弹性地基上厚板的计算分析

以弹性地基上Reissner板为研究对象,地基采用双参数模型,把地基效应归并到厚板的弯曲微分方程中。利用导出的双参数地基上厚板弯曲问题的基本解,从虚功原理出发,依据胡海昌的中厚板弯曲理论,推导出三个广义位移表示的边界积分方程。适用于任意边界条件、任意形状及任意荷载的薄板及中厚板的弯曲问题。文中给出了算例,并对各种参数变化进行了分析,获得了满意的结果。     

高层建筑筏板基础分析的样条虚边界元法

基于Reissner厚板理论和Winkler弹性地基假定(非单一基床系数),提出了非均匀弹性支承厚板弯曲分析的样条虚边界元法,并将该法应用于高层建筑筏板基础的分析.本文方法计算量少、计算精度高,可以求解具有不同边界条件和任意域内支承的薄板和厚板在任意荷载作用下的挠度和内力,可用来对工程中各种板结构弯曲问题进行统一的分析.工程算例显示了本文方法在高层建筑筏板基础和桩基承台分析中的正确性和实用性.     

Effect of transverse shear strains on plates resting on elastic foundation using modified Vlasov model

A four-noded quadrilateral (PBQ4) and an eight-noded quadrilateral (PBQ8) plate bending element based on Mindlin plate theory are adopted for the analysis of thin and thick plates resting on elastic foundation using modified Vlasov model. The terms of vertical deflection stiffness matrix and shear deformation stiffness matrix of the subsoil are evaluated using finite element method, and presented in explicit forms. Selective reduced integration technique is used in addition to full integration technique for both the types of the elements to avoid shear-locking problem that occurs under the thin plate limit. It has been demonstrated that the performance of the eight-noded quadrilateral element is excellent for thin and thick plates on elastic foundation when selective-reduced integration technique is used. General conclusion can be drawn from the results that the effect of the shear strain on the behavior of the plate resting on subsoil is always quite small for free plates compare to the supported ones.     

Application of B. N. Zhemochkin's Method to Analysis of a Bendable Slab on an Elastic Bed

An approach that makes it possible to analyze slabs of any planform on an arbitrary type of elastic bed is outlined on the basis of symbiosis of V. Rutts' and B. N. Zhemochkin's methods; this is of utmost urgency for analysis of slab foundations. Examples are cited for the analysis of slabs on an elastic foundation bed in Cartesian and polar coordinate systems.     

基于改进Vlasov模型的弹性地基上平板横向剪应变分析

运用Vlasov模型对弹性基础上的薄板和厚板进行分析,采用了基于Mindlin板理论的4结点四边形和8结点四边形弯曲单元。运用有限元法对底层土的竖向挠度刚度矩阵和剪切变形刚度矩阵进行推算。针对2种类型的板单元,采用完全积分方法和选择性简化积分方法进行分析,以避免极限状态下薄板的剪切闭锁问题。研究发现：在选择性简化积分方法中,8结点四边形板单元非常适用于分析弹性基础上的薄板和厚板。结果表明：相比有支撑的平板,剪应变对底层土上无支撑平板的影响非常小。     

任意形状弹性地基问题的无穷边界单元法

在研究建筑物与地基相互作用时,常遇到各种形状的地基问题。本文根据边界元理论,采用统一的Kelvin基本解导出适合于求解任意形状弹性地基问题的边界积分方程,引入两类无穷边界单元并给出完整的坐标、位移和面力形函数以及它们所应满足的条件。算例表明,本文方法是行之有效的,并具有节省单元、计算方便、精度高等优点。     

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

Web core panels, foam-filled sandwich panels with interior webs, are a structurally efficient option for transverse load bearing applications. In web core panels, the interaction between the webs and core material can have a substantial impact on web shear buckling strength and is a key element of lightweight structural design. The present work is an investigation of web buckling behavior in web core panels under a distributed load. To solve this problem, web shear buckling was analyzed for the case of pure shear loading with foam support, and this analytic model was extended to the case of panels with a transverse distributed load. The webs are modeled as simply supported plates resting on a Pasternak elastic foundation. To that end, a buckling model for plates on a Pasternak foundation is presented, along with closed-form approximations of the solution for square and infinitely long plates. An accurate model for the foundation constants is developed using energy methods. Applicability of the plate buckling model to web core panels with transverse loads is presented via a finite element study. In panels, the slenderness and spacing of the webs have a slight effect on the boundary conditions between the webs and face sheets. The effect is relatively small, however, and the model presented in this work underpredicts buckling strength by less than 25%. The model in this work is thus a reasonable approach to the practical design of web core panels.     

弹性地基板动力响应问题的多变量样条状态空间精细法

采用样条元与状态空间精细法分析弹性地基板的动力响应量。对空间域采用样条元计算,对时间域采用状态空间精细法。在计算过程中,不解线性方程组,直接进行精细迭代计算,程序简单,效率高。同时给出了数值算例,并与其他算法进行了比较,其计算结果比较接近。     

大型筒仓与地基静力相互作用研究

筒仓作为一种现代工程结构，在工程实际中得到广泛的应用，本以某大型筒仓结构为例，考虑到散体、结构、地基的相互作用与影响，考虑地基与基础及结构的耦合问题，采用半解析半数值的方法对弹性地基上的简仓结构进行了静力分析计算，计算了筒仓各结线的静位移以及地基和基础板随半径变化时的静位移变化规律。     

Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells — Part 2: Shape optimisation

This paper deals with the development of computational tools for structural shape optimisation of shells and folded plates in which the strain energy or the weight of the structure is minimised subject to certain constraints. Both thickness and shape variables defining the cross-section of the structure are considered. The analysis is carried out using curved, variable thickness finite strips formulated and tested in Part 1 of this paper. Optimal shapes are presented for several shells and folded plates of variable thickness including plates on elastic foundation. The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimisation. The tools developed in the present work can be used as an aid to structural engineers in designing novel forms for shells and folded plates and provide valuable insight into the structural behaviour. It is concluded that the finite strip method offers an accurate and inexpensive tool for the optimisation of a wide class of structures having regular prismatic-type geometry with diaphragm ends.     

Nonlinear analysis of imperfect laminated thin plates under transverse and in-plane loads and resting on an elastic foundation by a semi-analytical approach

The large deflection and postbuckling behavior of imperfect composite laminated plates exposed to a combined action of transverse loads and in-plane edge compressions and resting on an elastic foundation are investigated in this paper by a semi-analytical approach. The formulations are based on the classical laminated plate theory (CLPT), and include the plate–foundation interaction effects via a two-parameter model (Pasternak-type) from which Winkler elastic foundation can be recovered as a limiting case. The present approach employs a perturbation technique, one-dimensional differential quadrature approximation and the Galerkin procedure to model the nonlinear performance of the plate with arbitrary combination of simply supported, clamped or elastic rotational edge constraints. Studies concerning its accuracy and convergence characteristics are carried out through some numerical illustrations. Effects of foundation stiffness, plate aspect ratio, total number of plies, fiber orientation, initial geometrical imperfection, the character of boundary conditions, and load patterns on the nonlinear behavior of the plate are studied. Typical numerical results are given in dimensionless graphical forms.     

双参数弹性地基厚板分析的边界元法

以弹性地基上Ｒｅｉｓｓｎｅｒ板为研究对象，地基采用双参数模型，把地基效应归并到厚板的弯曲微分方程中。利用「４」导出的双参数地基上弯曲问题的基本解，从虚功原理出发，依据在胡海昌的中厚板弯曲理论，推导出三个广义位移表示的边界积分方程。适用于任意边界条件，任意形状及任意荷载的薄板及中厚板的弯曲问题。     

Effect of axial restraint in composite bars under nonlinear inelastic uniform torsion by BEM

In this paper, the effect of axial restraint in the elastic–plastic uniform torsion analysis of cylindrical bars taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The bar is axially elastically supported at the centroids of its end cross sections, treating the cases of free axial boundary conditions (vanishing axial force), restrained axial shortening or given axial force as special ones. The cross section of the bar is an arbitrary doubly symmetric composite one, consisting of materials in contact, each of which can surround a finite number of inclusions, while the case of a homogeneous cross section is treated as a special one. The stress–strain relationships for the materials are assumed to be elastic–plastic-strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometrically nonlinear term, often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross section is evaluated directly employing the primary warping function of the cross section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals. The significant increase of the torsional rigidity of the bar and the arising axial force due to the axial restraint are concluded.     

应用边界积分方程法分析任意形状和边界条件薄板的弹性和弹塑性弯曲问题

本文基于周边嵌固圆板的格林函数,采用间接法建立了任意边界薄板弯曲的边界积分方程,从而可以获得任意荷载、任意边界形状薄板弯曲问题的弹性和弹塑性解。 应用边界积分法,并假定板的材料性质适用单轴拉伸来表示有效应力-有效应变之间的关系和采用拟荷载法,来求薄板弯曲问题的弹塑性解,可以避免多次修改弹性刚度矩阵,每次叠代只要重新形成右端荷载向量,加速了计算的速度。它与通常有限单元法的薄板弹塑性分析相比,具有输入数据简单,计算量少,省时间,精度高等显著优点。 文中给出薄板弯曲的弹性解和弹塑性解实例,说明方法的效果。     

Two-dimensional analytical analysis of equilibrium shape of inflated geomembrane tube resting on rigid foundation with arbitrary shape

Geomembrane tubes are used as an alternative to old methods for flood protection and may be considered as inflatable structures. These tubes can be filled with air and/or water and placed on ground, or any foundation. In this paper, a new analytical method is developed to determine the equilibrium shape of a geomembrane tube filled with air and resting on rigid foundations of an arbitrary shape. Geometric and equilibrium relations of a tube element are used to obtain the equilibrium shape of tube in an explicit (closed) form. The material of the tube is assumed to be inextensible and its bending stiffness is neglected. Using the closed form solution presented in this paper, the equilibrium shape of geomembrane tubes resting on foundations with different shapes and with different internal pressures, can be easily determined and there is no need to solve the problem numerically. The validity of the present analytical approach is confirmed by comparing the results with selected references. The results of comparison show that the presented analytical formulation provides the same level of accuracy with less numerical effort.     

Simplified lower bound limit analysis of transversely loaded thin plates using generalised yield criteria

In this paper a simple method of deriving lower bound limit loads for thin plates is presented. This method is based on the method of elastic compensation, an iterative elastic technique, which has recently been extended to allow the analysis of structures using thin shell finite element analysis using generalised yield criteria. Here the method is modified to allow analysis of plates, including the effects of transverse shear. The elastic compensation method, combined with generalised yield criteria, is implemented using the finite element numerical analysis technique. Convergence studies are carried out and limit loads are obtained for a range of geometries, boundary conditions and loading. The calculated limit loads are compared with results available in the literature and with new elasto-plastic results and show that the method can be used to quickly obtain practical results.     

An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis

In this article, we investigate the vibration analysis of plates and shells, using an eight-node shell element that allows for the effects of transverse shear deformation and rotary inertia. The natural frequencies of plates and shells are presented, and the forced vibration analysis of plates and shells subjected to arbitrary loading is carried out. In order to overcome membrane and shear locking phenomena, the assumed natural strain method is used. To improve the eight-node shell element for free and forced vibration analysis, a new combination of sampling points for assumed natural strain method was applied. The refined first-order shear deformation theory based on Reissner–Mindlin theory, which directly addresses the transverse shear deformation without a shear correction factor, is adopted for the development of a new eight-node assumed strain shell element with rotary inertia effect. In order to validate the finite element numerical solutions, the reference solutions of plates based on the first-order shear deformation theory are presented. Results of the present theory show good agreement with the reference solutions. In addition, the effect of damping is investigated on the forced vibration analysis of plates and shells.     

采用FSDT无网格法对折板进行弯曲分析

采用基于一阶剪切变形理论(FSDT)的无网格Galerkin方法分析不同荷载和边界条件下的带加劲肋和无加劲肋的折板弹性弯曲问题。折板由不同平面的板组合而成,这些板的刚度矩阵由无网格法给出。借用有限元概念,将每一块板都视为一个单元,整块板的整体刚度矩阵就可以通过这些单块板的刚度矩阵而得到。加劲板也同样如此,采用无网格法给出加劲板的刚度矩阵。比有限元方法优越的是,在确定板刚度矩阵的时候不需要网格,这意味着在折板或加劲肋位置变化处的大变形或者裂缝发展时,可以避免耗时过长,以及网格重组带来的对精度的影响。为验证此法的精确度和收敛性,本文采用此法及ANSYS对多个数学模型进行计算,结果表明两组结果非常一致。     

弹性地基板的非线性分析

本文以路面工程为应用背景,针对弹性地基上承受横向载荷的板体进行了非线性有限元分析,采用考虑横向剪切变形的中厚板非协调单元模式,改进了数值性能,避免由于局部小面积受载时,剪切变形较大带来的误差,同时将地基刚度矩阵引入失衡力迭代格式中,保证解的收敛性.文中给出了载荷位于板中、板边、板角时的板体变形情况和破坏状况以及极限承载能力,并与塑性铰线理论、弹性薄板理论进行了比较和分析.     

Semi-analytical postbuckling and strength analysis of arbitrarily stiffened plates in local and global bending

A semi-analytical method for pre- and postbuckling analysis of imperfect plates with arbitrary stiffener arrangements, subjected to in-plane biaxial and shear loading, is presented. By using large deflection theory in combination with the Rayleigh–Ritz approach on an incremental form, the method is able to trace both local and global equilibrium paths. Ultimate strength predictions are made using the von Mises’ yield criterion applied to the membrane stresses as collapse criterion. A Fortran computer program based on the presented theory is developed and computed results are verified by comparisons with nonlinear finite element analysis. Relatively high numerical accuracy is achieved with small computational efforts. The method is therefore suited also for design optimisation and reliability studies.