包含两类变量的离散变量桁架结构拓扑优化设计

建立了包含截面和拓扑两类变量的离散变量结构拓扑优化设计的数学模型,该模型考虑了截面变量与拓扑变量间的耦合关系,反映了拓扑优化问题的组合优化本质,可以较好地解决"极限应力"、"最优解的奇异性"等困扰结构拓外优化设计的问题．同时采用相对差商法进行离散变量桁架结构拓扑优化,直接求解包含两类变量的离散变量结构拓扑优化设计数学模型,收到了比较满意的效果．     

Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method

The first two moments of the steady-state response of the spring and rotor models are determined by the polynomial dimensional decomposition (PDD) method and the Monte Carlo simulation (MCS) method in this paper. Both the analytical and numerical cases of the PDD method in the dynamical models are provided, and the response of the numerical case is calculated via the harmonic balance and PDD methods. The PDD can describe the amplitude–frequency characteristics of the dynamical models with random variables except the frequencies around the resonant frequencies. These results are shown as a three-DOF spring model with stiffness uncertainty, rotor models with four and nine random variables and nonlinear rotor model with thirteen random variables, respectively. The effects of larger uncertainties and polynomial order are also highlighted. The efficiency of the PDD method is verified via comparing with the MCS method. The applications of the PDD method to the rotor model can provide guidance to further study the rotor systems supported by bearings.     

频率约束板结构拓扑优化

本文利用ICM（独立、连续、映射）方法建立了频率约束下平板结构重量最轻的拓扑优化模型。采用指数函数作为单元重量、单元质量及单元刚度的过滤函数。通过瑞利商对刚度过滤函数倒变量的泰勒一阶展式,将频率约束近似显式化。利用对偶理论将含有大量设计变量的约束优化模型转化为易于求解的少设计变量拟无约束优化模型,通过序列二次规划将转化模型进行求解,提高了求解的效率。本文选择MSC.Patran&Nastran软件及PCL二次开发语言构架了平板结构频率约束拓扑优化问题的软件。数值算例表明：本文的方法具有迭代稳定性和收敛高效性。     

Age-Structured Population Dynamics with Nonlocal Diffusion

Random diffusive age-structured population models have been studied by many researchers. Though nonlocal diffusion processes are more applicable to many biological and physical problems compared with random diffusion processes, there are very few theoretical results on age-structured population models with nonlocal diffusion. In this paper our objective is to develop basic theory for age-structured population dynamics with nonlocal diffusion. In particular, we study the semigroup of linear operators associated to an age-structured model with nonlocal diffusion and use the spectral properties of its infinitesimal generator to determine the stability of the zero steady state. It is shown that (i) the structure of the semigroup for the age-structured model with nonlocal diffusion is essentially determined by that of the semigroups for the age-structured model without diffusion and the nonlocal operator when both birth and death rates are independent of spatial variables; (ii) the asymptotic behavior can be determined by the sign of spectral bound of the infinitesimal generator when both birth and death rates are dependent on spatial variables; (iii) the weak solution and comparison principle can be established when both birth and death rates are dependent on spatial variables and time; and (iv) the above results can be generalized to an age-size structured model. In addition, we compare our results with the age-structured model with Laplacian diffusion in the first two cases (i) and (ii).

     

Least squares based iterative identification algorithms for input nonlinear controlled autoregressive systems based on the auxiliary model

For the difficulty that the information vector in the identification model contains the unknown variables, we substitute these unknown variables with the outputs of the auxiliary model and then develop an auxiliary model based recursive least squares algorithm, an auxiliary model based least squares iterative (AM-LSI) algorithm, and derive an equivalent matrix decomposition based AM-LSI algorithm for input nonlinear controlled autoregressive systems based on the auxiliary model. The simulation results show that the proposed algorithms can estimate the parameters of a class of input nonlinear systems.     

The ICM method with objective function transformed by variable discrete condition for continuum structure

ICM (Independent Continuous Mapping) method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm. The project supported by the National Natural Science Foundation of China (10472003), Beijing Natural Science (3002002) and Beijing Educational Committee Foundations (KM200410005019) and Suspensoried by American MSC Company. The English text was polished by Keren Wang.     

主动约束阻尼板压电层电压拓扑优化研究

建立主动约束层阻尼板有限元模型,以结构模态阻尼比最大化为目标函数,压电层总电能消耗为约束条件,压电层单元控制电压为设计变量,对主动约束层阻尼板压电层电压进行了拓扑优化,获得了压电层电压最优拓扑分布。通过引入虚拟设计变量,将压电层电压控制不连续问题转化为连续问题。考虑实际工程应用的需要,采用指数函数对电压中间变量进行惩罚。在灵敏度分析基础上,采用移动渐进线(MMA)法,求解了主动约束层阻尼板电压拓扑优化问题。数值算例证实了电压拓扑优化模型以及数值求解方法的有效性。     

Mesohydrodynamics of membrane suspensions

Doi–Ohta rheological model of immiscible blends is extended by replacing the fluid interface with an elastic membrane. A symmetric tensor characterizing the in-membrane deformations joins the surface area and the orientation tensor (used in the Doi–Ohta theory) to provide morphological state variables. The governing equations of the model are solved numerically and the morphological and rheological predictions are presented. As an illustration, we regard the model as a first step in mesoscopic rheological modeling of suspensions of red blood cells. The material properties of the membrane enclosing the red blood cells, that are inferred from rheology, are indeed found to be close to the ones seen in direct experimental measurements. A more realistic model of human blood has to include additional morphological state variables describing larger structures (in particular whole red blood cells).     

Some new extensions to multi-mechanism models for plastic and viscoplastic material behavior under small strains

Multi-mechanism models (MM models) have become an important tool for modeling complex material behavior. In particular, two-mechanism models are used. They are applied to model ratcheting in metal plasticity as well as steel behavior during phase transformations. We consider a small-deformation setting. The characteristic trait of multi-mechanism models is the additive decomposition of the inelastic (e.g., plastic or viscoplastic) strain into several parts. These parts are sometimes called mechanisms. In comparison with rheological models, the mechanisms can interact with each other. This leads to new properties and allows to describe important observable effects. Up to now, each mechanism has one kinematic internal variable. As a new feature, we develop multi-mechanism models (in series) with several kinematic variables for each mechanism as well as with several isotropic variables for each flow criterion. We describe this complex situation by three structural matrices which express the mutual relations between mechanisms, flow criteria, kinematic, and isotropic variables. The well-known Chaboche model with a unique inelastic strain and several kinematic variables represents a special case of these general multi-mechanism models. In this work, we also present a matrix-based approach for these new complex MM models. The presented models can form the basis for developing numerical algorithms for simulation and parameter identification.     

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.     

基于Chebyshev展开的区间穿孔板超材料分析

目前对于声学超材料的传输特性分析和优化大多是基于确定的数值和确定的模型,然而在实际工程和结构设计中存在大量材料自身特性和几何物理参数的不确定性.如果忽略这些不确定变量对声学超材料传输特性分析和优化过程的影响,得到的结果可能不正确.针对这一现状,拟将切比雪夫区间模型引入多层穿孔板超材料,提出多层穿孔板超材料声学透射率的区间切比雪夫展开-蒙特卡洛模拟法(interval Chebyshev expansionMonte Carlo simulation method,ICE-MCSM).该方法采用截断切比雪夫多项式近似拟合多层穿孔板超材料的声学透射率响应曲线,构造声学透射率响应曲线的切比雪夫代理模型;然后采用蒙特卡洛模拟法(Monte Carlo simulation method,MCSM)随机生成一定数量的不确定区间变量的样本数据点,并将生成的不确定区间变量样本数据点代入切比雪夫代理模型,预测单个不确定区间变量和多个不确定区间变量条件下的多层穿孔板超材料声学透射率区间的上界和下界.数值分析结果表明,ICE-MCSM预测的声学透射率变化区间的上界和下界与直接蒙特卡洛法(direct Monte Carlo simulation method,DMCSM)预测的声学透射率上界和下界的结果非常接近.与DMCSM相比,ICE-MCSM具有更高的计算效率.因此,ICE-MCSM可有效且高效地分析不确定区间变量条件下多层穿孔板超材料声学透射率传输特性,具有良好的工程应用前景.     

对偶法求解应力与位移约束不同显式的优化模型

基于响应面法,通过内力将应力约束显式化为正变量的一阶近似,位移约束采用倒变量一阶近似,建立以桁架结构重量最小为目标的截面优化模型,采用对偶规划理论转化为拟无约束模型,采用序列二次规划算法求解。此方法同应力约束零阶近似和一阶近似(使用响应面方法显式化)等方法进行了算例比较,表明本文的优化模型有较好的求解效率。     

A model-reduction approach in micromechanics of materials preserving the variational structure of constitutive relations

In 2003 the authors proposed a model-reduction technique, called the Nonuniform Transformation Field Analysis (NTFA), based on a decomposition of the local fields of internal variables on a reduced basis of modes, to analyze the effective response of composite materials. The present study extends and improves on this approach in different directions. It is first shown that when the constitutive relations of the constituents derive from two potentials, this structure is passed to the NTFA model. Another structure-preserving model, the hybrid NTFA model of Fritzen and Leuschner, is analyzed and found to differ (slightly) from the primal NTFA model (it does not exhibit the same variational upper bound character). To avoid the “on-line” computation of local fields required by the hybrid model, new reduced evolution equations for the reduced variables are proposed, based on an expansion to second order (TSO) of the potential of the hybrid model. The coarse dynamics can then be entirely expressed in terms of quantities which can be pre-computed once for all. Roughly speaking, these pre-computed quantities depend only on the average and fluctuations per phase of the modes and of the associated stress fields. The accuracy of the new NTFA-TSO model is assessed by comparison with full-field simulations. The acceleration provided by the new coarse dynamics over the full-field computations (and over the hybrid model) is then spectacular, larger by three orders of magnitude than the acceleration due to the sole reduction of unknowns.     

Modeling Maher's Attribution Theory of Delusions as a Cusp Catastrophe

Maher's (1974, 1988) attribution theory of delusions was reformulated as a cusp catastrophe model and tested using 193 percipients' paranormal beliefs, paranormal experiences, and fear of the paranormal as measured by Kumar et al.'s (1994) Anomalous Experiences Inventory, and their tolerance of ambiguity as measured by McDonald's (1970) AT-20. The magnitude of the difference between percipients' fear and belief was used as the dependent variables, whereas experience and tolerance of ambiguity were used as asymmetry and bifurcation variables, respectively. Using the GEMCAT II software it was shown that this cusp provided a superior fit to the data than competing linear, fold, and cusp models. Consistent with Maher's formulation, two basic states were found to exist: one in which fear dominates belief, and a second in which belief dominates fear. Further, fear of the paranormal increased with greater intolerance of ambiguity while belief decreased with increasing tolerance. The model explains why paranormal beliefs are resistant to change in the face of counterargument or contradictory evidence.     

Mechanical behavior of amorphous polymers in shear

Based on the non-equilibrium thermodynamic theory, a new thermo-viscoelastic constitutive model for an incompressible material is proposed. This model can be considered as a kind of generalization of the non-Gaussian network theory in rubber elasticity to include the viscous and the thermal effects. A set of second rank tensorial internal variables was introduced, and in order to adequately describe the evolution of these internal variables, a new expression of the Helmholtz free energy was suggested. The mechanical behavior of the thermo-viscoelastic material under simple shear deformation was studied, and the “ viscous dissipation induced“ anisotropy due to the change of orientation distribution of molecular chains was examined. Influences of strain rate and thermal softening produced by the viscous dissipation on the shear stress were also discussed. Finally, the model predictions were compared with the experimental results performed by G‘ Sell et al. , thus the validity of the proposed model is verified.     

强迫谐振动下连续体结构拓扑优化

应用结构拓扑优化ICM(独立连续映射)方法,对强迫谐振动下结构拓扑优化问题建立了以重量极小为目标,位移幅值为约束的优化模型.位移幅值采用一阶泰勒展式近似,由于拓扑优化中设计变量数目通常很多,对强迫谐振动位移幅值的敏度分析推导了伴随法公式,使得一次敏度分析可以计算出对所有设计变量的偏导数,克服了采用直接法敏度分析中一次只能计算出对一个设计变量的偏导数的不足.算例表明用伴随法分析敏度在结构拓扑优化中可以大幅提高计算效率,ICM方法采用独立于截面及形状参数的拓扑优化设计变量更清晰地反映了拓扑优化的本质.     

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. I: theoretical formulation

In this paper, a variational approach is proposed to study the response of a single-crystalline magnetic shape memory alloy (MSMA) sample subject to external forces and magnetic fields. Especially, some criteria are derived to model the (quasi-static) movements of twin interfaces in the sample. By considering the compatibility condition, twin interfaces between two martensite variants are found to be flat planes with given normal vectors. To adopt the variational method, a total energy functional for the whole magneto-mechanical system is proposed. By calculating the variations of the total energy functional with respect to the independent variables, the equilibrium equations and the evolution laws for the internal variables can be derived. By further considering the variation of the total energy functional with respect to the variant distribution, some criteria for twin interface movements can be derived. The governing system of the current model is then formulated by composing the equilibrium equations, the evolution laws for the internal variables and the twin interface movement criteria. To show the validity of the governing system, some analytical results are constructed under certain simplified conditions, which can be used to simulate the magneto-mechanical response of the MSMA sample.     

一种适用于超音速边界层的湍流转捩模式

建立一种合理反映扰动模态和可压缩性影响的新型k-ω-γ转捩模式.其主要特点为:(1)假设脉动动能k 由湍流脉动部分和非湍流脉动部分组成,且在模化后者时采用了稳定性分析的结果; (2)在间歇因子γ方程的源项中,构造了具有``自动判断转捩起始位置'功能的函数; (3)通过构造新型的物面法向长度尺度,保证了模式中所有的表达式均由当地变量构成,可以方便地应用于现代CFD程序之中. 该模式在亚音速、超音速和高超音速条件下的边界层流动中进行了验证. 计算结果表明,该模式可应用于较宽马赫数范围内的自然转捩以及旁路转捩过程,所具有的捕捉流动转捩的性能优于国际上的现有模式.      

含模糊变量和区间变量的结构可靠性优化设计方法

提出了基于能度可靠性理论的含模糊变量和区间变量的结构优化设计方法.运用能度可靠性理论建立了含模糊变量和区间变量的结构混合可靠性模型,采用结构的最大失效可能度作为混合模型的可靠性度量,给出最大失效可能度的计算方法,并以混合可靠性模型的最大失效可能度为约束条件建立了混合结构优化设计模型.实例计算表明了本文方法的有效性.     

Gas Leakage Prediction Model of Large-Scale Explosions in Hard Rock Based on Quantification Theory

The toxic gas produced by the underground large-scale contained explosions have a great impact on the surrounding environment safety of the explosion project, so it is of great significance for the safety protection design to predict the leakage of the explosion gases to the environment. Based on the study of the one-dimensional spherically (axially) symmetric fluid dynamic model for seepage of the underground contained explosion gases, the qualitative and quantitative variables which impact the gas seepage, such as the explosion cavity, the gas pressure in the cavity and the rock mass permeability, among which the qualitative variables can describe the uncertainty of the geological mass, were analyzed. In accordance with the physical significance of variables and the quantification theory, the qualitative variables were quantified and such details as the principle for variable selection, significance assessment and recurrence test to establish a quantification prediction model, etc. were discussed. Based on 15 test samples on the hard rock conditions, we have established a quantification model for prediction of the contained explosion gases leakage at the specific site. The prediction accuracy of this model can meet the requirement of this project, and according to this model, it is known that such qualitative factors as groundwater status and rock properties have significant influence on the gas leakage. In this study, the prediction model is established based on physical analysis so that the quantitative prediction model could have its rationality and effectiveness well ensured, and the research methods and results in this paper could be promoted and applied in the similar engineering practices.