考虑受拉薄膜效应的板块平衡法修正及在混凝土双向板中的应用

经典塑性铰线理论中的板块平衡法无法考虑钢筋混凝土板在大变形时产生的受拉薄膜效应的影响。为解决这一问题,该文提出了一种可以考虑受拉薄膜效应的修正板块平衡法。该方法将钢筋混凝土板的受力行为分为屈服前和屈服后两个阶段。假设钢筋混凝土板在屈服前的变形为弹性,分别采用Navier法和板块平衡法确定板的屈服挠度和屈服承载力。为考虑屈服后钢筋混凝土板中产生的受拉薄膜效应,假设板底塑性铰线截面上钢筋的竖向分力为产生受拉薄膜效应的主要原因,而钢筋的水平分力则与截面上混凝土的压力组成力偶构成了钢筋混凝土板的截面抵抗弯矩。通过上述修正,可以获得由考虑受拉薄膜效应的修正板块平衡法计算的钢筋混凝土板的全过程荷载-挠度曲线。为验证该文方法,对大挠度足尺混凝土双向板进行了应用研究。通过对比可知,理论分析结果与试验结果较为接近,从而验证了修正板块平衡法的有效性。     

有限宽中心裂纹板在裂纹面受一对偏心反平面集中力的弹塑性分析

有限宽裂纹板的弹塑性分析是弹塑性断裂力学中最困难的问题之一。本文对有限宽裂纹板在裂纹面任意点受一对反平面集中力的情形采用裂纹线场分析方法,将各场量在裂纹线附近展开,利用平衡方程和屈服准则进行弹塑性分析,这种分析不需要作小范围屈服的假定。通过裂纹线上的弹塑性应力场在弹塑性边界上进行匹配得出荷载与裂纹线上塑性区长度之间的关系,进而分析得出荷载的不同位置和板宽所对应的临界荷载。     

冷弯薄壁箱形截面柱在偏心荷载作用下的弹塑性屈曲

本文对冷弯薄壁箱形截面柱分别在常位移梯度偏心加载和常荷载偏心距加载下的弹塑性屈曲后性能进行了全过程屈曲分析。分析中考虑了壁板初曲、截面弯角处冷作硬化以及应力应变曲线的圆滑过渡过柱屈曲后承载能力的影响。采用修正的Ilyushin屈服准则,将线性有限条理论推广应用于解决大挠度、弹塑性稳定问题,不仅大大地减少了计算工作量,而且具有较高的精度。进行了冷弯箱形截面柱的受压试验。试验与理论分析结果比较吻合。     

考虑压-拉薄膜效应的围框约束RC板极限抗力分

合理估算大变形条件下梁板构件的极限抗力,对工程设计计算具有重要意义。传统的RC （reinforced concrete）板极限抗力一般由小变形条件下的受压薄膜效应得到,然而RC板构件的灾变断裂大部分出现在大挠度阶段,因此考虑压-拉薄膜效应的极限抗力分析尤为重要。该文将RC板从加载到断裂全过程分为板端受压上升段、混凝土开裂下降段和钢筋拉伸上升段,根据正截面抗弯的钢筋混凝土弹塑性模型得到基于受压薄膜效应的荷载-挠度全曲线。利用经典的挠曲线微分方程并引入抗弯刚度软化系数对挠度进行修正,结合能量原理推导出大变形条件下基于受拉薄膜效应的RC板极限抗力,进一步得到考虑压-拉薄膜效应的荷载-挠度全曲线。计算结果表明,考虑压-拉薄膜效应的RC板极限抗力分析方法可以更合理地预测荷载-挠度全过程,计算结果与相关试验吻合良好,为合理评估RC板的极限承载力提供参考。     

考虑压-拉薄膜效应的围框约束RC板极限抗力分析

合理估算大变形条件下梁板构件的极限抗力,对工程设计计算具有重要意义。传统的RC(reinforced concrete)板极限抗力一般由小变形条件下的受压薄膜效应得到,然而RC板构件的灾变断裂大部分出现在大挠度阶段,因此考虑压-拉薄膜效应的极限抗力分析尤为重要。该文将RC板从加载到断裂全过程分为板端受压上升段、混凝土开裂下降段和钢筋拉伸上升段,根据正截面抗弯的钢筋混凝土弹塑性模型得到基于受压薄膜效应的荷载-挠度全曲线。利用经典的挠曲线微分方程并引入抗弯刚度软化系数对挠度进行修正,结合能量原理推导出大变形条件下基于受拉薄膜效应的RC板极限抗力,进一步得到考虑压-拉薄膜效应的荷载-挠度全曲线。计算结果表明,考虑压-拉薄膜效应的RC板极限抗力分析方法可以更合理地预测荷载-挠度全过程,计算结果与相关试验吻合良好,为合理评估RC板的极限承载力提供参考。     

比塑性功求解线性载荷下简支圆板极限载荷

为了获得线性载荷作用下的简支圆板极限载荷的解析解,本文提出了刚塑性第一变分原理的运动许可应变场,并首次以GM(几何中线)屈服准则塑性比功进行了塑性极限分析.首次获得了GM准则下圆板极限载荷的解析解,该解为圆板半径a、材料屈服极限σs及板厚h的函数.与Tresca、TSS及Mises预测的极限载荷比较表明:Tresca准则预测极限荷载下限,TSS屈服准则预测极限载荷的上限,GM屈服准则比塑性功解析结果恰居于两者之间;GM解略低于Mises解,两者相对误差为3.38%.此外,文中还讨论了挠度与相对位置r/a之间的变化关系.     

各向异性中厚度板壳的弹塑性大变形分析

本文提出了一个解各向异性中厚度板壳弹塑性大变形问题的一般有限元方法。几何非线性的描述采用Ｖ．Ｋａｒｍａｎ的位移应变关系；材料的弹塑性分析采用Ｈｉｌｌ推广的Ｈｕｂｅｒ－Ｍｉｓｅｓ屈服准则；借用Ｏｗｅｎ的剪切修正系数，正确计及了叠层复合材料壳体的横向剪切效应。特别是本文利用插值外推的思想，提出了一个带预测的弧长增量控制法，显著提高了计算塑性大变形和后屈曲路径的效率。几个数值算例表明本文给出的有限元方法对于各种各向异性壳体的弹塑性大变形分析有较好的精度。     

均布载荷作用下简支圆板塑性极限载荷的解析解

该文建立了受均布载荷作用简支圆板运动许可应变场,并首次以EA(等面积)屈服准则进行了塑性极限分析,获得了极限载荷的解析解。该解为圆板半径a、圆板厚度h以及屈服强度的函数。与Tresca、TSS以及Mises解比较表明,Tresca屈服准则预测极限载荷的下限,TSS屈服准则预测极限载荷的上限,EA和Mises屈服准则预测的极限载荷恰居二者中间,且EA解几乎与Mises解重合。此外,该文还讨论了挠度与相对位置r/a之间的变化关系。     

基于隶属度函数模糊弹塑性本构模型的研究

为了解决循环加卸载问题,将隶属度函数和模糊截集引入到塑性屈服函数中,并采用米塞斯屈服准则,将屈服函数模糊化,推导得到了模糊弹塑性本构模型。随着隶属度值的变化,该模型的弹塑性界面能连续过渡,且表达式简单,加卸载路径明了;利用该模型对钢桥面板在循环荷载作用下进行了分析,并通过有限单元法得到了数值解。通过分析发现,模糊弹塑性模型通过隶属度的演化能代替硬化规律,能很好地反映循环加卸载过程,是解决循环加卸载作用下弹塑性连续过渡的一种有效途径。     

裂纹面受两对集中剪力作用下的弹塑性分析

利用裂纹线场方法对理想弹塑性材料无限大板受两对集中剪力问题进行了弹塑性分析,并且获得了理论解。这个解包括:裂纹线附近弹塑性边界上的单位法向矢量、裂纹线附近的弹塑性解析解、裂纹线上的塑性区长度随荷载的变化规律及其承载力。分析不受小范围屈服假设的限制,并且不附加假使条件。结果在裂纹线附近足够精确。     

Buckling Analysis of Laminated Composite Plates Using Higher Order Semi—Analytical Finite Strip Method

Rectangular plates made of laminated composite material because of the advantageously high strength and stiffness to weight ratio are used frequently as structural component in various branches of engineering, chief of which are aerospace and marine engineering. Design concepts of these plates that lead to the increase in the buckling load can directly lower the structural cost and/or weight. The finite strip method is one of a number of procedures which can be used to solve the buckling problem of plate structures. In the present work the main concern is with the buckling behavior of plates with simply supported ends subjected to uni-axial pure compression loads. The solution is sought by implementing the higher order semi-analytical finite strip method which incorporates additional degrees of freedom for each nodal line by using Reddy’s higher order plate theory. Therefore the current method is more universal in dealing with different plate thicknesses. In addition, in this semi-analytical finite strip method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. The solution is based on the concept of principle of minimum potential energy and an eigen-value analysis is subsequently carried out. From the presented results it can be concluded that the higher order semi-analytical finite strip method is very reliable for the preliminary design of composite plates especially in the case of buckling analysis of relatively thick plates.     

Large deflection behaviour of thick composite plates

A rectangular quadratic finite element which includes large displacements, strains and rotations is developed in this paper. The effect of extra quadratic terms in the strain—displacement relationships on the large deflection of angle-ply plates is examined first. It is further shown that the fibre orientation and the boundary condition have a predominant effect on the nonlinear deflection of a unidirectional laminate. Basic work relating to the large deflection behaviour of thin and think antisymmetric and unsymmetric layered plates is also reported. Results are presented for simply supported and clamped boundary conditions.     

冲击荷载下弹粘塑性矩形薄板的动力响应

本文用空间有限元、时间差分法分析了受冲击荷载的矩形固支板的动力响应。分析中考虑了大位移引起的几何非线性;塑性、应变强化及应变率效应引起的材料非线性的影响。     

Post-buckling behavior of composite laminated plates under end shortening and pressure loading, using two versions of finite strip method

Two different versions of finite strip method, namely spline and semi-analytical methods, are developed for analyzing the geometrically non-linear response of rectangular composite laminated plates of arbitrary lay-up to progressive end-shortening in their plane and to pressure loading. The plates are assumed to be thin so that the analysis can be carried out based on the classical plate theory. The in-plane lateral deflection υ is allowed at the loaded ends of the plate, whilst the lateral expansion of the unloaded edges is either free or completely prevented. Geometric non-linearity is introduced in the strain–displacement equations in the manner of the von Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the effects of pressure loading. The comparison between the two sets of results obtained by different finite strip methods is very good. The study of the results revealed that the response of the laminates is significantly influenced by the application of the normal pressure loading. Particularly, the response of unsymmetric laminates is strongly affected by the sign of the normal pressure loading.     

A Fully Discretized Nonlinear Finite Strip Formulation for Pre-Buckling and Buckling Analyses of Viscoelastic Plates Subjected to Time-Dependent Loading

A semi-analytical fully discretized finite strip method is developed to investigate the pre-buckling and local buckling of viscoelastic plates with different boundary conditions subjected to time-dependent loading. The mechanical properties of the material are considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. The fully discretized finite strip equations are developed using a two-point recurrence formulation, which leads to a computationally superior formulation. Time history of maximum deflection of plates with different end conditions is calculated. The effects of thickness, length of plate, and transverse loading on critical buckling load are also studied.     

非线性样条有限条法及其应用

本文基于完全的增量形式Lagrange描述法,根据虚功原理导出了大挠度弹塑性样条有限条法,用以分析板、壳和薄壁结构与构件的几何与材料非线性问题。本文方法适用于任意边界支承条件和加荷方式,可以计入任意形式的初始缺陷的影响以及沿厚度方向的塑性开展。所给算例表明,该方法具有计算量少.连续性强、精度高、应用广泛等优点.     

The buckling of composite stiffened plates with some emphasis on the effects of fibre orientation and on loading configuration

The bucking characteristics of some composite stiffened plates are determined in this paper using a finite strip approach. The finite strip formulation is able to predict the complex buckling modes associated with in-plane shear loading and the method of approach can allow for other loading configurations whose associated pre-buckling stresses are not so obviously realised.

Two loading conditions have essentially been considered in the paper, that of in-plane shear and that of partial edge loads being reacted by shear. The strip displacement fields before and after buckling are represented by algebraic polynomials across the strip and trigonometric functions along the strip length. The inclusion of sufficient harmonics in the appropriate displacement representations thus allows the distorted nodal lines of the shear buckling mode and the complex pre-buckled stresses associated with partial edge loads to be determined with relative ease.     

An investigation on the post-buckling behavior of symmetric cross-ply laminated plates using a semi-energy finite strip approach

A geometrically non-linear finite strip for the post-buckling analysis of geometrically perfect thin symmetric cross-ply laminated plates under uniform end shortening is presented in this paper. The formulation of the aforementioned finite strip is based on the concept of the semi-energy approach. In this method, the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form. The postulated deflected form is substituted into von Kármán’s compatibility equation which is solved exactly to obtain the corresponding forms of the mid-plane stresses and displacements. The solution of von Kármán’s compatibility equation and the postulated out-of-plane deflected form are then used to evaluate the potential energy of the related finite strip. Finally, by invoking the Principle of Minimum Potential Energy, the equilibrium equations of the finite strip are derived. The developed finite strip is then applied to analyze the post-local-buckling behavior of thin flat laminates. The results are discussed in detail and compared with those obtained from finite element method (FEM) of analysis. It should be mentioned that the FEM analysis was carried out employing the general purpose ANSYS package. The study of the results has provided confidence in the validity and capability of the developed finite strip in handling the post-buckling problem of symmetric cross-ply laminated plates.     

Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads

This paper presents a method for the approximate analysis of local bending effects in sandwich plates with specially orthotropic face layers subjected to localised external loads. The local bending analysis is based on the assumption that the relative deflection of the loaded face against the deflection of the face not loaded can be modelled by application of an elastic foundation model. This is achieved by introducing a two-parameter elastic foundation model which takes into account the shearing interaction effects between the loaded face and the core material. An approximate solution to the complete problem is achieved by superposition of the local solution and an overall solution derived by application of classical sandwich plate theory. The results obtained are compared with finite element analysis results, and a good match between the solutions is observed. Finally a brief parametric study shows that the local bending effects are strongly influenced by the modular ratio and the thickness of the loaded face.     

Large deflections and large amplitude vibrations of axisymmetric circular plates

This paper is concerned with conventional and mixed finite element analysis of large deflection bending and free vibration of axisymmetric circular plates including shear deformation. Conventional and mixed finite element formulations are presented. Numerical results are included for isotropic as well as orthotropic, circular and annular plates under various edge conditions and loadings.