索穹顶结构的找力分析方法--不平衡力迭代法

索穹顶的刚度和承载能力都是通过施加预应力来获取的,预应力设计是对索穹顶进行任何其它分析的基础,所以它的找力分析(Force finding)是一项很重要的工作。本文提出一种找力分析方法———不平衡力迭代法,它可以克服整体可行预应力法的一些不足:即使在索穹顶构件分组发生错误时仍可找到满足已知形状的预应力分布,并且该方法具有良好的稳定性和运算效率,算例表明不平衡力迭代法非常适合大型复杂索穹顶结构的找力分析。     

Nonlinear long-term behaviour of spherical shallow thin-walled concrete shells of revolution

The nonlinear long-term buckling behaviour (creep buckling) of spherical shallow, thin-walled concrete shells of revolution (including domes) subjected to sustained loads is investigated herein. A thorough understanding of their nonlinear time-dependent behaviour, as well as the development of comprehensive analytical models for their analysis, has hitherto not been fully established and further studies are required. A nonlinear axisymmetric theoretical model, which accounts for the effects of creep and shrinkage, and which considers the ageing of the concrete material and the variation of the internal stresses and geometry in time, is developed for this purpose. The governing field equations are derived using variational principles, equilibrium requirements, and integral-type constitutive relations. A systematic step-by-step procedure is used for the solution of the integral-type governing equations. First, the nonlinear short-term behaviour is studied to provide a benchmark for the long-term analysis. Different theories for the analysis of the shell structure are examined for this purpose and compared with results obtained by the finite element method. A numerical study, which highlights the capabilities of the nonlinear theoretical model and which provides insight into the nonlinear long-term behaviour of shallow concrete domes, is presented. The results show that long-term effects are critical for the design and structural safety of shallow, thin-walled concrete domes, and so these effects need to be fully understood and quantifiable.     

Damage model and damage assessment for single-layer reticulated domes under exterior blast load

Long-span reticulated dome is often considered as a landmark building of a region, so it is very important to investigate the dynamic response and propose the damage assessment method of reticulated dome under blast loading. In this article, a fine finite element model of Kiewitt8 (K8) single-layer reticulated dome was established by using ANSYS/LS-DYNA. The effects of standoff distance, charge weight, rise–span ratio, span, and roof weight on the responses of K8 single-layer reticulated dome were numerically studied. The results showed that the blast-resistant performance of reticulated dome with smaller rise–span ratio and larger span under exterior blast load was more advantageous. Although the blast-resistant capacity of reticulated dome with large span and large roof weight was favorable, the plastic deformations of reticulated dome members were small and the utilization of material was low at failure state. According to the dynamic response characteristics of plentiful K8 single-layer reticulated domes at different damage levels, a damage model of K8 single-layer reticulated dome under exterior blast load was proposed in this article to indicate the damage level and determine the ultimate strength. Besides, a new damage criterion for K8 reticulated dome was also defined. This damage model was defined based on the physical phenomena at different damage levels, which made the strength failure criterion had definite physical meaning. Using the proposed damage criterion and a new search algorithm for pressure and impulse, the pressure–impulse diagrams for the typical K8 reticulated dome were derived from the numerical simulations to evaluate the damage level of reticulated dome under blast loading. Finally, a method to determine the safety standoff distance for reticulated dome under given TNT charge weight was also proposed.     

冲击荷载下单层球面网壳的失效机理

为研究单层球面网壳在冲击荷载下的失效机理,在ANSYS/LS-DYNA中建立60m跨度K8型单层球面网壳与圆柱形冲击物的数值模型并进行数值分析,总结了网壳结构的4种失效模式。通过对失效全过程的分析,从能量的角度将失效过程分为能量施加、能量传递与损失、能量消耗3个阶段。之后分别从能量传递与杆件破坏形式2方面揭示了网壳的失效机理。能量分析表明:剩余能量(Elf)对结构最终动力响应及失效模式起决定作用,而Elf只是初始冲击能量中除去冲击物穿透损失与网壳局部破坏损失后的剩余部分。通过对杆件破坏形式的分析发现:杆件的破坏可能滞后于冲击荷载的作用,且杆件的破坏形式决定其传递能量的能力,当杆件发生拉伸破坏时,其强度被充分利用,传递的能量最多,Elf值较大,网壳整体破坏严重。杆件的破坏形式与Elf及网壳整体的失效模式间有很好的对应关系。     

复合材料层合板蠕变屈曲与变形的优化问题

将瞬时弹性失稳荷载、持久临界荷载和后屈曲持久变形刚度作为复合材料层合板蠕变屈曲与变形的优化指标,对几组纤维铺设方式进行讨论,构造多目标优化模型,就纤维铺设角进行优化分析.考虑横向剪切变形效应,分别利用Lap lace变换和准弹性方法,导出了这三个优化指标的计算公式.     

Bistable characteristics of thick-walled axisymmetric domes

We apply a finite element analysis to examine the stability of spherical, thick-walled domes undergoing large deformation. We identify three energetic states, mono-stable, bi-stable, and pseudo-bi-stable that uniquely characterize the behavior of the dome during deformation. An empirical relation is developed using finite element simulations relating the stability of the dome to pertinent geometric parameters like height, length and thickness, which is verified experimentally. Using this relation, similar domes can be designed to have desired stability characteristics.     

Axisymmetric deformation of plates and shells with phase trasformations under thermal cycling

A mathematical formulation is given of nonlinear axisymmetric buckling problems for plates and shells in the two-phase zones of austenite-to-martensite transformation. Numerical solutions of the direct-and inverse-transformation problems are used to construct hysteresis loops for thermomechanically cycled, pressure-loaded circular plates and shallow spherical domes of titanium nickelide (NiTi) alloy. It is shown that dynamic instability of the dome deformation process can occur during transformation under loads notably lower than the upper critical values for the isothermal states of the material outside the transformation zone. A theoretical analysis gives external loads below which the dome remains stable in the thermally cycled material with phase transformations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 204–210, March–April, 2008.     

A New Six-axis Load Cell. Part I: Design

A new high precision six-axis load cell is presented in two companion papers. The first paper (this one) is focused on the presentation of the load cell, the conceptual design, the modelling and the embodiment design. The second paper refers to the error analysis, the construction and the experimental assessment of the performances. The new load cell is able to measure the three components of both a force and a moment acting on the load cell itself. The sensing structural element of the six-axis load cell is basically a three spoke structure. Strain gauges are conveniently located on highly stressed areas. The sensing structural element is constrained to the frame of the load cell by means of special joints conceived to avoid friction. The mechanical behaviour of the load cell is described by means of analytical equations that allow a quick preliminary design focused on the given technical specifications. A finite element model has been used to asses the mechanical behaviour of the load cell.     

Optimal Design of Viscoelastic Structures under Forced Steady-State Vibration

ABSTRACT

ABSTRACT With minimum dynamic response as the design criterion, we derive by means of variational analysis a general set of equations governing optimal design of one-dimensional, viscoelastic structures acted on by harmonically varying external loading. The equations are specialized to problems of minimizing transverse vibrational response of beams by attaching optimal, nonuniform cover layers made of a solid, viscoelastic material on the beams. Several numerical solutions to such problems are presented.     

移动载荷作用下浮冰的非线性动力学响应

本文考虑非线性、惯性和阻尼的影响, 研究了任意深度二维理想流体顶部浮冰的振动. 对相关的拟微分算子进行展开并将非线性项保留至三阶后, 完全非线性问题被简化为仅与自由面上的变量相关的三阶截断模型. 为了验证简化模型的准确性, 重点关注了自由孤立波解. 在不考虑阻尼的情况下, 采用多重尺度方法推导了三阶非线性薛定谔方程(NLS), 利用该方程预测了任意水深下原始欧拉方程中自由波包型孤立波解的存在性及三阶截断模型的准确性. 相比于Dinvay等所提出的二阶模型, 三阶截断模型的优势在于其对应的三阶NLS具有准确的非线性项系数, 能够在最小相速度附近更好地模拟冰层的动力学响应. 进一步地对自由孤立波解进行数值计算, 数值结果表明三阶截断模型在分岔曲线和孤立波波形上均与完全欧拉方程吻合良好, 准确性高于二阶截断模型. 基于三阶截断模型, 探究了匀速局域化载荷作用下的浮冰非线性动力学响应并将时间依赖解与实验测量数据进行比较, 数值计算结果与实验记录吻合良好.      

FULLY STRESSED DESIGN OF A SUPERSTATIC TRUSS WITH MULTIPLE LOADS(Ⅰ)

In this paper,we study the relationship between the number of redundant forces and the number of load conditions in a super-static truss without sick members in order to accomplish fully stressed design.This paper will not only improve the conclusion given by R.H.Gallagher et al.,but also clarify the choice of load conditions(number,magnitude and form).Moreover,it will explain that some counter-examples in literatures are invalid.     

基于Boussinesq方程的波浪模型

从欧拉方程出发,提供了另一种推导完全非线性Boussinesq方程的方法,并对方程的 线性色散关系和线性变浅率进行了改进. 改进后方程的线性色散关系达到了一阶Stokes波 色散关系的Pad\'{e}[4,4]近似,在相对水深达1.0的强色散波浪时仍保持较高的准确性,并且方程的非线性和线性 变浅率都得到了不同程度的改善. 方程的水平一维形式用预估-校正的有限差分格式求解, 建立了一个适合较强非线性波浪的Boussinesq波浪数值模型. 作为验证,模拟了波浪在潜 堤上的传播变形,计算结果和实验数据的比较发现两者符合良好.     

Extensions of the Prager-Shield theory of optimal plastic design

The Prager-Shield associated displacement field method for optimal plastic design is extended to multi-component specific cost functions and multiple load conditions, and a lower bound theorem based on kinematic requirements only is introduced. Since any statically admissible stress field results in an upper bound, the proposed theorem provides a simple method for establishing bounds on the optimal cost. By a simple substitution of parameters into the general equations presented, the optimality criteria can be obtained for particular design problems. Examples of optimal fibre-reinforced plates are given.     

Experimental investigation of the stability of monocoque domes subjected to external pressure

This paper describes the fabrication techniques, testing procedures and experimental results for eight 16-in.-diam rigid-vinyl plastic monocoque domes subjected to external-pressure loads. The domes tested were spherical, elliptical and torispherical, and all had fixed-edge support. They were fabricated in such a manner that wall-thickness tolerances and residual stresses could be minimized. In the test setup, a backup or support block was used to prevent complete collapse or yielding. The support allowed a complete buckle pattern to form, and the resulting pattern was always characteristic of a particular dome shape.These tests on domes withr/t values ranging from 240 to 600 produced remarkably consistent and high critical buckling coefficients (C) which exceeded 80 percent of the classical value (0.60). The results further indicateC to be independent ofr/t as well as the half-opening angle () of the dome shell over the range of values investigated.Paper was presented at 1965 SESA Spring Meeting held in Denver, Colo., on May 5–7.     

变厚度圆柱壳的强度优化设计

对在任意轴对称分布荷载作用下体积保持常数的变厚度圆柱壳的强度优化设计问题进行了研究。当中面形状固定时 ,采用阶梯折算法 ,用传递矩阵导出了变厚度圆柱壳的初参数解的显式表达式。根据Huber-Mises-Hencky强度准则 ,将变厚度圆柱壳的强度优化转化为极小化当量应力的非线性规划问题 ,并采用投影梯度法建立了问题的优化方法。文中对几个典型问题进行了计算。与等厚度圆柱壳相比较 ,优化圆柱壳的最大当量应力得到了显著降低。本文的研究方法和结果可以用于指导大型圆柱壳体的加肋设计     

多自应力模态索穹顶结构的几何构造分析

索穹顶结构是发展和推广Fuller张拉整体结构思想后唯一实现的一种新型大跨空间结构,它的几何构造分析是一项非常重要的工作。本文在对一般空间杆件体系的分类、自应力模态和机构位移模态研究的基础上,从索穹顶结构特有的杆件拓扑关系入手,提出了单位整体可行预应力这一新概念,并最终解决了多自应力模态下该体系稳定性判定问题;通过对若干类型索穹顶结构的几何构造分析,得出了一些对结构设计有用的结论。     

Prestress for maximum strength

The problem of designing prestress to maximize elastic capacity is treated analytically. Our formulation models structures comprised of a one-material elastic continuum, subject to a single deterministic load configuration.The equations needed to predict the optimal prestress design are derived. They are shown to comprise necessary and sufficient conditions for global maximum strength in the unconstrained design problem. The theory is demonstrated on the design of prestress for a thick-walled cylinder.     

Optimal spherical cupola of uniform strenght: Allowance for selfweigth

Summary This paper concerns the optimal design of a spherical cupola of given base radius that consists of a material obeying Tresca's yield condition. Five different combinations of selfweight, weight of non-carrying cover, snow-load and external as well as internal pressure are discussed. Finally, the results are compared with the optimal solutions for spherical shellgrids.

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Optimale sphärische Kuppel gleicher Festigkeit: Berücksichtigung von Eigengewicht

Übersicht Die Arbeit behandelt den optimalen Entwurf einer sphärischen Kuppel von gegebenem Basis-radius. Für den Werkstoff wird die Fließbedingung von Tresca angenommen. Es werden fünf verschiedene Kombinationen folgender Lasten betrachtet: Eigengewicht, das Gewicht einer nichttragenden Abdeckung, Schneelast und äußere sowie innere Druckbelastung. Schließlich werden die Ergebnisse mit den optimalen Lösungen für Gitterschalen verglichen.

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In memoriam William Prager

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The present project was originally undertaken by Prof. Dr.-Ing. Drs. h. c. W. Prager and the third author. Because of Professor Prager's sudden and unexpected death, it was completed by the third author and his associates     

Prestress design of cable domes with new forms

Cable domes have been employed as lightweight, large span roofs. In this paper, several new forms of cable domes are first presented and their geometric feasibility is discussed. A general method, referred to as the DSVD, is next proposed for the determination of the integral prestress modes for various cable domes. Optimum prestressing of domes with a single or with multiple integral prestress modes is also examined. The proposed method is verified through numerical simulations, and is believed to provide a helpful tool in the preliminary design of cable domes.     

Ponding Instability of Cylindrical Air-Supported Membranes under Nonsymmetrical Loadings

The paper deals with the stability of a cylindrical air-supported membrane subjected to an eccentric lineload and an accumulating ponding fluid in the depression caused by the load. A critical value of the load is calculated by solving the equations of equilibrium for the structure. Results of the analysis indicate that the eccentricity causes a significant increase in the value of the critical load. The elastic properties of the membrane are included in the analysis which leads to slightly lower critical loads than the corresponding “inextensional” membrane case.