Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics - Mechanical models of residually stressed fibre-reinforced solids, which do not resist bending, have been developed in the literature. However, in some residually...     

Hilbert’s Nullstellensatz for analytic trigonometric polynomials

This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if ${\left\{f_j\right\}}_{j=1}^{n\ge 2}$ are analytic trigonometric polynomials without common zero in the finite complex plane $?$ then there are analytic trigonometric polynomials ${\left\{g_j\right\}}_{j=1}^{n\ge 2}$ obeying ${\sum }_{j=1}^{n\ge 2}{f}_j{g}_j=1$ in $?$, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on $?$.     

碳纳米管增强型复合材料功能梯度板的自由振动模型与尺度效应

基于一种新的各向异性修正偶应力理论，建立了碳纳米管增强复合材料功能梯度板的自由振动模型。该模型能够描述尺度效应，且仅包含一个尺度参数。基于一阶剪切变形理论和哈密顿原理推演了板的运动微分方程，并以四边简支板为例给出了自振频率的解析解。讨论了板的几何尺寸、碳纳米管体分比含量和分布方式等因素对板的自振频率的影响。结果表明，本文模型所预测的板的自振基频总是高于经典弹性理论的Mindlin板模型的预测结果，两者间的差异在板的几何尺寸接近尺度参数的值时非常明显，且会随着板的几何尺寸的增大而逐渐消失。     

REBOUNDING OF GALILEAN CANNON FROM A RIGID WALL1)

研究了Galilean炮——即若干个直径递增的弹性球组成的球链---撞击刚性壁回弹的问题。采用三种力学模型：分离刚体的多次"弹性"碰撞、多刚体的接触碰撞、以及有限元模拟，对球链撞击问题进行了分析，旨在给出碰撞结束后末端小球的飞离速度与入射速度的比值。研究表明：球链碰撞反弹后将会散开，末端小球的飞离速度明显大于球链入射速度；当入射球链间存在间隙时，末端小球的速度增幅更加明显。通过实验展现了这种末端小球回弹速度增加的现象。     

围压与径向荷载共同作用下巴西盘裂纹应力强度因子的解析解

利用权函数法推导了围压和径向荷载共同作用下，考虑裂纹面摩擦的预制裂纹巴西盘应力强度因子计算公式，从理论上分析了围压、径向荷载和裂纹面摩擦对巴西盘应力强度因子的影响。结果表明，围压对I型应力强度因子有很大影响，I型应力强度因子随围压的增大而减小。当裂纹面闭合后围压和摩擦系数对II型应力强度因子同样具有显著影响，考虑裂纹面有效剪应力的权函数法理论解与有限元数值解相吻合，表明理论分析的正确性。     

双侧下颌支矢状劈开截骨术后患者可施加合适咬合力的数值研究

双侧下颌支矢状劈开截骨术在临床手术中广泛用于治疗缩颌、凸颌和颌面不对称患者的颌面畸形症状。本文用数值方法研究双侧下颌支矢状劈开截骨术并前移下颌骨后患者可施加的合适咬合力。首先，用缩颌患者的CT断层扫面数据建立下颌骨、关节盘、关节窝和相关软组织的高度几何相似性的几何模型；然后，用有限元模型模拟双侧下颌支矢状劈开截骨术后患者的咬合过程。通过分析发现，术后关节盘上的位移处于正常的范围，而应力却远远超过正常范围，因此，将应力因素作为确定术后患者可施加的合适咬合力的标准。当施加正常咬合力的25%时，关节盘上的应力分布和术前没有显著性差异，同时下颌骨上的应力水平也处于正常范围。     

Agave fructans and oligofructose decrease oxidative stress in brain regions involved in learning and memory of overweight mice

Obesity is currently a public health problem worldwide. Recently, non-reducing carbohydrates, that include β(2→1) and β(2→6) linkages in their structure, have been of particular interest in the field of obesity because they are involved in lipid metabolism. Some of these are agave fructans (AF) and oligofructose (OF). In this study, we evaluated both AF and OF on oxidative stress (OS) markers in the brain of overweight mice (OM). AF and OF decreased TBARS levels and carbonyls at different levels in hippocampus (HP), frontal cortex (FC) and cerebellum (CB) of OM. The results indicated that fructans may have anti-oxidative potential and can be used as an alternative treatment for the prevention of the consequences of this pathology.