A computational framework for the form-finding and design of tensegrity structures

A new computational framework is proposed for the form-finding and design of tensegrity structures with or without super-stability. The form-finding of tensegrities is formulated as two unconstrained minimisation problems where their objective functions are defined based on eigenvalues of a modified force density matrix. The Nelder–Mead simplex method is then used to solve the minimisation problems. Furthermore, another efficient method is suggested for the interactive form-finding and design of tensegrities with geometrical and force constraints. Examples of the form-finding of tensegrities are presented and the results obtained are compared and contrasted with those analytical results documented in the literature, to verify the accuracy and efficiency of the developed methods.     

Geometric and material nonlinear analysis of tensegrity structures

A numerical method is presented for the large deflection in elastic analysis of tensegrity structures including both geometric and material nonlinearities.The geometric nonlinearity is considered based on both total Lagrangian and updated Lagrangian formulations,while the material nonlinearity is treated through elastoplastic stress-strain relationship.The nonlinear equilibrium equations are solved using an incremental-iterative scheme in conjunction with the modified Newton-Raphson method.A computer program is developed to predict the mechanical responses of tensegrity systems under tensile,compressive and flexural loadings.Numerical results obtained are compared with those reported in the literature to demonstrate the accuracy and efficiency of the proposed program.The flexural behavior of the double layer quadruplex tensegrity grid is sufficiently good for lightweight large-span structural applications.On the other hand,its bending strength capacity is not sensitive to the self-stress level.     

Non-linear dynamic analysis of tensegrity structures using a co-rotational method

A new formulation is presented for the non-linear dynamic analysis of space truss structures. The formulation is based on the dynamics of 3D co-rotational rods. In the co-rotation method, the rigid body modes are assumed to be separated from the total deformations at the local element level. In this paper a new co-rotational formulation is proposed based on the direct derivation of the inertia force vector and the tangent dynamic matrix. A closed-form equation is derived for the calculation of the inertia force, the tangent dynamic matrix, the mass matrix and the gyroscopic matrix. The new formulation is used to perform dynamic analysis of example tensegrity structures. The developed formulation is applicable to tensegrity structures with non-linear effects due to internal mechanisms or geometric non-linearities, and is applied to two numerical examples. The efficiency of the proposed approach is compared to the conventional Lagrangian method, and savings in computation of about 55%, 54% and 37% were achieved.     

Geometrical nonlinear elasto-plastic analysis of tensegrity systems via the co-rotational method

An efficient finite element formulation is presented for geometrical nonlinear elasto-plastic analyses of tensegrity systems based on the co-rotational method. Large displacement of a space rod element is decomposed into a rigid body motion in the global coordinate system and a pure small deformation in the local coordinate system. A new form of tangent stiffness matrix, including elastic and elasto-plastic stages is derived based on the proposed approach. An incremental-iterative solution strategy in conjunction with the Newton-Raphson method is employed to obtain the geometrical nonlinear elasto-plastic behavior of tensegrities. Several numerical examples are given to illustrate the validity and efficiency of the proposed algorithm for geometrical nonlinear elasto-plastic analyses of tensegrity structures.     

A necessary condition for stability of kinematically indeterminate pin-jointed structures with symmetry

Stability conditions are the key to transform kinematically indeterminate structures into prestressed structures or deployable structures. From the viewpoint of symmetry, a necessary condition is presented for the stability of symmetric pin-jointed structures with kinematic indeterminacy. The condition is derived from the positive definiteness of the quadratic form of the tangent stiffness matrix. Numerical examples verify that the proposed necessary stability condition is in accord with the conventional theory of structural rigidity, and is considered to be more comprehensible. It is robust and easy to implement. Results show that a symmetric prestressed structure is guaranteed to possess integral prestress modes, if the necessary condition is satisfied. Further, a pin-jointed structure with fully symmetric mechanism modes is proved to be unstable, if it does not satisfy the condition.     

Analysis of data on the relation between eddies and streaky structures in turbulent flows using the placebo method

An artificially synthesized velocity field with known properties is used as a test data set in analyzing and interpreting the turbulent flow velocity fields. The objective nature of this approach is utilized for studying the relation between streaky and eddy structures. An analysis shows that this relation may be less significant than is customarily supposed.     

Numerical approach for detecting bifurcation points of the compatibility paths of symmetric deployable structures

New internal mechanisms of a deployable structure could be generated, when the structure undergoes significant transformations along its compatibility path. Because of such kind of kinematic bifurcation, the structure might not transform into the desired configuration. To design novel deployable structures, it is necessary to detect all possible bifurcation points of the compatibility paths and study the bifurcation behavior. Here, on the basis of the nonlinear prediction–correction algorithm with variable increment size, we will propose an efficient approach to detect all the possible bifurcation points of the compatibility path for a symmetric deployable structure. Null space of the Jacobian matrix is studied iteratively, to follow the complete compatibility path. The variable increment size at each step is determined by evaluating whether the configuration is close to the singular configuration. Numerical examples of several 2D and 3D symmetric deployable structures are presented, to verify the feasibility and computational complexity of the proposed approach. The results show that the proposed method is computationally efficient, and could detect different bifurcation points of the compatibility path. Further, it turns out that all the analyzed symmetric structures experience kinematic bifurcation on certain conditions.     

A method of calculation of the optimal lectotype for complex structures

A practical method of calculation for the optimal lectotype of complex structures is presented in this paper. On the basis of the initial structural style and designing experience, a calculating model for the optimal lectotype is established. After approximate processing of the objective functions and constraint conditions, the lectotype problem is transformed into one for solving canonical quadratic programming based on the Kuhu-Tucker condition and Lagrange multiplier. Thus the calculating process will become simpler, more reliable and accurate by introducing the weighted factor and utilizing an improved variable metric method [1].I hereby express my thanks to ray students Shuang-Bei Li, Yi-Min Song and others for their valuable help in making the calculation.     

Numerical stability of the method of Brownian configuration fields

We investigate numerical aspects of the Brownian configuration fields method, and in particular its numerical stability as the Weissenberg number increases. Our results show the method to be immune to the type of instability leading to numerical blowup in the simulation of macroscopic models. We discuss this finding in the light of the stability criterion proposed in Fattal et al. [R. Fattal, R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg using the log-conformation representation, J. Non Newtonian Fluid Mech. 126 (2005) 23–37].     

A two-scale method for identifying mechanical parameters of composite materials with periodic configuration

In this paper, a two-scale method (TSM) is presented for identifying the mechanics parameters such as stiffness and strength of composite materials with small periodic configuration. Firstly, a formulation is briefly given for two-scale analysis (TSA) of the composite materials. And then a two-scale computation formulation of strains and stresses is developed by displacement solution with orthotropic material coefficients for three kinds of such composites structures, i.e., the tension column with a square cross section, the bending cantilever with a rectangular cross section and the torsion column with a circle cross section. The strength formulas for the three kinds of structures are derived and the TSM procedure is discussed. Finally the numerical results of stiffness and strength are presented and compared with experimental data. It shows that the TSM method in this paper is feasible and valid for predicting both the stiffness and the strength of the composite materials with periodic configuration.The project supported by the Special Funds for Major State Basic Research Project (2005CB321704) and the National Natural Science Foundation of China (10590353 and 90405016). The English text was polished by Yunming Chen.     

平面梁杆结构几何非线性分析的一种简便方法

本文提出了一种新的几何非线性分析方法，适用于结点位移任意大，单元刚体转角任意大、单元局部弯曲比较小的平面梁杆结构。文中的刚度矩阵和附加荷载列阵都是以显式形式给出的，可直接应用。     

A method for the identification of dynamic constraint parameters in multi-supported flexible structures

In this paper, a new method for identifying the dynamical parameters of local constraining supports such as mass, stiffness, and damping was developed through combining the measured frequency transfer functions and structural modification techniques. Since measurement noise often leads to erroneous identifications, regularization techniques have been implemented to reduce noise amplification in the inverse problem. The developed technique has been validated by numerical tests on a multi-supported flexible structure, which can be seen as an idealized electricity generator rotor shaft. The results are satisfactory for noise-free data as well as under realistic noise levels. The sensitivity of the identified support features to noise levels is asserted through a parametric study     

周期结构后屈曲新算法及其应用

提出了周期结构后屈曲分析的一种新算法。在屈曲点附近,通过加载模型和诱导后屈曲边值问题之间的相互切换,避开屈曲点附近刚度矩阵的奇异性,并诱导结构产生预期的后屈曲变形,避免了以往后屈曲算法中引入几何初始缺陷后对系统带来的可能影响。通过对三种由超弹性材料所构成的周期孔隙结构的后屈曲分析,验证了本文所提出的后屈曲算法的有效性和灵活性。分析了周期孔隙材料多向加载对屈曲模式转换的影响,以及后屈曲变形对弹性波传播带隙的影响,为周期结构中弹性波传播的调控提供良好的基础。     

一种空间缆索结构静力分析的解析元法

将空间缆索结构简化为具有拉伸刚度的质点系,给出了缆索结构空间解析元法的基本方程和求解方法,单元间的作用力与坐标变化的关系可以用解析法得到,对所得到的反映结构特性的质点系方程组进行力的平衡迭代,求解方程组.采用自动的动态可变步长的迭代方法,能够提高计算效率,保证收敛.这种方法既考虑了几何非线性,又适用于材料非线性的计算,比有限元法优越之处还在于,它不用求解线性方程组,所以适用范围广,允许求解多自由度的几何可变体系,而有限元法在求解此类问题时经常不收敛.     

各向异性非均质梁截面特性计算的映射法

Ｇｉａｖｏｔｏ建立了确定各向异性梁截面特性和翘曲函数的二维有限元法。在此基础上，本文建立了一种映射法。在利用Ｇｉａｖｏｔｏ方法计算得某一具体截面的特性和翘曲函数后，与该截面具有相同形状不同尺寸的任意截面的特性和翘曲函数可用该截面的相应量通过显式确定，使计算大为简化。     

A model identification method of vibrating structures from incomplete modal information

ＡＭＯＤＥＬＩＤＥＮＴＩＦＩＣＡＴＩＯＮＭＥＴＨＯＤＯＦＶＩＢＲＡＴＩＮＧＳＴＲＵＣＴＵＲＥＳＦＲＯＭＩＮＣＯＭＰＬＥＴＥＭＯＤＡＬＩＮＦＯＲＭＡＴＩＯＮＺｈｅｎｇＸｉａｏｐｉｎｇ（郑小平）ＹａｏＺｈｅｎｈａｎ（姚振汉）ＱｕＳｈｉｓｈｅｎｇ（蘧时胜）...     

混凝土类材料SHPB实验中确定应变率的方法

由于混凝土类材料在SHPB实验中很难实现恒应变率加载,为了确定非恒应变率加载下的实验数据所对应的应变率,本文中针对不同强度(C20,C45,C70)和不同钢纤维含量(0%,0.75%,1.50%,4.50%)的混凝土进行了SHPB实验。对实验得到的30组恒应变率加载下的数据进行了分析总结,结果表明:实验数据所对应的恒应变率与全段平均应变率之间存在一定的比值关系,从而混凝土类材料SHPB实验数据所对应的应变率可以采用全段平均应变率的1.38倍来表征。通过对比非恒应变率加载和恒应变率加载下得到的应力应变曲线,验证了该确定应变率方法的合理性,并指出较短恒应变率加载下实验数据对应的应变率直接采用短平台段对应的应变率来表征是不合理的。     

Theory of the influence of changes in salt concentration on the configuration of intrinsically curved, impenetrable, rod-like structures modeling DNA minicircles

DNA molecules in the familiar double helical B form are treated here as though they have rod-like structures obtained by stacking the nearly planar base pairs comprising them one on top of another with each rotated by approximately one-tenth of a full turn with respect to its immediate predecessor in the stack. As each base in a base pair is attached to the sugar-phosphate backbone chain of one of the two DNA strands that have come together to form the Watson-Crick structure, and each phosphate group in a backbone chain bears one electronic charge, two such charges are associated with each base pair. Thus, each base pair is subject to not only the elastic forces and moments exerted on it by its neighboring base pairs but also to electrostatic forces, of sequentially remote origin, that, because they are only partially screened out by positively charged counter ions, can render the molecule's equilibrium configurations sensitive to changes in the concentration of salt in the medium. As there are cases in which, even though the intramolecular electrostatic forces of repulsion are strong, the distance of closest approach has value equal to that of the impenetrable diameter of the molecule, the theory presented here takes into account self-contact. Examples are given of cases in which the theory predicts that the radius of gyration of the minimum energy configuration of a small (549 base pair) circularized DNA molecule (called a “DNA minicircle”) has a remarkably strong dependence on the salt concentration.     

不确定结构时域响应分析的多项式维数分解法

针对具有不确定参数结构,提出时域不确定性传播和量化的多项式维数分解法,确定了结构响应统计量的演变过程.首先,采用参数概率模型来描述结构参数的不确定性,建立结构动力学方程,将结构响应表达为不确定参数的函数;进一步,将所关心的结构响应采用成员函数进行维数分解,并利用正交多项式基底对成员函数进行Fourier展开;最后,应用降维积分方法进行展开系数的求解,给出了响应均值和标准差的计算表达式.在数值算例中,将本文方法与蒙特卡洛方法进行对比,结果表明所建立方法具有较高的求解效率和计算精度.     

张拉结构非线性分析的五节点等参单元

本文针对张拉结构的特点，提出了一种五节点等参数单元有限元模型，采用四次多项式作为位移插值函数及单元初始形状函数，并假定索是理想柔性的且满足虎克定律，基于修正的Ｌａｇｒａｎｇｉａｎ坐标描述法，建立了非线性有限元基本方程和切线刚度矩阵，利用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法进行了实例计算。结果表明：本文方法精度极高，可供大跨度索网，索穹顶，拉线塔等张拉结构分析，设计时采用。