such as: unit tensor object, object formed on the basis of unit tensor object, the first, second and third form of the anisotropy failure function, and the first and the second type of object axis, were defined. On the basis of these terms the coefficients of their polynomials were formulated as values of the appropriate objects. The presented theory divides the six dimensional hyperspace of stresses into eight parts in which eight intersected hypersurfaces constitute the failure hypersurface. Six hypersurfaces may be assigned to two of three mutually coupled sets of elements. In general cases the theory may be used to describe the failure hypersurface for anisotropic structures where tensorial relationships do not occur. The obtained polynomial is transformed to tensor polynomial on the assumption that the failure stress tensorial relationships describe the failure hypersurface of anisotropic materials.     

Post buckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties

In this paper, the second order statistics of post buckling response of functionally graded materials plate (FGM) subjected to mechanical and thermal loading with nonuniform temperature changes subjected to temperature independent (TID) and dependent (TD) material properties is examined. Material properties such as material properties of each constituent’s materials, volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear kinematic using modified C⁰ continuity. A direct iterative based C⁰ nonlinear finite element method (FEM) combined with mean centered first order perturbation technique (FOPT) proposed by last two authors for the composite plate is extended for Functionally Graded Materials (FGMs) plate with reasonable accuracy to compute the second order statistics (mean and coefficient of variation) of the post buckling load response of the FGM plates. The effect of random material properties with amplitude ratios, volume fraction index, plate thickness ratios, aspect ratios, boundary conditions and types of loadings subjected to TID and TD material properties are presented through numerical examples. The performance of outlined present approach is validated with the results available in literatures and independent Monte Carlo simulation (MCS).     

An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates

An analytical solution based on a new exact closed form procedure is presented for free vibration analysis of stepped circular and annular FG plates via first order shear deformation plate theory of Mindlin. The material properties change continuously through the thickness of the plate, which can vary according to a power-law distribution of the volume fraction of the constituents, whereas Poisson’s ratio is set to be constant. Based on the domain decomposition technique, five highly coupled governing partial differential equations of motion for freely vibrating FG plates were exactly solved by introducing the new potential functions as well as using the method of separation of variables. Several comparison studies were presented by those reported in the literature and the FEM analysis, for various thickness values and combinations of stepped thickness variations of circular/annular FG plates to demonstrate highly stability and accuracy of present exact procedure. The effect of the geometrical and material plate parameters such as step thickness ratios, step locations and the power law index on the natural frequencies of FG plates is investigated.     

Buckling delamination of a sandwich plate-strip with piezoelectric face and elastic core layers

In this study, the buckling delamination problem of a sandwich plate-strip with a piezoelectric face and elastic core layers is studied. It is assumed that the plate-strip is simply supported and grounded along its two parallel ends and is subjected to uniformly-distributed compressive forces on these ends. Moreover, we suppose that the plate-strip has two interface inner cracks between the face and the core layers and it is also supposed that before the plate-strip is loaded (i.e. in the natural state), the surfaces of these cracks have insignificant initial imperfections. Due to compressive forces acting along the cracks we investigate the evolution of the initial imperfections of the cracks’ surfaces. Hence, the values of the critical buckling delamination force of the considered plate-strip are determined from the criteria, according to which, the considered initial imperfections of the cracks’ surfaces grow indefinitely by the compressive forces. Mathematical modeling of the considered problem is formulated within the scope of the exact nonlinear equations of electro-elasticity in the framework of the piecewise homogeneous body model, the solution of which is found numerically by employing the finite elements method. Numerical results showing the influences of the geometrical and material parameters as well as the coupling of the electrical and mechanical fields on the values of the critical force are presented and analyzed.     

Study of the Cost Functional for Free Material Design Problems

We study properties of the cost functional arising in free material optimization problems, with special emphasis on semicontinuity and its relation to convexity.     

Optoelectronic properties of benzotrithiophene isomers: A density functional theory study

Benzotrithiophene (BTT) isomers were investigated using density functional theory (DFT) and time‐dependent DFT (TD‐DFT) with the aim to explore their structures, linear optical properties, vertical and adiabatic ionization potentials (IP_v and IP_a), electron affinities (EA_v and EA_a), and reorganization energies (λ). The computed bond lengths and bond angles at the B3LYP/6–311+G (d, p) level of theory are in good agreement with experimental crystal structures of the known BTTs. These molecules are planar with zero dihedral angle, making them an ideal backbone for high charge mobility. The UV–visible spectra of BTT isomers are in the range 280–360 nm. All BTT isomers have low hole/electron reorganization energies, which is the main characteristic of good hole/electron transporting materials, and these isomers in turn have potential applications in the field of organic materials.     

Thermochemical investigation of Zr doping in LiNi8/12Co2/12Mn2/12O2 based on phase equilibria simulation

The doping behavior of Zr in LiNi_8/12Co_2/12Mn_2/12O₂ (LNCM) is investigated by a simulation of the phase equilibria for the Li-(M^*,Zr)-O system (M^* = Ni, Co, Mn) based on first-principles calculations followed by a thermochemical post-analysis of the resultant phase diagrams. The results indicate that the stable state at the synthetically stoichiometric composition of LNCM with Zr is a mixture of undoped LNCM with a Li₂ZrO₃ secondary phase; doping of Zr in the LNCM crystal is not thermodynamically favored. The energies of various states comprising LNCM supercells with defects, secondary phases, and Zr doping are examined, and the equilibrium doping concentration of Zr is calculated by considering the entire LNCM:Zr crystal as a statistical combination of these states. The doping concentration of Zr in the LNCM crystal is calculated to be very low, which enables balanced control between doping and coating, as recently reported through experimentation. The dopability of Zr is expected to increase with the depletion of O₂ supply during the heating of a system with a precisely controlled Li to M^* ratio, but this behavior is affected by the formation of defects, especially by M^* substitution for Li.     

Atomistic study of GaSe/Ge(111) interface formed through van der Waals epitaxy

Layered materials can be grown on various substrates through van der Waals epitaxy (vdWE) regardless of lattice mismatch. The atomistic study of the film-substrate interface in vdWE is becoming increasingly important due to their expected applications as two-dimensional (2D) materials. In this contribution, we have grown GaSe thin films on Ge(111) substrates by molecular beam epitaxy and studied the GaSe/Ge(111) interface using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM). Cross-sectional HAADF-STEM observations revealed that the grown layers adopt predominantly the expected wurtzite-like structure and stacking, but layers with zinc-blende-like structure, similar to Ga₂Se₃ but apparently different, and other layer stacking sequences, exist locally near the film-substrate interface. These results demonstrate that even in vdWE, structural changes can occur in the grown layers adjacent to the substrate, highlighting the importance of such interface for synthesizing and applying ultimately thin 2D materials.     

MIL-101(Fe)高效催化 β-蒎烯与甲醛的Prins缩合制备诺卜醇

通过水热晶化法制备了MIL-101(Fe)金属有机骨架材料, 利用X射线衍射(XRD)、 傅里叶变换红外光谱(FTIR)、 热重分析(TG)、 扫描电子显微镜(SEM)、 透射电子显微镜(TEM)和X射线光电子能谱(XPS)对催化剂的结构和形貌进行了表征. 结果表明, 该材料用于催化β-蒎烯与甲醛的Prins缩合制备诺卜醇反应的效果优异; 催化剂合成温度、 合成时间、 催化剂用量、 反应溶剂、 反应温度和反应时间对β-蒎烯的反应结果均有一定影响. 在相似的反应条件下, 合成的MIL-101(Fe)催化β-蒎烯制备诺卜醇反应的最佳条件为使用150 ℃下反应15 h合成的催化剂MIL-101(Fe), 在90 ℃下反应8 h得到的β-蒎烯转化率高达97.3%, 诺卜醇选择性达到96.7%.