薄壁钢结构的材料和几何非线性等参样条有限条法的研究进展

给出了等参样条有限条法(ISFSM)用于分析开孔薄壁钢结构的材料非弹性和几何非线性的研究进展。简要介绍了ISFSM理论。提出了运动学方程、应力-位移关系和假定的本构关系。通过增量平衡条件,推导出正切刚度矩阵。讨论了板带连续和边界条件的要求。特别强调了塑性理论和求解速率方程的方法,以及相关的欧拉后退法和材料模量一致的假定。开孔薄壁钢结构的非弹性后屈曲性能分析的准确性和有效性,证实了目前的等参样条有限条法的有效性。     

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Analytical developments

This paper presents the analytical developments of the application of the Isoparametric Spline Finite Strip Method (ISFSM) to the material inelastic and geometric nonlinear analysis of perforated thin-walled steel structures. The general theory of the ISFSM is briefly introduced. The formulations of the kinematics, strain–displacement and constitutive assumptions are presented, and the tangential stiffness matrix is derived by applying the incremental equilibrium condition. The requirements for strip continuity and boundary conditions are also discussed. In particular, the plasticity theory and the methods to integrate the ‘rate equations’ are emphasized, and the related ‘backward Euler return method’ and use of a ‘consistent material modulus’ are highlighted. The present isoparametric spline finite strip analysis is verified against a number of analyses of perforated and non-perforated plates and plate assemblages, as described in the companion paper (Yao and Rasmussen, submitted for publication) [1], demonstrating its accuracy and efficiency for the predictions of the inelastic post-buckling behavior of perforated thin-walled steel structures.     

Elastic buckling analysis of perforated thin-walled structures by the isoparametric spline finite strip method

This paper presents the application of the isoparametric spline finite strip method to the elastic buckling analysis of perforated folded-plate structures. The general theory of the isoparametric spline finite strip method is introduced. The kinematics assumptions, strain–displacement and constitutive relations of the Mindlin plate theory are described and applied to the spline finite strip method. The corresponding matrix formulation is utilised in the equilibrium and stability equations to derive the stiffness and stability matrices. A number of numerical examples of flat and folded perforated plate structures illustrate the applicability and accuracy of the proposed method.     

开孔冷弯型钢柱的试验研究

分析研究了开孔冷弯型钢柱的弹性屈曲和试验响应间的关系。对24个腹板开孔和不开孔的短柱和柱进行了压力试验。利用壳单元建模,对每一个构件都进行了有限元屈曲分析,从而可以获取边界条件、局部开孔、扭曲和整体弹性屈曲反应对构件的影响。腹板上的开孔,可能影响构件局部和扭转屈曲的半波长度,同时可能会导致临界弹性屈曲荷载的改变。从试验结果分析可知,尽管在某些试验中出现了延性下降等现象,但总体而言,腹板开孔对试验构件的极限强度影响很小;同时发现,在局部和扭转屈曲中,弹性屈曲也与荷载-位移曲线有关。试验中对柱子采用摩擦轴承的边界条件,其中柱端磨平且直接由钢板传力。尽管构件的延性等问题还需要更进一步研究,但这种边界条件对于评估短柱和普通柱屈曲性能是有效的,而且还可以缩短试验构件的准备时间。     

Linear elastic isoparametric spline finite strip analysis of perforated thin-walled structures

This paper describes the application of the isoparametric spline finite strip method to the linear elastic analysis of tri-dimensional perforated folded plate structures. The general theory of the isoparametric spline finite strip method is introduced. Kinematics assumptions and the procedure for combining in-plane (membrane) and bending effects are set out. Particular attention is paid to the procedure for rotating the stiffness matrix and load vector from local to global coordinates. The reliability of the method is demonstrated by comparisons with finely meshed finite element analysis results. Square stiffened perforated plates in compression and bending are analysed.     

A comparative study of analytical squeeze film damping models in rigid rectangular perforated MEMS structures with experimental results

Several analytical models exist for evaluating squeeze film damping in rigid rectangular perforated MEMS structures. These models vary in their treatment of losses through perforations and squeezed film, in their assumptions of compressibility, rarefaction and inertia, and their treatment of various second order corrections. We present a model that improves upon our previously reported work by incorporating more accurate losses through holes proposed by Veijola and treating boundary cells and interior cell differently as proposed by Mohite et al. We benchmark all these models against experimental results obtained for a typical perforated MEMS structure with geometric parameters (e.g., perforation geometry, air gap, plate thickness) that fall well within the acceptable range of parameters for these models (with the sole exception of Blech’s model that does not include perforations but is included for historical reasons). We compare the results and discuss the sources of errors. We show that the proposed model gives the best result by predicting the damping constant within 10% of the experimental value. We study the validity of the proposed model over the entire range of perforation ratios (PR) by comparing its results with numerically computed results from 3D Navier-Stokes equation. These results are also compared with other analytical models. The proposed model shows considerably better results than other models, especially for large values of PR.     

Material and geometric nonlinear isoparametric spline finite strip analysis of perforated thin-walled steel structures—Numerical investigations

The theoretical developments of a material inelastic and geometric nonlinear analysis by use of the isoparametric spline finite strip method (ISFSM) are presented in a companion paper (Yao and Rasmussen (submitted) [1]). In the present paper, the numerical implementation of the analysis is reported, including nonlinear solution techniques, inelastic material models, selective reduced integration strategies, convergence criteria, and solution procedures. The reliability and efficiency of the method are demonstrated by a number of numerical examples, including analyses of flat plates with different material plasticity models, a classical nonlinear shell problem, perforated flat and stiffened plates, and perforated stiffened channel section storage rack uprights.     

受压或受弯开孔薄板的弹性屈曲性能

开发、论证并总结了一组闭合公式,可以估算在弯矩或压力作用下,板的单个或多个开孔对其临界弹性屈曲应力的影响。公式适用于四边简支和三边简支的板(这在设计中又称为加劲板和非加劲板)。由于有限壳单元特征值屈曲分析需要运用商业有限元程序,而这些程序又不是专为结构分析而开发的,不能很方便地用于工程设计,所以可以采用这些公式作为这种屈曲分析方法的简化替代。这些公式的形式与板稳定性近似分析的经典形式相似,并通过有限壳元对其进行了参数分析并验证。有限元参数分析证实了开孔可能会导致板产生独特的屈曲模式,开孔的几何尺寸和间距可能会增加或者减少板的临界弹性屈曲应力。这些公式及其使用限制可适用于工程中通常采用的开孔形状、位置和间距,同时研究也指出,若需得到足够精确的计算,则还是有必要采用壳单元的有限元分析。     

Load capacity of cold-formed column members of lipped channel cross-section with perforations subjected to compression loading – Part I: FE simulation and test results

An investigation was carried out into the influence of perforations of various shapes on the buckling behaviour of cold-formed column members of lipped channel cross-section. A finite element analysis using ANSYS, an experimental investigation, and design code predictions using the AISI Specification, British Standards (BS) and EU Standards, are employed to determine the buckling load capacity. An experimental investigation of the buckling behaviour of flat and fixed ended columns is presented, and the findings from this are used to validate finite element results, and compare with design code predictions. The numerical results of load vs. displacement behaviour are shown to be in good agreement with those reported from the tests. It is shown that the ultimate failure load of the lipped channels under compression varies greatly with the presence of perforations.     

Gas exchange dynamics in modified atmosphere packaging of soft cheese

Modified Atmosphere Packaging (MAP) is a shelf-life extension technique that has been widely applied to horticultural, meat and dairy products. It relies on the interaction between product, packaging material and environment, which determines the gas composition inside the package at steady state. Therefore, MAP design needs to take into consideration O₂ consumption and CO₂ production rates of the product and the mass transfer coefficients for the gas exchange through the packaging material and how they are affected by environmental factors such as storage temperature. In this work, a mathematical model was developed for designing MAP systems for a soft cheese (camembert-type). The model was used to evaluate the effect of perforations on O₂ and CO₂ concentrations of package containing cheese, at constant and varying storage temperatures. The predicted gas composition was compared with those obtained experimentally at 293 and 285 K with packages having different numbers of perforations (1), (2) and (3). Experimental values of gas composition observed at steady state with one perforation were 0.050 and 0.148 (v/v) at 285 K for O₂ and CO₂ respectively, and 0.003 and 0.207 (v/v) at 293 K. Gas composition was found to take values between 0.009–0.058 for O₂ and 0.154–0.200 for CO₂, when the packages with a single perforation were exposed to storage temperature varying between 285 and 293 K during 14 days of storage. The model developed was able to accurately predict the gas exchange dynamics of the package throughout the storage period whether the temperature of storage was constant or not.