半平面正交各向异性弹性层矩阵回代法

本文对半平面正交各向异性弹性层问题通过富里叶变换,并利用层间的应力位移协调条件,采用矩阵回代方法确定各层待定系数,计算了三层介质和刚性地基问题的数值结果。这种方法具有计算机时少、收敛性好等优点。     

水位变化对于移动荷载作用下土体动力响应的影响研究

采用上覆弹性层饱和地基土模型描述水位于地表以下的地基动力响应问题,利用改变弹性层厚度模拟土体中水位的变化。基于Biot饱和多孔介质动力方程和层间连续性条件,求解出上覆弹性层饱和半空间频域波数内位移场表达式,通过Fourier逆变换得到3维空间域的结果,研究了水位变化对于土体动力响应的影响。数值计算结果表明,水位的变化会对地基中波的传播产生一定影响。当水位离地面较深时,地面竖向位移值与弹性半空间情况类似;随着水位上升,弹性层和饱和半空间界面上的反射波会对地面竖向位移产生影响,导致地表位移值较弹性半空间下的结果有所增大,当水位接近地表时,位移值变化类似于饱和地基土。     

分数阶微分双参数黏弹性地基矩形板动力响应

基于弹性地基Pasternak双参数模型,利用分数阶微分得到黏弹性地基双参数模型,并在此基础上建立采用分数阶微分Kelvin模型的双参数黏弹性地基上弹性和黏弹性矩形板在动荷载作用下的动力方程;利用Galerkin方法和分段处理的数值计算方法求解四边简支的弹性和黏弹性地基板的动力方程,通过自由振动算例验证该求解方法的正确性;并分析冲击动荷载作用下分数阶微分Kelvin模型的分数阶、粘滞系数、水平剪切系数和模量参数对位移响应的影响。结果表明：分数阶微分黏弹性模型可以描述不同黏弹性材料的力学行为;分数阶取值0.5前后,矩形板位移响应值出现了不同的衰减发展形态;粘滞系数、水平剪切系数和模量系数取值越大,位移响应衰减速度越快。     

粘弹性层状地基轴对称问题的求解

由粘弹性体经Laplace和Hankel变换的基本方程式,得到了轴对称问题情形下无限粘弹性层不同深度应力位移向量间的传递矩阵,利用传递矩阵以及边界、层间完全接触条件求解了多种粘弹性模型的成层地基空间轴对称问题。     

考虑水平摩阻力的弹性地基梁大变形弯曲分析

设水平摩阻力与垂直支承反力成正比,建立了任意对称荷载作用下有限长弹性地基梁大变形的平衡微分方程式.进行了合理的位移形函数假设,利用Galerkin方法建立非线性代数方程组,采用迭代法进行求解,得到了弹性地基梁的位移和内力解.通过实例计算可知,水平摩阻力对弹性地基梁的挠度和剪力影响很小,而对弯矩和轴力影响很大.当要考虑弹...     

正交异性层合厚板的混合状态Hamiltonian元

本文给出一种求解正交异性层合厚板混合状态Hamilton正则方程的半离散半解析方法。该方法沿板厚方向未作任何有关位移和应力的人为假设,采用状态控制方程给出解析解答,并采用分层迁移法进行计算,保持了层与层之间位移和应力的连续,大大地减少了未知量数目。      

含弹性介质的结合面接触问题数值分析

提出了中间含有弹性接触层的粗糙结合面的力学模型,并运用层状弹性体系力学中的洛普位移函数法,得出了含有弹性层的粗糙结合面接触问题的应力、位移公式。最后分析了当弹性层厚度、弹性模量及泊松比变化时,弹性层中应力、变形的变化规律。     

非均质混杂叠层梁的分层剪切理论

本文研究了正交各向异性混杂叠层梁的应力与变形计算.叠层梁是由几层弹性性质明显不同的非均质子层梁组成.对每一子层梁应用剪切理论,并假设相邻子层梁的交界面是理想连接.文中导出了关于子层梁剪切转角ψ_i的二阶常微分方程组.求解微分方程组可得到叠层梁应力与位移关于剪切转角的ψ_i解析表达式.叠层梁组分材料中任一点应力可按有效模量理论和整体——局部方法[3]求得.     

应力边界元法解平面热弹性问题

本文提出了求解平面热弹性问题的应力边界元法。利用应力法由平面热弹性问题的基本方程出发,简要地叙述了边界积分方程的建立,给出了位移单值条件。这种方法适用于应力边界值问题。作为数值计算例,计算了圆形区域和具有偏心圆孔的圆形区域的热应力,得到了满意的结果。应力边界元法也可应用于平板弯曲问题。     

任意荷载作用下层状横观各向同性弹性地基的直角坐标解

首次建立了在直角坐标系下层状地基力学问题的通用解法,改变了过去仅能在柱坐标系下进行求解此类的状况。首先将坐标系的原点选在荷载影响范围以外足够远处,从直角坐标系下的横观各向同性弹性问题的基本方程出发,利用Laplace变换及其微分性质,建立了单层横观各向同性弹性地基的状态控制方程,并利用状态空间理论给出了单层地基的解答。然后再利用传递矩阵技术,给出了任意荷载作用下的层状横观各向同性弹性地基的解析解。用提供的方法求解层状横观各向同性地基的非轴对称问题比在极坐标下求解简单、快捷。     

IR spectroscopic determination of the refractive index and thickness of hydrogenated silicon layers

IR spectroscopic techniques widely used to determine the thickness and refractive index of layers and thin films of various materials are adapted for determining those of hydrogenated silicon layers. Based on a literature analysis, three formulas are chosen which enable the refractive index and thickness of such layers to be determined from reflection and transmission spectra. The formulas are applicable, with some restrictions, to other samples in the form of relatively transparent layers (films) on transparent substrates. Experimental data are presented that illustrate the use of the formulas.     

Approximate Torsional Analysis of Multi-layered Tubes with Non-circular Cross-Sections

In this paper an approximate formulation for torsional analysis of tubes with multi-layered non-circular cross-sections is presented. A previously presented method based on Bredt’s theory is extended to achieve these formulas. Layers are assumed to be isotropic and may possess different thicknesses and material properties. The obtained formulas for shear stress and angle of twist are applicable to thin to moderately thick closed cross-sections. It is shown that depending on the properties of the layers, maximum shear stress does not necessarily happen on the outer boundary. Furthermore, the effect of different cross-sectional shapes on torsional response is studied. Using the presented method, one can achieve desirable shear stresses and angles of twist for a polygonal multi-layered tube with a proper choice of bluntness. The method can be extended for torsion problem of FGM tubes as well. The presented formulas for torsion problem are relatively accurate and suitable to be implemented in optimization programs.     

用初参数法解多层地基的动力问题

本文应用Ｆｏｕｒｉｅｒ积分变换，求出平面多层地基动力问题的初参数解，这些公式简单明了，便于数值计算，不论弹性层数目多少，都不必求解联立方程。     

圆弧形单向纤维增强树脂复合材料的I型层间断裂韧性测试及分析

层合板的I型层间断裂韧性的测量方法通常为单向纤维增强树脂复合材料的末端切口(End notched flexure, ENF)试样的双悬臂梁(Double cantilever beam, DCB)试验。为了得到带有弧度的层合复合材料结构的I型层间断裂韧性,对圆弧形末端切口(Arc-ENF)试样进行DCB试验。基于梁的弯曲理论和Irwin-Kies公式得到Arc-ENF试样的柔度公式与I型临界能量释放率G_IC公式,并且利用ABAQUS软件对DCB试验进行数值模拟。最终,通过对比分析理论公式计算结果、数值模拟结果和DCB试验结果来验证柔度公式和G_IC公式的合理性和有效性,对带有任意弧度的DCB试样的I型层间断裂韧性的测试与分析具有参考价值。      

基于能量原理的隔震结构地震响应预测法研究

建立地震作用下隔震结构在最大地震响应时刻的能量平衡方程,给出隔震结构隔震层和非隔震层的弹性振动能、塑性能的表达式,推导出基于能量平衡的隔震结构地震响应预测式。以顶部隔震、层间隔震、基础隔震结构为仿真对象,利用时程分析法的数值解验证了地震响应预测式的准确性,比较研究了三种隔震结构的抗震性能。结果表明：对于不同的输入地震波...     

Reflection of light in the vicinity of the Brewster angle from a multilayer system of ultrathin inhomogeneous dielectric films

An analysis of the influence of nanoscopically stratified dielectric overlayer on the reflection parameters of linearly polarized light from transparent substrates is carried out. The second-order formulas for characteristic Brewster angles are derived and their accuracy is estimated by using exact numerical methods for the solution of the inhomogeneous reflection problem. The possibilities are discussed for determining the parameters of nanometre-scale dielectric layers by means of characteristic reflection angles. A novel scanning angle differential reflectance method in the vicinity of the classical Brewster angle, whose sensitivity is in principle the same as that of ellipsometry, is developed.     

具有厚壁内衬圆筒的缠绕张力算法

缠绕张力作为缠绕工艺中的关键因素,其合理设计直接影响制品性能。针对缠绕张力的设计,提出缠绕张力算法。基于各向异性缠绕层弹性变形及各向同性内衬厚壁筒理论,给出外压作用下缠绕层的径向应力及环向应力;在弹性范围内采用应力叠加原理建立剩余张力与缠绕张力之间的解析算法。结合三种典型的张力缠绕模型,给出剩余张力具体关系式;分析等剩余张力,得到不同特例下的剩余张力解析公式。依据该解析算法研究芯模内、外径比及张力锥度系数对各向同性材料缠绕层剩余张力分布的影响,表明芯模内、外径比与锥度系数变化对缠绕层剩余张力分布有显著影响,且该文算法简单、合理、可靠;对各向异性复合材料缠绕层等剩余张力分析,其结果与现有网格理论结果一致,且该文缠绕张力上下层变化平缓,易于张力控制的实现。     

成层地基与浅埋结构物动力相互作用的简化分析

基于任意侧向位移下挡土墙地震土压力理论,建立了新的地基-浅埋式结构物相互作用力与其相对位移之间的关系,并对该关系加以推广,应用到成层地基及深基础情形。提出了一种实用的求解成层地基-浅埋式结构物动力相互作用的简化质-阻-弹模型,该方法概念简单合理,参数确定简便,不需迭代,计算量小,可适用于以下情形:1) 结构物可视为粘弹性介质;2) 地基和浅埋式结构物可简化为一维运动;3) 结构物运动对土体运动的影响忽略不计。     

Static analyses for 2–2 multi-layered piezoelectric curved composites

Based on the general theory of elasticity, the static behavior of 2–2 multi-layered piezoelectric curved composites is investigated. The exact solutions of the mechanical and electrical fields of the curved composites are obtained by utilizing Airy stress function method. Both the piezoelectric coefficient and the thickness for different layers are taken as variables. Different from other investigations based on the elementary theory of elasticity, the present investigation gives exact solutions for these variables by introducing several recurrence formulas, which make the present results very useful. The theoretical results obtained in the present paper are compared with the numerical results and good agreements are found.     

Distributed bragg reflector resonators with cylindrical symmetry and extremely high Q-factors

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE0qp mode cylindrical resonant cavity that constitutes a distributed Bragg reflection (DBR) resonator. The analysis considers an arbitrary number of alternating dielectric and free-space layers of cylindrical geometry enclosed by a metal cylinder. The layers may be arranged along the axial direction, the radial direction, or both. Given only the aspect ratio of the cavity, the desired frequency and the dielectric constants of the material layers, the relevant dimensions are determined from only a set of simultaneous equations, and iterative techniques are not required. The formulas were verified using rigorous method of lines (MoL) calculations and previously published experimental work. We show that the simple approximation gives dimensions close to the values of the optimum Bragg reflection condition determined by the rigorous analysis. The resulting solution is more compact with a higher Q-factor when compared to other reported cylindrical DBR structures. This is because it properly takes into account the effect of the aspect ratio on the Bragg antiresonance condition along the z-axis of the resonator. Previous analyses assumed the propagation in the z-direction was independent of the aspect ratio, and the layers of the Bragg reflector were a quarter of a wavelength thick along the z-direction. When the aspect ratio is properly taken into account, we show that the thickness of the Bragg reflectors are equivalent to the thickness of plane wave Bragg reflectors (or quarter wavelength plates). Thus it turns out that the sizes of the reflectors are related to the free-space propagation constant rather than the propagation constant in the z-direction.