On the correspondence between the three- and four-dimensional parameters of the three-dimensional rotation group

A fundamental kinematic theorem due to Euler permits synthesizing a series of three- and four-dimensional orientation parameters that correspond to each other in spaces of the same dimension. We use the theorem about the homeomorphism of two topological spaces (the three-dimensional sphere S ³ ? R ⁴ with a single punctured (removed) point and the three-dimensional space R ³) to establish a one-to-one mutually continuous correspondence between the four- and three-dimensional kinematic parameters prescribed in these spaces. The latter can be proved using the stereographic projection of points of the sphere S ³ onto the hyperplane R ³. For the normalized (Hamiltonian) Rodrigues-Hamilton parameters, we present a method of stereographic projection of a point belonging to the three-dimensional sphere S ³ onto the oriented space R ³. We present a family of local kinematic parameters obtained by the method of mapping four symmetric kinematic parameters of the space R ⁴ onto the oriented real space R ³. In contrast to the well-known four symmetric global parameters of the Rodrigues-Hamilton orientation, the synthesized three-dimensional orientation parameters are local (have two singular points ±360°). The differential equations of rotation in the three-dimensional orientation parameters are obtained by the projection method. We present the three-dimensional parameters corresponding to the classical Hamiltonian quaternions defined in the four-dimensional vector space R ⁴.     

Identification of the viscoelastic parameters of a polymer model by the aid of a MCMC method

A procedure to identify the viscoelastic material parameters of a solid amorphous polymer and to estimate their values is presented. Stress–strain material data is obtained for the polymer by a compression experiment. The material behavior of the polymer is modeled according to the generalized Maxwell model, which is fitted to the experimental data by the method of least squares to obtain a first approximation for the model parameters. The identification of the model parameters is completed by a Markov chain Monte Carlo (MCMC) method, which generates the probability distributions of the relevant parameters of the material. The utilized MCMC method enables us to determine a suitable complexity (i.e., the number of Maxwell elements) for the generalized Maxwell model, so that the model best fits the data and, simultaneously, leads to an identifiable set of parameters. The numerical results imply that the uniqueness of the solution is lost when the number of model parameters becomes redundant.     

边坡预裂爆破参数优化研究

边坡工程施工中常用到预裂爆破,预裂爆破参数对爆破降震起着非常重要的作用。通过大量的预裂爆破试验,得出了适用于该边坡的炮孔直径、炮孔间距、线装药密度、不耦合系数等一系列常规预裂爆破参数。通过ANSYS/LS-DYNA数值模拟,得出了与4种炮孔直径对应的理想的预裂爆破参数,且与爆破试验的结果基本一致。通过回归分析,得出了用于该边坡选取预裂爆破参数的简易公式,用以指导该工程的后续施工。实践证明,采用爆破试验与数值模拟相结合的方法,对于爆破参数的优化选择,效果明显。     

模态参数不确定性分析的贝叶斯方法研究

在结构损伤诊断和参数识别中,实测结构模态参数不可避免地存在误差。本文将模态参数视为随机变量,采用贝叶斯方法对模态参数的不确定性进行分析。分析中选用高斯联合概率密度函数作为先验密度函数,通过多次独立的模态参数测试,得到传递函数的条件概率密度函数和模态参数的后验估计表达式,再利用拉普拉斯渐近方法求解边缘概率密度函数,得到模态参数的最大后验估计。在钢筋混凝土框架结构的模态试验中,利用本文方法给出了结构模态参数的估计值,结果表明,本文方法具有良好的收敛性。     

基于夏比冲击试验的材料失效模型参数

结合夏比冲击试验和ABAQUS显式动力数值模拟,对Q370d钢进行了Johnson-Cook失效模型参数研究。首先,在不考虑材料失效的情况下,通过3种不同厚度的无缺口试件冲击实验对有限元模型参数设置和材料本构模型的准确性进行了验证,同时还讨论了试件断裂区网格的合适尺寸;在此基础上,基于正交设计,通过大量的有限元数值模拟得到失效模型参数样本,利用回归分析求得冲击功与失效模型参数的回归方程组;最后结合夏比V型缺口冲击试验,求解Q370d钢的失效模型参数,并对断裂截面的力学特性进行了分析,可为工程应用提供参考。     

Determination of the radial variations of the density and the shear modulus of a flaw from the angular dependence of the scattering amplitude

The inverse scattering theory is applied to determine the continuous variation of the elastic parameters of spherically symmetric flaw which is located within an isotropic and homogeneous host medium. From the angular dependence of the scattering amplitude, the phase shift for the transverse wave with polarization perpendicular to the scattering plane can be deduced for different partial waves. The knowledge of this set of phase shifts for two frequencies enables one to obtain the radial variation of the density and the shear modulus parameters of the flaw from the solution of a special difference equation which approximates the differential equation for the displacement of the transverse mode. The method has been applied successfully to obtain several different profiles for the density and the shear modulus parameters.     

Determination of the Parameters of Hydraulic Models of the Vascular Bed by the Input Impedance Method

On the basis of hydraulic models of the vascular bed, the possibility of quantitatively estimating the resistances, inertia coefficients and compliances of model elements, as well as the changes in these parameters, from the hydraulic input impedance is evaluated. It is shown that the input impedance method makes it possible to find stable estimates for the hydraulic model parameters using the least squares method. No significant differences between the parameters of hydraulic models of the vascular bed calculated by the input impedance method and measured independently were found. The possibility of using the input impedance method to estimate the arterial response of an organ is discussed.     

转子系统振动变参控制中的瞬态响应

本文以可变参数的挤压油膜阻尼器作为控制元件，研究了转子在稳态转速及加速运动过程中进行变参控制时的瞬态响应问题。结果说明了对转子系统的振动进行分段变参控制，无论是在稳态还是在加速运动过程中，一般都可以取得满意的控制效果，不仅可以减小转子系统的振动，而且还可以使转子系统平稳地通过具有较大振动的共振区，但变参位置不应在多值转速区内。     

An inverse algorithm for the identification and the sensitivity analysis of the parameters governing micropolar elasto-plastic granular material

The article concerns the complex determination process of the material parameters governing micropolar granular material with elasto-plastic material properties. Proceeding from a gradient-based method, we split the total set of parameters and the overall identification procedure into two major categories. These are, firstly, the identification of the parameters of a standard non-polar elasto-plastic continuum, and, secondly, the determination of the remaining parameters governing the micropolar part of the constitutive model. While the first set of parameters can be obtained from homogeneous triaxial tests on, e. g., granular, cohesive-frictional materials like sand, the second set can only be determined from inhomogeneous tests, such as biaxial tests including the onset and the development of shear bands. Following this, one can obtain the first part of the identification process from a simple inverse algorithm applied to the elasto-plastic material model of non-polar solids, while the second part requires a fully inverse computation in the sense of a back analysis of the underlying boundary-value problem. In the present article, this procedure is carried out by use of the semi-discrete sensitivity analysis. Finally, the whole model is applied to the data of Hostun sand taken at the universities of Grenoble and Stuttgart. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday.     

On the solution of the model of two co-affected species

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Identification of the elastic stiffness of composites using the virtual fields method and digital image correlation

This paper presents an effective methodology for characterizing the mechanical parameters of composites using digital image correlation combined with the virtual fields method.By using a three-point bending test configuration,this method can identify all mechanical parameters of the material with merely a single test.Successful results verified that this method is especially effective for characterizing composite materials.In this study,the method is applied to measure the orthotropic elastic parameters of fiber-reinforced polymer-matrix composites before and after the hygrothermal aging process.The results indicate that the hygrothermal aging environment significantly influences the mechanical property of a composite.The components of the parameters in the direction of the fiber bundle decreased significantly.From the accuracy analysis,we found that the actual measurement accuracy is sensitive to a shift of the horizontal edges and rotation of the vertical edges.     

计算近场地震作用下隔震结构支座破坏易损性曲线的概率凸集混合模型

用凸集模型模拟隔震结构参数的不确定性,而用随机模型模拟地震动输入的不确定性,提出了计算近场地震作用下在考虑双不确定性因素时隔震结构支座发生破坏的易损性曲线计算新方法;计算结果将给隔震支座力学参数的设计提供参考;通过计算对比可知,若不考虑结构参数不确定性将低估隔震支座破坏的地震易损性;对计算实例中基底最大位移敏感度分析发现,隔震支座的力学参数(如屈服力、屈服后刚度等)对基底最大位移影响较大,上部结构质量的影响次之,而上部结构的刚度对其影响不大;此外,本文的研究内容也为考虑结构参数和输入地震动双不确定性因素的情况下,计算各类结构地震易损性曲线提供了一种新的思路和途径。     

Dynamics of the general Lorenz family

The present work is devoted to investigating the dynamical entities of the general Lorenz family, which contains four independent parameters. The classical Lorenz system, the Chen system, and the Lü system are all contained by the system considered in this paper as special cases. First, the properties of the equilibria, in particular, the stability of the non-hyperbolic equilibrium obtained by using the center manifold theorem and the technique of the polar transformation, the pitchfork bifurcation and the degenerate pitchfork bifurcation, Hopf bifurcations, and the local stable and unstable manifold character, are all analyzed when the parameters are varied in the space of parameters. Based on the theoretic analysis and numerical simulations, the dynamics of the system are discussed subtly under all kind of the critical state. Second, the properties of the existence of homoclinic and heteroclinic orbits for the system are rigorously studied. Finally, the existence of singularly degenerate heteroclinic cycles for a suitable choice of the parameters is investigated.     

On the measurement of some parameters of planetary atmospheres by means of the radiation generated by the descent of landers

The results are given of investigations into the possibility of determining the parameters of planetary atmospheres (the element composition and density) by measuring the spectrum of the radiation from the high-temperature gas formed by a lander when it enters the atmosphere of a planet at hypersonic velocity in the altitude range H = 70–150 km. The example of Venus demonstrates the possibility of determining these parameters under both night and day conditions of observation. The results are recommended for investigating such parameters at the time of aerodynamic deceleration in the descent of the landers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 36–45, January–February, 1981.     

The monodromic Galois groups of the sextic equation of anisotropic elasticity

It has previously been shown that the conventional algebraic Galois group of the sextic equation of anisotropic elasticity for cubic crystals is the symmetric group and the equation is therefore algebraically unsolvable in radicals. As an equation with four parameters it has also 15 monodromic Galois groups corresponding to different, relaxed, meanings of solvability in radicals. Three of these are appropriate, to solve explicitly for the functional dependence of the roots on the two directional parameters or on the two elastic parameters or on all four parameters. From the definition of a monodromic group as the root permutations induced by all complex circuits of the relevant parameters, it is shown numerically that these three monodromic groups must be either the alternating or the symmetric. The equation is therefore also unsolvable for these weaker and more appropriate meanings of solvability.Formally Division of Tribophysics.     

Prediction of the effective elastic moduli of materials with irregularly-shaped pores based on the pore projected areas

Statistical modeling is used to correlate geometric parameters of pores with their contributions to the overall Young’s moduli of linearly elastic solids. The statistical model is based on individual pore contribution parameters evaluated by finite element simulations for a small pore subset selected using the design of experiments approach, so there is no need to solve the elasticity problem for all pores in the material. A polynomial relating pore geometric parameters to the contribution parameters is then fitted to the results of the simulations. We found a good correlation between normalized projected areas of the pores on three coordinate planes and their contributions to the corresponding effective Young’s moduli. The model is applied and validated for two large sets of pore geometries obtained by X-ray microcomputed tomography of a carbon/carbon and a 3D woven carbon/epoxy composite specimens.     

基于爆炸切割试验的有机玻璃本构模型参数反演

为了获取爆炸切割数值模拟中有机玻璃（PMMA）的材料本构模型参数,建立了一种基于神经网络的有机玻璃Johnson Holmquist ceramics (JH-2)本构模型参数反演方法：基于从爆炸切割试验和现有研究得到的JH-2本构模型经验参数,确定本构模型参数的调整区间;使用LS-DYNA数值模拟软件对2.5 mm宽爆炸切割索切割14 mm PMMA平板过程进行数值模拟并收集平板损伤数据集;建立PMMA平板本构模型参数与损伤数据之间的神经网络模型;通过训练完成的神经网络模型对PMMA平板的JH-2本构模型参数进行反演。为验证通过反演参数的可靠性,进行了4.2 mm宽爆炸切割索切割19 mm PMMA平板试验和有限元数值模拟,计算结果中的平板损伤情况与实验结果相差较小,表明通过反演获得的JH-2本构模型参数能较好地应用于PMMA平板爆炸切割数值模拟。传统材料参数获取方法,该参数反演方法相较于可以通过较少的试验及测试,获得比较准确的材料本构模型参数。     

Determining the parameters of the fractional exponential heredity kernels of linear viscoelastic materials

The parameters of the fractional exponential creep and relaxation kernels of linear viscoelastic materials are determined. Methods that approximate the kernel by using the Mittag-Leffler function, the Laplace-Carson transform, and direct approximation of the creep function by the original equation are analyzed. The parameters of fractional exponential kernels are determined for aramid fibers, parapolyamide fibers, glass-reinforced plastic, and polymer concrete. It is shown that the kernel parameters calculated through the direct approximation of the creep function provide the best agreement between theory and experiment. The methods are experimentally validated for constant-stress and variable-stress loading in the modes of additional loading and complete unloading Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 12–25, September 2008.     

混凝土K&C模型材料参数分析与模拟

混凝土K&C模型材料参数一般取国外文献中的原始数值,没有根据混凝土强度等级和单元尺寸的不同而作相应的调整．根据相关的试验研究成果,提出了一种确定K&C模型强度参数值的方法,并阐述了K&C模型损伤参数值的调整方法,使得数值计算结果更加合理．运用有限元显式动力分析软件ANSYS/LSDYNA,采用流固耦合方法模拟爆炸荷载作用下钢筋混凝土板的动态响应,混凝土K&C模型取本文确定的参数值,计算结果与试验结果吻合较好,从而验证了K&C模型材料参数取值的正确性．     

ABAQUS混凝土损伤塑性模型中损伤因子的率相关性及实现方法

ABAQUS程序中最常用的混凝土损伤塑性（concrete damage plasticity, CDP）模型无法实现损伤因子与应变率相关。为了准确描述混凝土材料在高应变率下的损伤特性,基于CDP模型定义了新的应变率场变量,编制了VUSDFLD用户子程序,开发了能够考虑损伤因子率相关性的改进的CDP（modified CDP,MCDP）模型。MCDP模型采用能量法求解混凝土拉压损伤因子,主求解程序能够随着应变率场变量的变化而自动更新不同应变率对应的损伤参数,计算得到的混凝土单轴静态加载结果与CDP模型吻合较好。MCDP模型对高应变率下动态压缩性能的模拟结果表明:混凝土材料在不同应变率下的拉压损伤对其动态力学性能有显著影响,编制的VUSDFLD子程序和MCDP模型能够有效地解决损伤应变率相关的模拟难题,可以准确地模拟爆炸荷载作用下钢筋混凝土梁的动态响应,为预测爆炸冲击等强动载作用下混凝土结构的响应和破坏提供了更可靠的技术途径。