正交正放类网架结构分析的分解刚度法

把正交正放类网架结构简化为构造上正交异性的夹层板,采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析。基于分解刚度思想对三类屋面网架(正放四角锥网架、两向正交正放网架和正放抽空四角锥网架)进行了静力分析和固有振动分析,对三类竖向承重网架墙体进行了稳定性分析,给出了简便实用的计算公式。通过与有限元法分析结果的对比,表明了本文提出的方法作为一种简化的计算方法,其精度是比较高的,绝大多数的误差都小于5%,可以应用于工程结构的初步设计。此外,与其他的简化计算方法相比它的精度比较高而且计算过程大大简化了。     

Some observations on state space grids and closely related nonlinear methods

State space grids are the most frequently used form of nonlinear analysis in this special issue. This article elaborates on hypotheses one can test using them, the role of entropy constructs, and expansions to experimental designs and analysis that one can reasonably make to study system stability questions or systems with three or more interacting agents.     

Limit analysis of orthotropic plates

The limit analysis problem for plates in bending is considered. The failure criterion for the material is assumed as orthotropic, with possible non-symmetric strength properties. According to Kirchhoff’s hypothesis, the plate is conceived as a superposition of layers, individually in plane stress situation, and continuity is enforced by means of a kinematic assumption. By exploiting previous results, recently established by the authors, the expression of the dissipation power per unit plate area is defined on this basis and the kinematic (upper bound) theorem of limit analysis is cast in a form suitable for numerical solutions. To this purpose, efficient algorithms successfully employed in the isotropic case can be used with minor modifications. The effectiveness of the procedure is demonstrated by solving some homogeneous plate examples. Results permit the assessment of the influence of different aspects, such as the ratio between strengths along the orthotropy directions, the tensile to compressive strength differential and the inclination of the orthotropy axes with respect to the sides. The effects of in-plane edge constraints are also discussed and it appears that they are emphasized considerably by anisotropy. Even if referred to specific cases, some conclusions can be regarded as fairly general.     

网架结构拟夹层板法的有限元验证

用拟夹层板法和有限元法对网架结构进行分析,对三类屋面网架（正放四角锥网架、两向正交正放网架和正放抽空四角锥网架）进行了均布荷载、局部荷载（半跨均布荷载）作用下的静力分析以及固有振动分析,对三类竖向承重网架墙体进行了稳定性分析。通过与有限元法分析结果的对比,表明了拟夹层板法作为一种简化的计算方法,其精度是比较高的,绝大多数的误差都小于5％,是可以直接用于工程结构设计的一种有效方法。此外,拟夹层板法还可作为一种在宏观上检验有限元建模正确与否的实用方法。     

Limit analysis of circular and annular plates

Summary The problem of the plastic collapse load of circular and annular plates is dealt with. For simply supported and built-in edge plates, different loading conditions are considered and the annular plates are studied for varying geometries. The solutions obtained according to both Tresca's and Mises' yield conditions are exact in the sense of limit analysis.

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Zur Grenztragfähigkeits-Theorie bei Kreis- und Kreisringplatten

Übersicht Es werden Traglasten von Kreis- bzw. Kreisringplatten ermittelt. Dabei werden gelenkig gelagerte sowie eingespannte Kreisplatten bei verschiedener Belastung und Kreisringplatten bei verschiedener Geometrie betrachtet. Die mit Hilfe der Fließbedingungen nach Tresca bzw. v. Mises erhaltenen Lösungen sind exakt im Sinne der Grenztragfähigkeits-Theorie.

     

Limit analysis of arch-beam structures by dynamic programming

Summary We study one-dimensional structures like arch-beams in the limit state of plastic collapse, on the ground of a two-dimensional yielding surface (bending moment and normal generalized stress). The proposed method, which is able to give a numerical solution of the problem of finding the limit load, rests on the upper bound theorem of limit analysis and uses dynamic programming. We examine also some questions linked with numerical procedures. A future work devoted to applications will complete the treatment.

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Sommario Si studiano le strutture monodimensionali ad arco nello stato limite di collasso plastico, sulla base del dominio bidimensionale (momento flettente e sforzo normale). Il metodo proposto, atto a fornire una soluzione numerica del problema della ricerca del carico limite, si fonda sul teorema cinematico dell'analisi limite e sull'impiego della programmazione dinamica. Si prendono anche in esame talune questioni connesse con l'algoritmo di calcolo. Un successivo lavoro di carattere applicativo completerà la trattazione.

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This paper has been supported by National (italian) Research Council (C.N.R.).     

Limit analysis of masonry structures with free discontinuities

We formulate a novel procedure for the limit analysis of two-dimensional masonry structures subject to arbitrary loading conditions. The proposed approach works in the framework of free discontinuity methods, on examining collapse mechanisms that exhibit free crack opening discontinuities. The load bearing capacity and the collapse mechanism of the structure are obtained through a fully variational approach, by minimizing a kinetic functional that admits the collapse crack pattern as a variable. Numerical examples illustrate the practical application of the proposed procedure to the limit analysis of a variety of masonry walls and arches subject to foundation settlements, vertical and horizontal forces.     

Mechanical analysis of C/C composite grids in ion optical system

The ion thruster is an engine with high specific impulse for satellites and spacecrafts, which uses electric energy to boost the spacecraft. The ion optical system,also known as gate assemblies which consist of acceleration and screen grids, is the key component of the ion thruster. In this paper, the static mechanical properties of the C/C composite grids are evaluated based on the structural design. Representative volume element(RVE) is adopted to simplify the braded composite structure as a continuum material. The dynamical behavior of the 100 mm ion thruster optics in the launch environment(1 000 gshock-load) is numerically modeled and simulated with the half-sine pulse method. The impact response of the C/C and molybdenum gate assemblies on the stress distribution and deformation is investigated. The simulated results indicate that the magnitudes of the normal displacement of the composite grids subject to the uniformly distributed load are on the same level as molybdenum grids although the normal stiffness of the composite grids is much smaller. When sub ject to impact loading,the stress distribution in the C/C composite grids is similar to molybdenum grids while the stress magnitude is much smaller. This finding shows that the C/C gate assemblies outperform molybdenum grids and meet the requirement of long lifetime service in space travel.     

Limit and shakedown analysis of pressurized pipelines containing defects

In this paper, the integrity assessment of pressurized pipelines containing defects is performed by direct simplified methods of limit and shakedown analysis. The defects considered are part-through slots of various geometrical configurations. The engineering situation considered here has practical importance in the pressure vessel and pipe industry. The results are compared with those obtained by a step-by-step procedure using the professional code ABAQUS and where possible, with those provided by semi-empirical formulae used in engineering. The simplified methods are found more economical and more reliable than marching solutions achieved by step-by-step evolutive elastic-plastic analysis. The effects of various part-through slots on the load-carrying capacities of pipelines are investigated. The project was supported by the National Science and Technology Commission of China and by the Department of Structural Engineering, Technical University of Milan, Italy     

Limit analysis for a general class of yield conditions

The paper describes a generalisation of the programming method described by Ponter and Carter (1997) for the evaluation of optimal upper bounds on the limit load of a body composed of a rigid/perfectly plastic material. The method is based upon similar principles to the `Elastic Compensation' method which has been used for design calculations for some years but re-interpreted as a non-linear programming method. A sufficient condition for convergence is derived which relates properties of the yield surface to those of the linear solutions solved at each iteration. The method is demonstrated through an application to a Drucker–Prager yield condition in terms of the Von Mises effective stress and the hydrostatic pressure. Implementation is shown to be possible using the user routines in a commercial finite element code, ABAQUS. The examples chosen indicate that stable convergent solutions may be obtained. There are, however, limits to the application of the method if isotropic linear solutions are used for an isotropic yield surface. In an accompanying paper (Ponter and Engelhardt, 2000) the method is extended to shakedown and related problems.     

Limit analysis of plates with piecewise linear yield surface

Summary Rigid-plastic plates having a piecewise linear yield surface are studied by limit analysis. Extremum principles for the evaluation of specific dissipation power are defined by means of linear programming concepts. The law governing the plastic collapse of plates is formulated on the basis of the well-known kinematic theorem of limit analysis. A general procedure for the approximate determination of the collapse load is proposed. The paper ends with a brief numeric investigation of the uniformly loaded square plate.

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Sommario Si studiano attraverso l'analisi limite le piastre costituite di materiale rigido-plastico aventi superficie di snervamento di tipo poliedrico. I principi di estremo riguardanti la valutazione della potenza specifica di dissipazione vengono definiti attraverso i concetti della programmazione lineare. Attraverso il noto teorema cinematico dell'analisi limite, si formula la legge che regola il collasso plastico delle piastre. Viene proposto un procedimento per la determinazione approssimata del carico di collasso del tutto generale. Si conclude infine con una breve indagine numerica relativa al caso di piastra quadrata con carico uniforme.

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The results presented in the paper form part of a Research supported by the National Research Council (C.N.R.).     

Limit and shakedown analysis under hydrogen embrittlement condition

A modified shakedown theorem and its solving technique are presented to involve hydrogen embrittlement of steel into limit and shakedown analysis. Firstly, the shakedown theorem for hydrogen embrittled material is derived from a limited kinematic hardening shakedown theorem and hydrogen enhanced localized plasticity mechanism of hydrogen embrittlement. In the presented theorem, hydrogen’s effect is taken into account by the synergistic action of both strength reduction and stress redistribution. Secondly, a novel solving technique is developed based on the basis reduction method, in which the complicated constraints in the resulting nonlinear mathematical programming are released. At last, three numerical examples are carried out to verify the performance of the proposed method and to reveal hydrogen’s effect on the limit and shakedown load of structure. The numerical results are discussed and compared with those from literatures, which proves the accuracy and high efficiency of the introduced solving technique. It is concluded that the proposed theorem can predict the limit and shakedown load of hydrogen embrittled structure reasonably.     

Non linear analysis of space trusses

Summary A combined nonlinear analysis of spatial truss systems is per formed. Local buckling of elements is accounted for.The approach given herewith is able to describe the post buckling behavior of the system.

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Sommario Si effettua lo studio di sistemi reticolari spaziali considerando la non linearità di comportamento dovuta. sia ai grandi spostamenti sia ad una legge costitutiva non lineare.L'analisi si estende alla fase post-critica e tiene conto dell'instabilità locale di singole aste.

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This research has been carried out with the financial support of ENEL (Electricity Board of Italy).