Generalized P(N)-graded Lie superalgebras

We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but suffcient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras. Our result is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov's theorem for type P(N). We also obtain a generalization of Kac's coordinatization via Tits-Kantor-Koecher construction. Actually, the motivation of this generalization comes from the Fermionic-Bosonic module construction.     

The recent progress of functionally graded CNT reinforced composites and structures

In the last decade,the functionally graded carbon nanotube reinforced composites(FG-CNTRCs)have attracted considerable interest due to their excellent mechanical properties,and the structures made of FG-CNTRCs have found broad potential applications in aerospace,civil and ocean engineering,automotive industry,and smart structures.Here we review the literature regarding the mechanical analysis of bulk CNTR nanocomposites and FG-CNTRC structures,aiming to provide a clear picture of the mechanical modeling and properties of FG-CNTRCs as well as their composite structures.The review is organized as follows:(1)a brief introduction to the functionally graded materials(FGM),CNTRCs and FG-CNTRCs;(2)a literature review of the mechanical modeling methodologies and properties of bulk CNTRCs;(3)a detailed discussion on the mechanical behaviors of FG-CNTRCs;and(4)conclusions together with a suggestion of future research trends.     

Effects of graded porous structure on local strain distribution under compression in silicone rubber

Silicone rubber samples with gradually changing pore sizes within the range of 70–610 μm are produced using an improved spacer method. The samples are scanned using an X‐ray computed tomography to evaluate their graded structure as compared to uniform rubber. A compressive test reveals that graded porous silicone rubber has characteristic stress–strain curves whose slope changes within a specific strain range depending on the porous structure. Analysis results of local strain based on a digital image correlation of the graded porous silicone rubber under compression demonstrate that the characteristic stress–strain properties are caused by shifts in the main deformation region in the graded structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1033–1042     

Torsion simple modules over the quantum spatial ageing algebra

Various classes of simple torsion modules are classified over the quantum spatial ageing algebra (this is a Noetherian algebra of Gelfand-Kirillov dimension 4). Explicit constructions of these modules are given and for each module its annihilator is found.     

Effect of material nonhomogeneities on the HRR dominance

This work studies the asymptotic stress and displacement fields near the tip of a stationary crack in an elastic–plastic nonhomogeneous material with the emphasis on the effect of material nonhomogeneities on the dominance of the crack tip field. While the HRR singular field still prevails near the crack tip if the material properties are continuous and piecewise continuously differentiable, a simple asymptotic analysis shows that the size of the HRR dominance zone decreases with increasing magnitude of material property gradients. The HRR field dominates at points that satisfy |α⁻¹ ∂α/∂x_δ|1/r, |α⁻¹ ∂²α/(∂x_δ ∂x_γ)|1/r², |n⁻¹ ∂n/∂x_δ|1/[r|ln(r/A)|] and |n⁻¹ ∂²n/(∂x_δ ∂x_γ)|1/[r²|ln(r/A)|], in addition to other general requirements for asymptotic solutions, where α is a material property in the Ramberg–Osgood model, n is the strain hardening exponent, r is the distance from the crack tip, x_δ are Cartesian coordinates, and A is a length parameter. For linear hardening materials, the crack tip field dominates at points that satisfy |E_tan⁻¹ ∂E_tan/∂x_δ|1/r, |E_tan⁻¹ ∂²E_tan/(∂x_δ ∂x_γ)|1/r², |E⁻¹ ∂E/∂x_δ|1/r, and |E⁻¹ ∂²E/(∂x_δ ∂x_γ)|1/r², where E_tan is the tangent modulus and E is Young’s modulus.     

End Effects in Anti-plane Shear for an Inhomogeneous Isotropic Linearly Elastic Semi-infinite Strip

The purpose of this research is to further investigate the effects of material inhomogeneity on the decay of Saint-Venant end effects in linear isotropic elasticity. This is carried out within the context of anti-plane shear deformations of an inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation with variable coefficients on a semi-infinite strip. In previous work [1], the elastic coefficients were assumed to be smooth functions of the transverse coordinate so that the material was inhomogeneous in the lateral direction only. Here we develop a new technique, based on a change of variable, to study generally inhomogeneous isotropic materials. The governing partial differential equation is transformed to a Helmholtz equation with a variable coefficient, which facilitates analysis of the influence of material inhomogeneity on the diffusion of end effects. For certain classes of inhomogeneous materials, an explicit optimal decay estimate is established. The results of this paper are applicable to continuously inhomogeneous materials and, in particular, to functionally graded materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

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。     

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.     

功能梯度材料板件三维分析的半解析梯度有限元法

将半解析有限元与梯度有限元相结合,形成一种半解析梯度有限元来求解功能梯度材料板件问题。该方法兼有有限元法的适应性强、程序统一,半解析有限元法的节省单元与计算工作量,梯度有限元法的适应构件内部材料性能任意梯度分布等特点,并实现用一维数值计算给出构件三维分析结果。算例分析表明了方法的精度、功能与上述特点,充分揭示了功能梯度材料板件力学响应的三维形态。半解析梯度有限元法可推广应用到其他功能梯度材料面结构的各类分析中。