考虑几何非线性钢筋混凝土板壳的有限条法

在变厚度任意配筋的钢筋混凝土板壳考虑材料非线性分析的有限条法的基础上，将几何非线性的影响引入到钢筋混凝土板壳的有限条分析中，利用“拟刚度矩阵法”，消除了有限条法在非线性分析时刚度矩阵与级数项的耦合，大大简化了有限条在处理非线性问题时的数值计算，结合算例证明了理论方法的有效性和精度。     

基于Koiter理论的板片空间结构缺陷敏感性研究

目前对板片空间结构缺陷的研究主要集中在数值分析方面,尝试基于Koiter理论进行近似解析方法的研究。通过把板片空间结构的网架或网壳部分连续化为板或壳,将板片空间结构简化为双层板或双层壳。再分别对完善的双层板和双层壳进行大挠度方程求解,研究完善结构的初始后屈曲性能。在求解大挠度方程时,省略了边界条件中的耦合项,从而能够应用伽辽金法求解。最后基于Koiter理论,得出板型板片空间结构对缺陷不敏感,而扁壳型板片空间结构对缺陷敏感的结论。     

双曲扁壳有限条分析

本文考虑了双曲扁壳的曲率影响,应用有限条法导出扁壳条元的刚度矩阵,与普通有限元法比较,单元刚阵阶数较低,总刚阵极稀疏,未知量少,易于在小型计算机上求解工程实际问题。文中应用作者编制的CS3微型计算机程序,给出算例数值结果,表明本文方法是有效的。     

带肋扁壳的拟双层壳分析法

本文把蒂肋扁壳的肋看作为一层同壳，且连续化为下层壳，并与蒂肋壳的壳板即上层壳组成件同工作的拟双层壳计算模型，进而可按弹性小挠度薄壳理论分析计算蒂肋扁壳。文中椎导建立了一般情况下带肋扁壳混台法的基本方程式。这种构造上的拟札层壳一般不存在中面，因而壳体的薄膜内力、弯矩与薄膜应变、弯曲应变是耦合的，存在一个耦合矩阵，它可充分反映肋与壳板偏心矩e的影响。对于两向正盘正放与三向带肋扁壳文中作了详细的讨论，并说明了在一定条件下，基本方程式可简化为一个构造上正史异性甚至各向同性单层扁竞的基本方程式，以方便计算和工程应用。文中附有算倒两则。     

板壳结构非线性屈曲分析的修正拉格朗日法

本文采用退化曲壳有限单元,推导了板壳结构非线性有限元分析的、修正的拉格朗日法(Updated Lagrauge简称U.L.法,下同),并编制了非线性有限元程序.利用本文理论方法既可分析板壳的太变形问题,同时也可考虑材料进入非线性后的太应变问题.通过对一些板壳屈曲问题的分析对比,证明了本文理论方法的正确性和有效性.     

均布荷载作用下矩形薄板挠度解法的比较

在薄板弯曲理论的基础上,为了了解板壳结构的受力特点、形变特点,通过对板壳理论的经典算法与有限单元法的解法差异的比较,求解均布荷载作角下四边固定矩形薄板小挠度问题.     

方底钢筋混凝土球扁壳基于双剪屈服准则的极限分析

利用双剪屈服准则建立了用机动法计算钢筋混凝土球扁壳的塑性屈服线理论,给出塑性屈服线求极限荷载的方法,使其更加合理。建立了矩形底的钢筋混凝土扁壳的屈服条件,并用无矩和有矩理论求解出方形底周边铰支的球扁壳的极限载荷。     

非线性扁球网壳的优化设计

分析了非线性变壁厚扁球壳的有矩内力,将其表达成辐角ψ的函数.运用塑性理论中的Tresea屈服条件,进行结构弹塑性阶段的内力研究.并用优化理论的满应力指数法分段进行壁厚的满应力优化设计.给出扁球网壳各杆件的最优尺寸.通过一个算例说明非线性扁球网壳优化设计的过程,并给出内力计算的表格和材料选用的表格.实现非线性扁球网壳的优化设计.     

板壳弯曲问题的平面波试函数解

本文从Trefftz思想出发，利用广义函数平面波理论，提出了广义函数平面波法求解偏微分方程试函数解的方法。用该方法具体求解了弹性地基板和双曲扁壳弯曲问题，大量算例表明该方法可靠，有效，计算精度满足工程设计需要。     

关于摄动有限元法中几种结构形式的摄动变分方程

作者在分析几何非线性问题时，把摄动法引人变分方程，推导了梁、板、扁壳的各级摄动变分方程，用这些方程可以方便地进行有限元的计算。     

Analysis of shallow shells by spline finite strip method

A spline finite strip method is presented in this paper for the analysis of shallow shell structures. It makes use of β₃-splines and conventional shape functions to describe the displacement field of strips. Based on Vlasov's shallow shell theory, the stiffness and load matrices are derived in accordance with the standard finite element procedure. Numerical examples are given and compared with other available solutions. In all cases, good agreement is observed.     

Stability analysis of stiffened plates by finite strips

The stability analysis of stiffened plates by means of the finite strip method is presented. The studies are based on the thin shallow theory, giving nonlinear strain displacement relations, but linear curvature displacement relations. The nonlinear equilibrium equations are obtained by the principle of incremental virtual work, using finite strip discretization. The higher order strip with one internal nodal line is applied. It is shown that considerable improvements can be obtained using this kind of strip. It is especially true for the postbuckling analysis. Numerical examples of the strength of stiffened plates in compression are carried out, covering a range of plate and stiffener slenderness.     

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.     

Comparison of elastic solutions for three-point bending of curved pipes

In this paper the linear elastic shell theory problem of the three-point bending of a curved pipe is considered. Such a loading arises in the industrial pipe ram bending process. Summaries are given for solutions to this problem based on the Mushtari-Vlasov-Donnel (MVD) and Sanders linear shell theories. Numerical results for displacements and stresses are obtained using the two shell theories, and these are compared with results from the finite element method (FEM). The present study gives practical information about the behavior of curved pipes subjected to ram bending. As well it provides information about the solution characteristics of thin-shell theories in toroidal coordinates.     

Buckling mode decomposition of single-branched open cross-section members via finite strip method: Derivation

This paper provides the first detailed presentation of the derivation for a newly proposed method which can be used for the decomposition of the stability buckling modes of a single-branched, open cross-section, thin-walled member into pure buckling modes. Thin-walled members are generally thought to have three pure buckling modes (or types): global, distortional, and local. However, in an analysis the member may have hundreds or even thousands of buckling modes, as general purpose models employing shell or plate elements in a finite element or finite strip model require large numbers of degrees of freedom, and result in large numbers of buckling modes. Decomposition of these numerous buckling modes into the three buckling types is typically done by visual inspection of the mode shapes, an arbitrary and inefficient process at best. Classification into the buckling types is important, not only for better understanding the behavior of thin-walled members, but also for design, as the different buckling types have different post-buckling and collapse responses. The recently developed generalized beam theory provides an alternative method from general purpose finite element and finite strip analyses that includes a means to focus on buckling modes which are consistent with the commonly understood buckling types. In this paper, the fundamental mechanical assumptions of the generalized beam theory are identified and then used to constrain a general purpose finite strip analysis to specific buckling types, in this case global and distortional buckling. The constrained finite strip model provides a means to perform both modal identification relevant to the buckling types, and model reduction as the number of degrees of freedom required in the problem can be reduced extensively. Application and examples of the derivation presented here are provided in a companion paper.     

Compound strip method for the buckling analysis of continuous plates

A special finite strip method is developed for the analysis of linear buckling of flat plate systems that are continuous over non-rigid supports. This approach incorporates the effect of support elements in a direct stiffness methodology. The stiffness contribution of the support elements adds directly to the plate strip stiffness matrices at the element level prior to assembly. This summation of plate and support stiffness contributions forms a substructure, which is termed a compound strip. The compound strip methodology may be readily employed for the enhancement of computer programs based on traditional finite strip procedures. The validity of the compound strip method for elastic buckling analysis is demonstrated in two examples. The critical loads based on compound strip methodology compare favorably with those obtained with the finite element method.     

简支平顶组合抛物面薄壳屋盖的自由振动和受迫振动的级数解

折板结构是由多块条形平板组合而成的空间结构,是一种既能承重,又可围护,用料较省,刚度较大的薄壁结构,可用作车间、仓库、车站、商店、学校、住宅、亭廊、体育场看台等工业与民用建筑的屋盖.目前折板结构建筑中绝大部分采用折叠式V形折板屋盖,比较单一,影响了推广应用范围.本文提出一种力学性能好,外观优美的平顶组合抛物面薄壳屋盖结构.借助斜坐标系和阶跃函数,建立了平顶组合抛物面薄壳屋盖的曲面方程,然后应用薄壳振动理论和变分法求得了简支平顶组合抛物面薄壳屋盖受迫振动响应的挠度和内力表达式.本文还可以解决组合抛物面薄壳屋盖的静力、自由振动和受迫振动等问题,故本文实际上包含了两种组合薄壳屋盖六个问题的解.     

Finite element analysis of singly and doubly curved dams of constant or variable thickness

In this paper rectangular and triangular strain based shell finite elements are applied to the analysis of doubly curved dams. The elements having only the five essential external degrees of freedom per corner node, satisfy the exact representation of rigid body modes and are based on shallow shell formulation.     

Accurate dynamic response of laminated composites and sandwich shells using higher order zigzag theory

Forced vibration response of laminated composite and sandwich shell is studied by using a 2D FE (finite element) model based on higher order zigzag theory (HOZT). This is the first finite element implementation of the HOZT to solve the forced vibration problem of shells incorporating all three radii of curvatures including the effect of cross curvature in the formulation using Sanders' approximations. The proposed finite element model satisfies the inter-laminar shear stress continuity at each layer interface in addition to higher order theory features, hence most suitable to model sandwich shells along with composite shells. The C₀ finite element formulation has been done to overcome the problem of C₁ continuity associated with the HOZT. The present model can also analyze shells with cross curvature like hypar shells besides normal curvature shells like cylindrical, spherical shells etc. The numerical studies show that the present 2D FE model is more accurate than existing FE models based on first and higher order theories for predicting results close to those obtained by 3D elasticity solutions for laminated composite and sandwich shallow shells. Many new results are presented by varying different parameters which should be useful for future research.