弹性力学中哈密顿正则方程的可分型及其有限元法

本文给出弹性力学中可分的哈密顿系统及其相应的变分原理，用有限元法求解了强厚度复合材料叠层板问题。     

层状正交各向异性材料弹性波导问题的数值计算

研究复合材料弹性波导问题的数值计算方法。将问题导向哈密顿体系,在哈密顿体系中以位移向量和应力向量综合成全状态向量,在杂交体系中建立动力-部分杂交元,导出一套哈密顿体系下新的半解析法。本文中给出了该方法在分层正交各向异性材料的弹性波导问题的数值算例。计算结果展现了该方法在弹性波导问题的应用前景。     

旋转系统中弹性结构振动问题的哈密顿体系方法

建立了旋转弹性结构耦合振动问题的哈密顿基本体系，得到了包括外动量在内的外载直接影响的哈密顿正则控制方程，将所研究的问题归结为辛几何本征值和本征解的求解问题，以梁结构旋转振动为算例，给出了本征值与转动角速度之间的一些特征和关系，提示了结构在旋转过程中振动的一些规律，给出求解类似问题的一种新的方法和途径。     

卫星轨道计算的辛几何算法应用

本文将哈密顿力学的辛几何算法应用于地球卫星轨道的轨道计算,并同传统的数值积分法进行了详细比较,计算结果证实了辛几何算法能够保持系统能量守恒,能够避免传统数值算法所引入的人为耗散性。     

基于哈密顿体系求解空间粘性流体问题

本文通过变分原理将哈密顿体系引入到小雷诺数空间粘性流体问题中导出一套哈密顿算子矩阵的本征函数向量展开求解问题的方法基于直接法求解流体力学基本方程通过求零本征解及其约当型得到几种常见的基本流动求解非零本征值及本征向量的叠加继可分析流场端部效应从而在该领域用哈密顿体系辛几何空间中研究问题的方法代替了传统在拉格朗日体系欧氏空间分析问题的方法     

平面裂纹应力强度因子的半解析有限元法

利用弹性平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,推导了一个圆形奇异解析单元列式,该单元能准确地描述平面裂纹尖端场。将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和载荷的平面裂纹应力强度因子及扩展问题。对典型算例的计算结果表明本文方法简单有效,具有令人满意的精度。     

支承运动情况下旋转梁的刚-柔耦合振动分析

利用哈密顿原理建立了支承运动情况下旋转梁的刚-柔耦合振动非线性动力学方程组及边界条件。根据假设模态法，利用边界条件以及模态函数的性质，得到一组模态坐标与刚性角位移耦合时变系数常微分方程，运用数值方法比较了非耦合和耦合时刚性角位移的结果，计算了梁的动力响应并分析了模态截断的影响，最后运用梁端部弹性振动的相轨迹分析了该时变系统的稳定性。     

薄板哈密顿求解体系及其变分原理

将哈密顿求解体系推广应用于薄板弯曲问题。首先导出薄板哈密顿对偶微分方程,然后导出薄板哈密顿变分原理的泛函表示式HP。有两点值得指出第一,以挠度w、转角xy、弯矩xM和等效剪力xV取为对偶变量,与相关文献的取法不同。第二,对于薄板问题,由Hellinger-Reissner泛函HRP导出哈密顿泛函HP时既要消元,又要增元,与在厚板问题中只需要消元的推导方法不同。薄板哈密顿求解体系的理论成果将为研究薄板解析解和有限元解提供新的有效工具。     

厚板哈密顿求解体系及其变分原理与正交关系

将哈密顿求解体系推广应用于Reissner-Mindlin厚板问题。首先导出了厚板哈密顿对偶微分方程,然后采用换元乘子法导出了厚板哈密顿变分原理的泛函表示式,最后提出并证明了厚板理论的两个正交关系。厚板哈密顿体系的理论成果将为研究厚板解析解和有限元解提供新的有效工具。     

轴向运动导电薄板的磁弹性振动

针对磁场环境中轴向运动导电薄板的磁弹性振动问题进行研究。在给出薄板运动的动能、应变能以及电磁力虚功表达式的基础上,应用哈密顿变分原理,推得磁场中轴向运动矩形薄板的磁弹性振动方程。基于麦克斯威尔电磁场方程并考虑相应的电磁关系式,得到薄板所受电磁力的表达式。针对横向磁场中矩形板的自由振动问题,通过位移函数的设定并应用伽辽金积分法,得到三种边界约束条件下轴向运动薄板的磁弹性振动微分方程。通过数值算例,给出了不同边界条件下矩形板的磁弹性振动特性曲线图,分析了轴向运动速度和磁感应强度等参量对薄板固有振动频率的影响,讨论了临界速度的变化规律。     

Young's modulus measurements of soft tissues with application toelasticity imaging

Ultrasound elasticity imaging is a promising method that may eventually allow early detection of many tissue pathologies. However, before elasticity imaging can be applied to its numerous potential clinical applications, the quantitative accuracy of tissue elasticity measurements must be established. Simple 1-D ultrasound elasticity measurements were performed on muscle and liver and compared with independent and established mechanical measurements to investigate both the accuracy and consistency of ultrasound elasticity measurements. In addition, some interesting properties of soft tissue and aspects of the measurement process which should be considered in elasticity measurements are discussed     

Bestimmung des Elastizitätsmoduls aus der Nachgiebigkeit angerissener Bruchmechanik-Proben

Determining the moduls of elasticity from the compliance of precracked specimens . A new method is described which allows the determination of the modulus of elasticity of solid materials. Compliance tests with precracked fracture mechanics specimens in a simple tensile test machine yield accurate measurements of the modulus of elasticity in the orientation and material condition desired for fracture mechanics calculations.     

Plane elasticity problems by barycentric rational interpolation collocation method and a regular domain method

Barycentric rational interpolation collocation method (BRICM) for solving plane elasticity problems with high accuracy is presented. The plane elasticity problems on a circular or rectangular domain can be solved directly by BRICM. Embedded the irregular domain into a regular (circular or rectangular) domain, the governing equations of plane elasticity on regular domain are discretized by the differentiation matrices based on barycentric rational interpolation to form a system of algebraic equations. Discrete boundary conditions are obtained using barycentric rational interpolation. The irregular boundary conditions are imposed by the additional method to form an over-constraint linear system of algebraic equations. Numerical experiments are presented to illustrate the efficiency and high computing precision of proposed method.     

Comparison of ultrasound echo‐tracking technology and pulse wave velocity for measuring carotid elasticity among hemodialysis patients

This study aims to investigate the correlation between carotid elasticity in hemodialysis patients as evaluated by ultrasound echo‐tracking technology and aortic pulse wave velocity. A total of 103 patients with end‐stage renal disease who underwent stable hemodialysis were enrolled. An ultrasonic echo‐tracking method was used to evaluate the elastic modulus and the stiffness index (β), which were compared with pulse wave velocity (PWV). Blood glucose, blood lipids, and serum creatinine were also tested. These indices were analyzed to determine the independent factor for arterial elasticity. The carotid elastic modulus and β were in good correlation with PWV among hemodialysis patients (P = 0.000). Diabetes and age are independent risk factors for arterial elasticity among hemodialysis patients. Ultrasound echo‐tracking technology is a sensitive and accurate method for evaluating arterial elasticity and is a good alternative to traditional PWV.     

管线钢管屈服强度的稳定性试验

针对目前API Spec 5L-2009《管线钢管规范》中采用冷压平方法测试管线钢管屈服强度的不稳定性问题,采用双肩圆试样拉伸、展平率法板试样拉伸、预拉伸至弹性极限Rp0.02板试样拉伸和预拉伸至弹性极限Rp0.01板试样拉伸四种方法对不同取样方向的管线钢管试样进行了拉伸试验,并对四种方法测得的屈服强度结果进行分析比较。结果表明:双肩圆试样拉伸法由于不是全厚度试样,因而不能真实地反映管线钢管的屈服强度,且试样加工比矩形平板状试样更为繁琐;展平率法板试样拉伸方法由于同一取样角度只计算一个试样的展平率,因而试验结果比较分散,且需要采用滞后环法对试验数据进行处理,工作量较大;预拉伸至弹性极限板试样拉伸方法可以方便、准确地计算出管线钢管的屈服强度,但预拉伸至弹性极限Rp0.02时的非比例伸长延伸率稍大,因此建议采用预拉伸至弹性极限Rp0.01板试样拉伸的方法测试管线钢管的屈服强度。     

Identification of boundary displacements in plane elasticity by BEM

The purpose of this study is to present a possible application of BEM for numerical identification of the boundary conditions for Navier equations in plane elasticity with internal measurements, based on insufficient and noisy information for unique identification. The inverse problem is re-formulated as a minimization problem by the direct variational method. The minimization problem is then recast using the gradient method into successive primary and adjoint boundary value problems in the corresponding plane elasticity problem. For numerical solution of the elasticity problems, the conventional direct boundary element method is employed. From the simple numerical examples considered, it is concluded that our identification scheme is stable and the approximate solutions are convergent to the minimum.     

Detection of lumen-intima interface of posterior wall for measurement of elasticity of the human carotid artery

In our series of studies on noninvasive assessment of the regional elasticity of the arterial wall, the displacement gradient (change in thickness) of the arterial wall caused by the heartbeat was measured by the phased tracking method. Because the displacement gradient corresponds to the strain due to the change in blood pressure, the elasticity can be evaluated from the displacement gradient of the arterial wall and the blood pressure, which are noninvasively measured at the upper arm. In the measurement of the elasticity of the arterial wall by our method, the region in which the elastic modulus is estimated must be assigned beforehand; currently, the lumen-intima boundary of the arterial wall is manually determined by the operator. For the real-time measurement of the elasticity of the arterial wall, a fast, automated method is necessary for detection of the boundary. In this paper, a cost function is proposed for differentiation of the arterial wall from the lumen. The proposed cost function was applied to ultrasound data, which were noninvasively obtained for five human carotid arteries. In comparison with the case of detection using only the amplitude of the echo, the root mean square error between the automatically detected lumen-intima boundary and the manually assigned boundary was significantly improved by using the proposed cost function. Furthermore, the lumen- intima boundary was automatically detected in a short period. Such a method is required for real-time measurement of the elasticity of the arterial wall, though detection of the outer boundary of the adventitia, which is not described in this paper, is also necessary to realize real-time elasticity measurement by our method.     

An autocorrelation-based method for improvement of sub-pixel displacement estimation in ultrasound strain imaging

In ultrasound strain and elasticity imaging, an accurate and cost-effective sub-pixel displacement estimator is required because strain/elasticity imaging quality relies on the displacement SNR, which can often be higher if more computational resources are provided. In this paper, we introduce an autocorrelation-based method to cost-effectively improve subpixel displacement estimation quality. To quantitatively evaluate the performance of the autocorrelation method, simulated and tissue-mimicking phantom experiments were performed. The computational cost of the autocorrelation method is also discussed. The results of our study suggest the autocorrelation method can be used for a real-time elasticity imaging system.     

大尺寸超声振动体的研究

文章中介绍了大尺寸超声振动体的研究进展。包括分析耦合振动的表观弹性法；用表观弹性法对短圆柱体、空心圆柱体和矩形六面体的振动进行分析；用开槽、开狭缝、附加弹性体和二次设计等方法对超声振动体的振动进行控制。对有关结果与用有限元方法进行计算的结果进行了比较，并作出了评价。     

Higher-order and higher floating-point precision numerical approximations of finite strain elasticity moduli

Two real-domain numerical approximation methods for accurate computation of finite strain elasticity moduli are developed and their accuracy and computational efficiency are investigated, with reference to hyperelastic constitutive models with known analytical solutions. The methods are higher-order and higher floating-point precision numerical approximation, the latter being novel in this context. A general formula for higher-order approximation finite difference schemes is derived and a new procedure is proposed to implement increased floating-point precision. The accuracy of the approximated elasticity moduli is investigated numerically using higher-order approximations in standard double precision and increased quadruple precision. It is found that, as the order of the approximation increases, the elasticity moduli tend toward the analytical solution. Using higher floating-point precision, the approximated elasticity moduli for all orders of approximation are found to be more accurate than the standard double precision evaluation of the analytical moduli. Application of the techniques to a finite element problem shows that the numerically approximated methods obtain convergence equivalent to the analytical method but require greater computational effort. It is concluded that numerical approximation of elasticity moduli is a powerful and effective means of implementing advanced constitutive models in the finite element method without prior derivation of difficult analytical solutions.