Stability Conditions for Brittle-Plastic Structures with Propagating Damage Surfaces∗

The incremental problem for a brittle-plastic body is considered for which stable propagation of a damage interface occurs within the material. The stability conditions are derived and applied to several simple illustrative examples.     

Principle of analysis of brittle-plastic rock mass

Based upon Il’yushin’s postulate and the plastic potential theory, a procedure for calculating the abrupt change in stresses from the peak strength surface to the residual strength surface is proposed. The stability criterion for a brittle-plastic body loaded proportionally is presented. Finally, three examples have been solved analytically and numerically, including an engineering example of the steep rock slope of a shiplock system for the Three Gorges hydroelectric power project in China.     

粉砂岩峰后破坏区应力脆性跌落的试验和本构方程研究

对粉砂岩试样进行常规三轴压缩试验,得到了其在不同围压下的应力-应变全程曲线.结果表明,岩样应力-应变曲线峰前(破坏前区)部分的力学性质较为稳定,其力学行为可用经典强度理论进行描述;应力-应变曲线峰后(破坏后区)部分,岩样处于非稳定状态,其力学行为难以用经典强度理论来描述,而脆塑性模型恰好可以描述试验岩样的应力非连续变化特征.岩石的应力脆性跌落是有条件发生的,应力脆性跌落系数是围压的函数,并给出应力脆性跌落系数与围压的关系.对完整岩样而言,使用弹性-线性软化-残余塑性三线性非理想脆塑性模型可以描述岩样的本构特征,而对含有节理岩样而言,采用双线性弹性-线性软化-残余塑性四线型非理想脆塑性模型与试验更为相符.     

结构随机动力稳定性的定量分析方法

提出了结构随机动力稳定性的定量分析方法,讨论了经典的随机动力稳定性概念,指出结构动力稳定性不仅与结构参数有关,也与作用在结构上的外部载荷密切相关,据此引入了一种判定结构动力稳定性的新准则,明确了结构随机动力稳定性的基本涵义.在概率守恒原理基础上,推导了概率耗散系统的广义概率密度演化方程.引入结构动力失稳的物理机制作为引起概率耗散的驱动力,利用概率耗散系统概率密度演化方程、可以方便获得结构响应的概率密度演化过程,从而定量求解结构的动力稳定概率.据此,可以定量评价结构系统依概率为1或依给定概率意义上的结构随机动力稳定性.采用本文所建议方法对典型结构动力系统进行了随机动力稳定性分析,并与蒙特卡洛方法计算结果进行对比.数值结果表明了所建议方法的有效性.      

Stability conditions of prestressed pin-jointed structures

Pin-jointed structures are first classified to trusses, tensile structures, and tensegrity structures in view of their respective stability properties. A sufficient condition for stability of an equilibrium state is derived for tensegrity structures. The condition is based on the bilinear forms of the linear and geometrical stiffness matrices considering the flexibility of members. The stability is defined by the positive definiteness of the tangent stiffness matrix, whereas the definition of prestress-stability is based on the geometrical stiffness matrix and the infinitesimal mechanisms. Numerical examples verify that the so-called super-stability condition might not be satisfied by a stable tensegrity structure, and that a prestress-stable structure can be unstable if the prestresses are moderately large.     

MULTI-SCALE STRUCTURES IN EMULSION AND MICROSPHERE COMPLEX SYSTEMS

Multi-scale structures involved in emulsion and microsphere complex systems are presented and discussed. The stability and spatio-temporal structures of emulsions, as well as nano-structures formed on the surface of microspheres after polymerization, are affected by the molecular emulsifier/stabilizer structures and the adsorbed emul-sifier/stabilizer nano-structures on the oil/water interface. The broad size distribution and variation of surface features of droplets are responsible for variations of the adsorbed emulsifier/stabilizer structures and the stability of the emulsions. On the other hand, preparation of a uniformly sized emulsion and employment of a combined emulsifier/stabilizer system can preserve the stability of the emulsions and microspheres. The above phenomena should be modeled by a multi-scale method, In order to maintain the stability of individual emulsion systems and realize the desired nano-structures of microspheres by choosing adequate emulsifier/stabilizer and experimental parameters.     

考虑稳定性约束的五零能模式材料结构设计方法研究

五零能模式材料是一种声学超材料,虽然它一般采用固体材料设计,并且单胞常应用微桁架构型,但理论上这种材料设计的结构是不稳定的。本文从分析设计结构整体出发,探讨一种通过施加预载荷,确保五零能模式材料结构稳定性的方法,并给出了保证结构稳定性的充分条件,且应用典型的五零能模式材料单胞构型加以验证。同时,为方便提出的稳定性条件在设计过程中的实施,将五零能模式材料结构的设计过程描述为五零能模式材料的变换过程,采用结构尺寸优化模型来描述。当材料单胞为微桁架构型时,这一结构尺寸优化模型简单,结构稳定性约束和五零能模式材料性质约束均为线性约束。     

A novel robust design method for improving stability of optimized structures

It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability of optimized structures. A new approach is proposed, in which certain perturbation loads are introduced and the corresponding compliance is added to the objective function as a penalization. The stability of the optimized structures can thus be improved substantially by considering structural responses to the original and the introduced loads. Numerical examples show the simplicity and effectiveness of the proposed method.     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

开孔结构的稳定性分析及其应用

缺陷对结构稳定性的影响是直接与结构失效分析有关的重要课题．本文把板壳结构中存在的孔洞作为一种几何缺陷,简述了开孔柱壳非线性分析的理论、变分原理、有限元方法及其对稳定性分析的应用．考察了孔洞的存在对轴压柱壳临界载荷的影响      

Fast approximations of dynamic stability boundaries of slender curved structures

Curved beams and panels can often be found as structural components in aerospace, mechanical and civil engineering systems. When curved structures are subjected to dynamic loads, they are susceptible to dynamic instabilities especially dynamic snap-through buckling. The identification of the dynamic stability boundary that separate the non-snap and post-snap responses is hence necessary for the safe design of such structures, but typically requires extensive transient simulations that may lead to high computation cost. This paper proposes a scaling approach that reveals the similarities between dynamic snap-through boundaries of different structures. Such identified features can be directly used for fast approximations of dynamic stability boundaries of slender curved structures when their geometric parameters or boundary conditions are varied. The scaled dynamic stability boundaries of half-sine arches, parabolic arches and cylindrical panels are studied.     

桁架结构稳定分析的几何非线性欧拉稳定理论

目前,桁架结构稳定分析有两个理论:经典的特征值理论和几何非线性临界点理论。前者发展较早,在许多结构力学书中都有叙述。但是经过工程应用检验,它过高地估计了结构抗稳定的能力。后者是20年前提出的,提出者认为适用于所有的扁桁架。经过几年的研究,作者连续提出三个稳定理论:线性与非线性欧拉理论;非线性临界点-欧拉理论和两个计算方法,进行桁架结构的线性和非线性截面优化设计。经过理论研究和对前人文献中数值例题的计算和比较,发现特征值理论不符合实际,临界点理论只适用于大扁度的桁架,而不适用于一切扁桁架。研究结果提供了若干有用的结论,给出了各种稳定理论的适用范围,指出了国际文献中若干例题的正确和错误,补充了桁架结构的稳定分析理论,使之更为完整和实用了。     

高层筒体结构整体稳定及二阶位移分析的改进条元法

根据柱壳理论,构造了一种柱壳曲条,本文结合柱壳曲条和平壳条元求解高层筒体结构的整体稳定及二阶位移。采用三次H erm ite插值函数模拟条元横截面的翘曲位移变化,能较好地反映筒体受力“剪切滞后”效应;采用一族能较好地逼近弯剪型变形曲线的正交多项式作基函数来描述位移沿竖向变化。用最小势能原理建立稳定及二阶位移分析方程。该方法适用于任意平面形状的高层建筑筒体结构及剪力墙结构的稳定及二阶位移分析。与其它方法相比,该方法具有精度高、通用性强、计算量小等优点。     

Symmetric prismatic tensegrity structures: Part I. Configuration and stability

This paper presents a simple and efficient method to determine the self-equilibrated configurations of prismatic tensegrity structures, nodes and members of which have dihedral symmetry. It is demonstrated that stability of this class of structures is not only directly related to the connectivity of members, but is also sensitive to their geometry (height/radius ratio), and is also dependent on the level of self-stress and stiffness of members. A catalogue of the structures with relatively small number of members is presented based on the stability investigations.     

Dihedral ‘star’ tensegrity structures

This paper presents conditions for self-equilibrium and super stability of dihedral ‘star’ tensegrity structures, based on their dihedral symmetry. It is demonstrated that the structures are super stable if and only if they have an odd number of struts, and the struts are as close as possible to each other. Numerical investigations show that their prestress stability is sensitive to the geometry realisation.     

RBF collocation method and stability analysis for phononic crystals

The mesh-free radial basis function (RBF) collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric (MQ), Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs. The choice of the shape parameter and the effects of the knot number are presented.     

Towards a Cosserat-theory describing motion of an originally rectangular structure of blocks

A continuum theory predicting the static stability and the on-setting motion of certain kinds of block structures in a realistic manner, can only by established using a Cosserat-approach. In former papers only the static stability of a very restricted group of such structures was treated. New results of this type and, additionally, multi-body-simulations and an appropriate Cosserat-model for plane systems is presented and discussed.     

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.     

Secondary Instabilities of Wakes of a Circular Cylinder Using a Finite Element Method

This study investigates secondary instabilities of periodic wakes of a circular cylinder with infinitely long span. It has been known that after the wake undergoes a supercritical Hopf bifurcation (the primary instability) that leads to two-dimensional von Kantian vorlex street, the secondary instability occurs sequentially, which results in the onset of three-dimensional flow. Williamson (1996) has reviewed that the periodic wakes over a range of moderate Reynolds number from 140 to 300 are characterized by two critical modes. Mode A and Mode B, which are respectively associated with large-scale and fine-scale structures in span. In order to understand a sequence of bifurcation in transitional wake, in this paper, the stability of periodic Row governed by the linearized Navier-Stokes equations is analyzed by using the Floquet stability theory. By employing the finite elemental discretization with a fine mesh, the numerical results for both simulation and stability analysis have high spatio-resolution. The obtained stability results are in good agreement with experimental data and some relevant numerical results. By means of visualizations of the three-dimensionally critical flow structures. the existence of Mode A and Mode B is verified from the spatial structures in both the two modes.     

A catastrophic model for vibrational buckling of elastic arches

This paper represents an attempt at the application of catastrophe theory to thedynamic stability of engineering structures.The authors not only obtain a catastrophicmodel of vibrational buckling of elastic arches,but also give the critical condition of losingstability.