Geometrically exact displacement-based shell theory

The deformed geometry often is the most important information for applications of highly flexible plates/shells, and a geometrically exact shell theory should be displacement-based in order to directly and exactly describe any greatly deformed geometry. The main challenges of modeling a shell undergoing large deformation are how to describe its deformed reference plane and its differential element's large rotations and how to derive objective strains in terms of global displacements and rotations that contain both elastic straining and rigid-body movement. This paper presents a truly geometrically exact displacement-based shell theory without singularity problems. The theory fully accounts for geometric nonlinearities, all possible initial curvatures, and extensionality by using Jaumann strains and stresses, exact coordinate transformation, and orthogonal virtual rotations. Moreover, transverse shear deformations are accounted for by using a high-order shear deformation theory. The derived fully nonlinear strain–displacement relations enable geometrically exact forward analysis (obtaining the deformed geometry under a set of known loads) and inverse analysis (obtaining the required loads for a desired deformed geometry). Several numerical examples are used to demonstrate the accuracy and capabilities of the geometrically exact shell theory. Moreover, different theoretical and numerical problems of other geometrically nonlinear shell theories are shown to be mainly caused by the use of Mindlin plate theory to account for transverse shears, Green–Lagrange strains to account for geometric nonlinearities, and/or Euler and Rodrigues parameters to model large rotations.     

Starr verankerte dünnwandige windbelastete Kreiszylinderschalen mit Dachscheibe

Anchoring forces of cirular cylindrical shells. The wind force distribution according to the new german standard DIN 1055‐4:2005‐03 “Action on structures – Wind loads” is shown and transferred into Fourier series for various values of the Reynolds constant. The values are given in tables. Using a computer program developed by the author anchoring forces of closed circular cylindrical shells are calculated, based on the shell theory, for various non‐dimensional geometries and for rigid anchors. The results of these calculations are presented in tables for easy use by designers. An example shows the influence of elastic anchors.     

弗留盖圆筒壳理论的广义变分原理

弹性力学广义变分原理是弹性力学体系的重要组成部分。证明了基于精确的弗留盖弹性圆筒壳理论广义变分原理的正确性。     

三维框架结构几何非线性分析综述

结构非线性分析是预测结构承载力或极限强度的有效方法.对三维框架结构的几何非线性、屈曲、后屈曲的研究进展进行综述,主要涵盖以下关键问题:(1)解析或半解析方法;(2)用于增量迭代非线性分析的公式;(3)三维框架在变形状态下的节点平衡;(4)非线性有限元的刚体测试;(5)增量分析中的迭代机制;(6)单元节点力的计算;(7)...     

带帽桩复合地基复合桩土应力比的计算及影响因素分析

在分析带帽刚性桩复合地基试验成果的基础上,提出复合桩土应力比的概念,以合理反映带帽桩复合地基的力学性状。以土力学和弹性理论为基础,基于合理假定,采用等沉面的思想,考虑复合桩体发生上、下刺入变形现象,推导出能够反映层状不均质地基和带帽桩复合地基空间三维沉降变形特征的复合桩土应力比隐式计算公式。通过工程算例,分析了桩体中心间距、桩长、桩帽尺寸、垫层变形模量、下卧层土体变形模量、桩帽间土体变形模量和静止侧压力系数等因素的影响,提出了利用复合桩土应力比进行带帽桩复合地基按桩帽间土体沉降量控制优化设计的思路。     

大型筒仓结构与地基的动力相互作用研究

本以某大型筒仓结构为例，考虑到散粒体-结构-地基的相互作用，利用部分集中质量-筒仓耦合相互作用法，对弹性地基上的筒仓结构（包括单体筒仓和筒仓群或排仓）进行了多种工况、系统的有限无动力分析计算。经与刚性地基上的筒仓动力响应的比较，得出以下结论：在对地基施以相同的水平激励时，弹性地基上筒仓的动力响应大于刚性地基上筒仓的动力响应；刚性地基上群仓的动力响应大于单体仓的动力响应；弹性地基上单体仓的动力响应大于群仓的动力响应。     

多体系统非连续变形的弹性及弹塑性分析方法(II)—— 数值算例

应用多体系统非连续变形的弹性及弹塑性分析方法从不同角度对刚性体、弹性体和弹塑性体组合多体系统进行具体的数值计算与分析,探讨接触界面的力学参数和材料强度参数对系统的变形、应力和接触应力以及塑性区的影响,得出十分有意义的结果与比较合理的结论.算例表明非连续变形计算力学模型作为一种新颖而强有力的数值分析与数值模拟方法,能够对一般的刚性体、弹性体和弹塑性体所构成的复杂的多体系统进行静、动力及接触非线性和材料非线性耦合数值分析与模拟,具有广泛的应用前景.     

考虑下卧弹性基岩的地下结构抗震分析模型

针对广泛采用的振动方法仅能考虑下卧刚性基岩条件的问题,基于等效节点荷载地震动输入方法和等位移边界,提出了可以考虑下卧弹性基岩恢复力和反射/透射地震波向地层深处逸散效应的地下结构抗震实用分析模型。介绍了等效节点荷载输入原理,通过数值算例验证了等位移边界的适用性。通过均质和成层场地算例,验证了分析模型正确性。以上海场地为例,对比分析振动方法与本文分析模型,地表位移和隧道结构内力响应初期相近,而后期差异显著,体现了下卧刚性基岩和弹性基岩不同场地条件的区别。下卧弹性基岩场地条件地下结构抗震分析,采用本文模型更符合实际情况。     

Axial compression of metallic spherical shells between rigid plates

Aluminium spherical shells of R/t values between 15 and 240, were axially compressed in an INSTRON machine between flat plates. The modes of their collapse, load-compression and energy-compression curves, and mean collapse loads are presented. A simple analytical model has been developed for the prediction of load-compression and energy-compression curves for the metallic spherical shells, by using the concepts of stationary and rolling plastic hinges. The results thus obtained match well with the experimental results. These results have also been compared with the solutions proposed in earlier studies. Behaviour of these shells is compared with the response of spherical shells (aluminium, mild steel and galvanised steel) of shallow depth, which were also subjected to axial compression between rigid plates. Their load-deformation curves are presented, and their energy-compression behaviour and mean collapse loads are discussed.     

Buckling and post-buckling behaviour of elastic seven-layered cylindrical shells – FEM study

The paper is devoted to buckling and post-buckling problems of an elastic seven-layered cylindrical shell under uniformly distributed pressure. The shell is an untypical sandwich structure composed of main corrugated core and two three-layer faces. Numerical FEM model for the shell has been elaborated. The calculations have been performed with the use of the ANSYS code for elastic shells of different dimensions. The linear and non-linear analyses of the shells have been performed with the use of the finite elements method. Critical pressure and equilibrium paths for the family of seven-layered shells subjected to uniformly distributed external pressure are calculated. The influence of corrugation pitch of main core and the length of the shell on the critical pressure has been determined. The results of these investigations are presented on the graphs.     

Thin-walled structures as impact energy absorbers

The key structural components of the majority of transportation vehicles are designed as thin-walled components. During a crash event, a number of structural components must sustain abnormal loadings in order to meet stringent integrity requirements. At the same time other components must dissipate impact energy in a controlled manner that limits the deceleration of a vehicle to a required safety limit. The present paper focuses on the crushing mechanics of thin-walled components. The analysis method is based on the Superfolding Element (SE) concept, which originates from experimentally observed folding patterns of crushed shell elements. The paper presents milestones of the underlying theory of plastic shells and basic design considerations that are coupled with the SE-based predictive techniques in a CAE software. The paper also presents basic examples of the design process of typical energy absorbing components.     

Coupled dynamic instability of thin-walled structural systems

The dynamics of thin-walled structural systems are presented for both the pre- and the post-buckling states. The influence of the coupling effect of axial compression and initial imperfection on the dynamical response of columns, plates and cylindrical shells is discussed. The theoretical procedure used to study the subject is presented, together with illustrative examples. The use of the results obtained for the prediction of buckling loads of cylindrical shells by means of nondestructive vibration tests is also presented. The implications of the results on the design of thin-walled systems is discussed. The work is done in the scope of the elastic stability, and damping is not included in the analysis.     

Thermal buckling of FGM shells resting on a two-parameter elastic foundation

This paper focuses on the thermal buckling analysis of FGM shells resting on the two-parameter elastic foundation. Material properties of the constituents are graded in the thickness direction according to the power-law distribution. The surrounding elastic medium is modeled as an elastic foundation of the Pasternak-type. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell subjected to thermal load and resting on a two-parameter elastic foundation have been derived. Critical temperature differences of FGM truncated conical shells with or without elastic foundations subjected to non-linearly distributed temperature across the thickness of the shells are obtained by solving eigenvalue problems. The appropriate formulas for FGM cylindrical shells with or without elastic foundations are found as a special case. In order to assure the accuracy of the present study, convergence properties of the critical temperature are examined in detail.     

Effects of imperfections of the buckling response of composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling response and failure of unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells are presented. The shells considered in the study have six different shell-wall laminates two different shell-radius-to-thickness ratios. The shell-wall laminates include four different orthotropic laminates and two different quasi-isotropic laminates. The shell-radius-to-thickness ratios includes shell-radius-to-thickness ratios equal to 100 and 200. The numerical results include the effects of traditional and nontraditional initial imperfections and selected shell parameter uncertainties. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The nontraditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, nonuniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. The cylinder parameter uncertainties considered include uncertainties in geometric imperfection measurements, lamina fiber volume fraction, fiber and matrix properties, boundary conditions, and applied end load distribution. Results that include the effects of these traditional and nontraditional imperfections and uncertainties on the nonlinear response characteristics, buckling loads and failure of the shells are presented. The analysis procedure includes a nonlinear static analysis that predicts the stable response characteristics of the shells, and a nonlinear transient analysis that predicts the unstable response characteristics. In addition, a common failure analysis is used to predict material failures in the shells.     

Elastic flexural-torsional buckling of steel beams with rigid and continuous lateral restraints

A simple model of the elastic buckling of steel beams with rigid and continuous lateral restraints has been developed. It is based on a method of displacements that associate lateral restraint conditions. A numerical procedure for resolving the resulting partial differential equations is proposed in which rotations are approximated by trigonometric functions. The effects of moment distribution and continuous restraints on the elastic flexural-torsional buckling of beams are also studied and design approximations and procedures developed. This study also highlights that the restraint of the tensioned part of the beam is not sufficient to limit lateral buckling. The use of these solutions is demonstrated by two examples.     

Elastic buckling of elliptical tubes subjected to generalised linearly varying stress distributions

The structural behaviour of elliptical hollow sections has been examined in previous studies under several loading conditions, including pure compression, pure bending and combined uniaxial bending and compression. This paper examines the elastic buckling response of elliptical hollow sections under any linearly varying in-plane loading conditions, including the most general case of combined compression and biaxial bending. An analytical method to predict the elastic buckling stress has been derived and validated against finite element results. The predictive model first identifies the location of the initiation of local buckling based on the applied stress distribution and the section geometry. The critical radius of curvature corresponding to this point is then introduced into the classical formula for predicting the elastic local buckling stress of a circular shell. The obtained analytical results are compared with results generated by means of finite element analysis. The comparisons between the analytical and numerical predictions of elastic buckling stress reveal disparities of less than 2.5% for thin shells and, following an approximate allowance for the influence of shear, less than 7.5% for thick shells.     

Tailoring the elastic postbuckling response of thin-walled cylindrical composite shells under axial compression

The buckling of cylindrical shells has long been regarded as an undesirable phenomenon, but increasing interests on the development of active and controllable structures open new opportunities to utilize such unstable behavior. In this paper, approaches for modifying and controlling the elastic response of axially compressed laminated composite cylindrical shells in the far postbuckling regime are presented and evaluated. Three methods are explored (1) varying ply orientation and laminate stacking sequence; (2) introducing patterned material stiffness distributions; and (3) providing internal lateral constraints. Experimental data and numerical results show that the static and kinematic response of unstable mode branch switching during postbuckling response can be modified and potentially tailored.     

Plastic buckling of thin hemispherical shell subjected to concentrated load at the apex

This study presents the analytical, numerical, and experimental results of thin hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal and vertical translation and the load is vertically applied by a rigid cylindrical boss at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for rigid-perfectly plastic shells are formulated on the basis of Drucker–Shield's limited interaction yield condition. The effect of the radius of the boss, used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Both axisymmmetric and 3D models are implemented in the numerical work to verify the presence of non-symmetric deformation modes in the case of thin shells. In the end, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load–deflection curves obtained using three different approaches. A secondary bifurcation point is detected in thin shells in which the deformation degenerates from symmetric to non-symmetric behavior. The bifurcation point depends on the (R/t₀) ratio and the material parameters.     

结构力学中反对称荷载作用下对称刚架的弯矩图规律

在结构力学的学习过程中,绘制弯矩图是基本功,属于重点考查内容,也是结构内力分析的起始性关键环节。超静定结构的弯矩图比较复杂,严重影响了学生对基本内容的理解和掌握。文章旨在通过对比静定对称刚架的弯矩图,分析反对称荷载作用下超静定对称刚架的弯矩图特点,从而找出对称刚架弯矩图的一般性规律。     

Size effects in two-dimensional layered materials modeled by couple stress elasticity

In the present study, the effect of material microstructure on the mechanical response of a two-dimensional elastic layer perfectly bonded to a substrate is examined under surface loadings. In the current model, the substrate is treated as an elastic half plane as opposed to a rigid base, and this enables its applications in practical cases when the modulus of the layer (e.g., the coating material) and substrate (e.g., the coated surface) are comparable. The material microstructure is modeled using the generalized continuum theory of couple stress elasticity. The boundary value problems are formulated in terms of the displacement field and solved in an analytical manner via the Fourier transform and stiffness matrix method. The results demonstrate the capability of the present continuum theory to efficiently model the size-dependency of the response of the material when the external and internal length scales are comparable. Furthermore, the results indicated that the material mismatch and substrate stiffness play a crucial role in the predicted elastic field. Specifically, the study also addresses significant discrepancy of the response for the case of a layer resting on a rigid substrate.