Reliability based limit design of steel frames with limited residual strain energy capacity

The aim of this paper is to take into consideration the influence of the limited load carrying capacity of the connections on the plastic limit state of elasto-plastic steel (or composite) framed structures under multi-parameter stochastic loading and probabilistically given conditions. In addition to the plastic limit design to control the plastic behaviour of the structure, bound on the complementary strain energy of the residual forces is also applied. This bound has significant effect for the load parameter. If the design uncertainties (manufacturing, strength, geometrical) are expressed by the calculation of the complementary strain energy of the residual forces a reliability based extended limit design problem is formed. The formulations of the problems yield to nonlinear mathematical programming which are solved by the use of sequential quadratic algorithm. The bi-level optimization procedure governed by the reliability index calculation. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reliability based limit analysis of steel frames with limited residual strain energy capacity

The main structural elements of steel framed multi–storey structures are the columns, the beams and their connectionsmagenta, which can be considered rigid, pinned or semi–rigid. The aim of this paper is to analyze the effect of the semi–rigid connections on the limit analysis of steel structures under multi–parameter static loading where to control the plastic behavior of the structure a bound on the complementary strain energy of the residual forces is applied. The bound value is assumed to be uncertain and is modelled by a random variable. By the use of this constraint a reliability based problem formulation is constructed. The formulation of the problem yields a nonlinear mathematical programming with a nested algorithm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

随动强化材料壳体的安定分析

在循环加载下壳体结构的安定分析,特别是对于具有应变强化的材料制成的壳体结构的安定分析具有很大的实际意义.文中对随动强化材料的安定定理有了进一步的认识并应用它去分析壳体结构的安定载荷.对于一个真实状态其残余应力与塑性应变之间是相关的.但我们在定理中所示的与时间无关的残余应力场(σ_ijr)和与时间无关的几何容许的塑性应变场(σ_ijp)可以是不相关的.明确指出这点对于工程应用带来很多方便,否则将是十分困难的.为此还给出了该定理的新的证明方法.我们还应用了上述定理对一个半球封头的圆柱壳体进行了安定分析.根据所求得的弹性解,各种可能的残余应力和塑性应变分布,结构的安定分析可归结为一个数学规划问题.计算结果表明应变强化材料的安定载荷要比理想塑性材料的安定载荷高出30～40%,这说明在安定分析中考虑材料强化是重要的,可使壳体结构的设计承载能力有相当大的提高,同时对改进目前壳体结构的设计提供了科学依据.     

The influence of semi-rigid connections on the shakedown of elasto-plastic frames

The main structural elements of steel framed multi-storey structures are the columns, the beams and their connections. The assumption has been widely applied in the past that the connections are either rigid or pinned. The actual behaviour of the connections is however somewhere between these limits, they are semi-rigid. The aim of this paper is to analyze the effect of the semi-rigid connections on the shakedown of steel structures under multi-parameter static loading. In the analysis, to control the plastic behavior of the structure, bound on the complementary strain energy of the residual forces is applied. The formulation of the problem yields to nonlinear mathematical programming. The results of the numerical calculation show that the semi-rigid connections can influence significantly the magnitude of the shakedown parameter. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Integrated process for structural–topological configuration design of weight-reduced vehicle components

Due to the speedy development trends of design stages, the material distributions and geometric configurations in view of the weight-reduction design of structures are the details taken into account from the stage of conceptual design with low cost, high performance and quality. In this point, a structural–topological configuration with a feasible design of structure is important. This paper presents the integrated process using three optimization techniques, in which the geometric boundaries and physical dimensions of the structure and material distribution of structure-configured elements are hierarchically optimized in the specifications of the maximum rigidity, plastic strain, residual deformations and lightweight.     

非协调有限元的全塑性分析

本文采用满足相容条件的非协调有限元模型以解决全塑性分析中有限元解的数值精度问题.文中讨论了该模型适用于全塑性分析的机理和判据,还设计了一个确定塑性极限载荷的算法.     

The effect of microdamage on fatigue-crack growth

The theory of fatigue-crack growth, based on a synthesis of fracture mechanics and continuum mechanics of microdamage accumulation, is applied to the problem of crack growth under cyclic loading, taking into account the plastic deformations in the tip zones. The model of a thin plastic zone, which is a region of considerable plastic deformations at the crack tip, is supplemented by taking into account the effect of microdamage on the value of the specific fracture work and the limit stresses in the tip zone. Governing equations which describe fatigue-crack growth taking these factors into account are derived. The effect of the material characteristics and the load parameters on the growth rate and the distribution of microdamage in the tip zone and on its extensions is investigated by a computational experiment. Particular attention is given to the initial stage when crack growth may occur abruptly and the growth rate depends substantially on the initial conditions     

Optimal plastic design for partially pressigned strength distribution

The optimal plastic design of structures having a partially predefined strength distribution is considered. Sufficient conditions for optimality as well as upper and lower bounds on minimum structural volume are established and examples involving a continuous beam and a grillage are given. It is shown that most existing theories for optimal plastic design and limit analysis can be derived from the optimality criteria presented.     

An extended sequential limit analysis based on moving coordinates for pressurized spherical cap membranes with large shape change

Sequential limit analysis (SLA) is an effective and normally used method to calculate the plastic limit load of structures with large deformation. However, attribute to the assumption of neglecting the changing behavior of shape and plane stress direction, the conventional SLA method would be inaccurate in the plastic response prediction for the large-shape-change structures, especially for the pressurized spherical cap. This research develops a novel analytical model for the pressurized spherical cap based on the advanced SLA method, which features introducing the moving coordinate system and considering of the changing behavior of shape and plane stress direction into the conventional method. With the proposed method, the effects of geometry and material parameters on the plastic limit load are analyzed. Compared with the validating FE simulation results of ABAQUS software, the newly extended SLA method performances a more precise prediction of the load deflection response and plastic limit load than the normal one. Due to the limit yield degree and bending moment, the accuracy of the new model will increase with the increase of yield strength and radius. The larger the initial deflection of the pressurized spherical cap is, the smaller the relative error between the analysis results of advanced SLA and FE method is. Moreover, this newly proposed SLA remains effective and accurate within a wide range of the initial thickness-curvature radius ratio, especially for low elasticity modulus materials.     

矩形网格扁壳结构的非线性弹性理论

本文在基本假设的前题下,分析了矩形网格离散结构的变形以及变形量与内力之间的本构关系.在此基础上,通过建立等级模型,运用虚功原理推导出网格扁壳的作线性基本控制方程与边界条件.     

Die rotationssymmetrische dünne Zylinderschale aus ideal-plastischem Material

Summary II. In the second part of this paper post-elastic deformations of an elastic-plastic cylindrical shell are considered. For the relatively simple case of an infinite shell subjected to a ring force the various phases accompanying the settling of plastic deformations are discussed in detail. It is shown by numerical treatment of the exact differential equations that the deformations remain small in the elastic-plastic phase up to more than 90% of the exact collapse load predicted by the rigid plastic analysis, but that nevertheless they tend to infinity as this collapse load is approached.

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I. Teil s. ZAMP19; 185 (1968).     

Design of novel morphing structures based on bistable composites with piezoceramic actuators

Instead of attempts to avoid the large out-of-plane deformations of multilayered fiber-reinforced composites caused by residual stresses, these deformations can be advantageously used for technical applications such as novel morphing structures, where only a discontinuous energy impulse of an actuator is necessary to change the configuration of the structure. For the design of such innovative morphing structures with piezoelectric actuators, novel nonlinear semi-analytical and numerical simulation models have been developed and verified experimentally. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 475–494, July–August, 2006.     

An iterative elastic SBFE approach for collapse load analysis of inelastic structures

The paper proposes a novel numerical approach that incorporates the use of a modified elastic compensation method, within a polygon scaled boundary finite element framework, to determine the maximum load capacity of structures at plastic collapse. The distinctive feature of the proposed scheme is its effective computational ability in performing a series of successive elastic analyses by systematically adjusting elastic material properties of structures up to failure. The quadtree structural discretization within a polygon scaled boundary finite element platform enables model construction of sophisticated geometries at modest computing effort and thus the effective analysis of large-scale structures. The approach overcomes the challenges associated with stress singularity and locking phenomena under incompressibility conditions, even in the presence of high-order nonlinear yield loci. The robustness and accuracy of the proposed scheme are validated through a number of benchmarks and available practical engineering applications in 2D and 3D spaces. These illustrate the influences of some key algorithmic parameters, and the satisfaction of a lower-bound limit given by the present analysis method for a sufficiently fine discretization.     

超静定桁架在多工况下的满应力设计(Ⅰ)

本文研究无病态杆的超静定桁架的杆数、自由度数和实现满应力的工况数之间的关系.文中不仅修正了R.H.Gallagher等人的结论,而且阐述了对工况性态(数目、大小和方式)的选择条件.指出某些反例恰恰是违背工况选择原则的后果.     

A phenomenological method of calculating the residual stresses and plastic deformations in a hollow surface-hardened cylindrical sample

A phenomenological method is proposed for calculating the residual stress and plastic deformation fields in a hollow surface-hardened cylindrical sample. Versions of the hardening are considered that lead to isotropy and anisotropy in the plastic deformations in the surface layer. A hardening anisotropy parameter is introduced that relates the axial and circumferential components of the residual plastic deformation tensor. The experimentally determined axial and/or circumferential components of the residual plastic stress tensor are used as the initial information. The tensor fields of the residual stresses and deformations are constructed assuming the hypothesis of surface hardening anisotropy and the absence of secondary plastic compression deformations and that the tangential components of the residual stress tensor and the plastic incompressibility of the material are small. A technique is developed for identifying the parameters of the proposed method. The adequacy is checked using experimental data for test pieces of type 45 and 12X18H10T steels hardened by hydro-shot blasting treatment and of type 45 steel hardened by treatment with a roller. Good agreement is observed between the calculated and experimental results. It is noted that the anisotropic hardening procedure leads to a substantial difference between the circumferential and axial components of the residual stresses in the hardened layer, unlike the case of isotropic hardening where they are practically identical.     

Initial stage of plastic exfoliation of a rectangular inclusion under conditions of one-sided contact with a medium

We investigate the initial stage of quasistatic development of plastic deformations in the vicinity of the tips of a rigid rectangular inclusion whose pair of faces do not contact with a medium. Deformation is caused by shear forces that act at infinity in parallel with this pair of faces of the inclusion. The cases of plastic deformations localized in bands that develop from the tips of the inclusion and distributed continually are investigated. The characteristics of plastic zones for loads much smaller than the yield strength are obtained.     

有限变形的极限分析定理

本文建立了有限变形的极限分析的变分原理(定理1),证明了它与有限变形的极限分析的全套方程和条件等价.本文又证明了:根据此变分原理求得的有限变形的极限载荷乘子,介于有限变形的极限分析的上限定理和下限定理所分别给出的上限解和下限解之间.     

塑性极限分析的不可微模型及其光滑化算法

藉助于凸规划的Lagrange对偶理论,建立了Mises屈服条件下理想刚塑性材料Hill最大塑性功原理的对偶问题,并据此建立了极限分析的一个不可微凸规划模型．该模型不仅避免了对屈服条件的线性化,而且其离散化形式为线性约束下Euclid模之和的极小化问题．针对Euclid模的不可微性,提出理想刚塑性体极限分析的一种光滑化算法．通过计算平面应力和平面应变问题的极限荷载因子和相应的坍塌机构,验证了算法的有效性．     

热荷载作用下薄板的优化设计

板壳结构是一大类广泛使用的结构元件.在热荷载作用下,当热膨胀受到约束时,板壳结构产生内力及挠度,严重时影响结构的正常服役.由于热荷载的特殊性,简单地均匀加大板壳结构的厚度并不能有效地减少热变形和热应力,热结构设计因此特别困难.该文研究在给定材料体积的条件下,通过优化板壳结构的厚度分布来减少弹性薄板结构在热载荷下的变形.以结构的变形能为优化目标,在给定材料体积的条件下,建立了设计板壳结构厚度分布的优化问题列式,并采用变分法,推导出优化准则,给出了修改厚度的迭代公式.应用商用有限元软件的热结构分析功能,对程序进行二次开发,从而实现该优化算法.算例结果表明,采用该方法优化弹性薄板的厚度分布,可以大幅度地减小结构热变形,是一种有效的热结构设计方法.     

Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material

Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening.