An effective four node degenerated shell element for geometrically nonlinear analysis

The development of a new four node degenerated shell element is presented for the analysis of the shell structures undergoing large deformations. In the formulation of the new element, the assumed covariant transverse shear strains are used to avoid the shear locking problem, and the assumed covariant membrane strains which are separated from the covariant inplane strains by mid-surface interpolation, are applied to eliminate the membrane locking problem and also to improve the membrane bending performance. This element is free of serious shear and membrane locking problems and undesired spurious kinematic deformation modes. An incremental total Lagrangian formulation is presented which allows the calculation of arbitrarily large displacements and rotations. The resulting nonlinear equilibrium equations are solved by the Newton-Raphson method combined with load or arc-length control. The versatility and accuracy of this new degenerated shell element is demonstrated by solving several numerical examples.     

Finite element modeling and shake-table testing of unidirectional infill masonry walls under out-of-plane dynamic loads

The dynamic out-of-plane response of unreinforced masonry walls is investigated. The study combines analytical, numerical, and experimental methodologies. The paper focuses on structural schemes that involve supporting at the base and the top and yield a unidirectional (one-way) flexural action. First, the modeling concepts for the nonlinear dynamic analysis are discussed and used as a basis for a finite element formulation. The element is based on a first-order shear deformation theory with large displacements, moderate rotations, small strains, material nonlinearity, and a Rayleigh type of viscoelastic damping. The nonlinearities due to cracking and the inelastic response under cyclic compression are introduced through the constitutive model for the mortar. The experimental part includes shake-table testing under different levels of out-of-plane excitation and compressive loading. The experimental results and the numerical model quantify a range of physical phenomena, including the dynamic arching and rocking effects, the coupling of the axial (in the height direction) and the out-of-plane responses, the role of axial loading, and the vulnerability of the masonry construction to dynamic loads. The comparison between the numerical results and the experimental results examines the capabilities of the model and gains insight into the nonlinear dynamics of the masonry wall.     

Transient dynamic response of composite circular cylindrical shells under radial impulse load and axial compressive loads

Free and forced vibration of composite circular cylindrical shells are investigated based on the first love's approximation theory using the first-order shear deformation shell theory. The boundary conditions (BCs) are considered as clamped-free edges. The dynamic response of the composite shells is studied under transverse impulse and axial compressive loads. The axial compressive load was less than critical buckling loads. The modal technique is used to develop the analytical solution of the composite cylindrical shell. The solution for the shell under the given loading conditions can be found using the convolution integrals. The effect of fiber orientation, axial load, and some of the geometric parameters on the time response of the shells has been shown. The results show that dynamic responses are governed primarily by natural period of the structure. The accuracy of the analysis has been examined by comparing results with those available in the literature and experiments.     

单层网壳结构在地震作用下的弹塑性动力响应研究

采用U L有限元列式 ,基于各向同性强化模式 ,Von Mises屈服准则和Prandtl Renss增量理论 ,针对强烈地震作用 ,考虑结构的几何和材料非线性 ,研究单层网壳在多维地震作用下的弹塑性动力响应计算。提出了一种有效的适用于网壳结构非线性动力响应的增量 /迭代有限元计算方法 ,考虑了转角大位移的精确计算 ,并对一个短程线形单层球面网壳结构进行了地震响应的双重非线性时程分析研究 ,探讨了结构的延性抗震性能     

基于高阶剪切变形理论及径向基函数的各向同性叠合板的屈曲分析

基于三阶剪切变形理论及径向基函数,预测弹性板的临界荷载。该理论说明了沿钢板厚度方向的横向应力呈抛物线分布的原因。结果表明:径向基函数能精确地预测钢板的临界荷载和失效模式。     

Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory

The third-order shear deformation theory of Reddy and collocation with radial basis functions is used to predict the buckling loads of elastic plates. The theory accounts for parabolic distribution of the transverse strains through the thickness of the plate. It is shown that the collocation method with radial basis functions produces highly accurate critical buckling loads and modes.     

Buckling of thin and moderately thick anisotropic cylinders under combined torsion and axial compression

The effects of anisotropy, transverse shear stiffness, length, and their interactions on buckling under pure torsion and under combined axial compression and torsion were investigated using a previously derived analytical model based on deep shell theory including anisotropy and transverse shear stiffness. The model was verified only for buckling under pure axial compression, hence results for buckling under torsion have now been compared with the results of previous analyses, and the comparison showed that the model has good accuracy for buckling under torsion. Investigation showed that the buckling loads of a cylindrical shell are affected not only by anisotropy and transverse shear stiffness but also by shell length. This means that the shallow shell theory (Donnell-type theory) is not appropriate and deep shell theory including anisotropy and transverse shear stiffness must be used.     

复合圆柱形壳在径向冲击荷载和轴压荷载作用下的瞬时动力响应

基于首次逼近理论,利用第一阶剪切变形理论对圆柱形壳的自由和强迫振动进行分析。边界条件（BCs）考虑为悬臂状态。分析复合壳体在横向冲击和轴向压力作用下的动力响应（轴压荷载小于临界屈曲荷载）,同时对复合柱形壳进行了建模分析。利用卷积积分对给定荷载状况下的壳体进行分析。揭示纤维方向、轴向荷载及一些几何参数对壳体时间响应的影响。结果表明：动力响应主要由结构的自振周期所控制。     

Orthotropic von Karman plates using higher order elements

The nonlinear behaviour of orthotropic plates subject to transverse loading is studied in this paper using higher order finite elements. The formulation procedure for elements with up to 25 nodes is established and derivation of the tangential stiffness matrix based on the classical von Karman nonlinear theory is presented. These elements are derived by employing a high order polynomial displacement function to represent the in-plane and the bending displacements. By adopting separate variables for the transverse deflections and the rotations of the plate, the effect of transverse shear deformation can be included in modelling thin to moderately thick plates, thus enabling the effect of transverse shear on the nonlinear behaviour of plates to be included. The Newton-Raphson method for solving nonlinear equations is adopted to obtain the final state of equilibrium of the system. Several numerical examples are presented and the results are compared with available experimental data as well as analytical and numerical solutions obtaned by other conventional methods. Satisfactory agreement on the nonlinear performance of the plates as predicted by the present method is demonstrated.     

对称双圆弧柱壳的非线性屈曲

对于潜艇艇体耐压壳结构,屈曲特性在设计中被广泛关注。针对一种新型潜艇耐压艇体结构-对称双圆弧环肋柱壳,推导了相应的弹塑性失稳系数。采用非线性大挠度理论,给出了静水压力作用下含初始缺陷的对称双圆弧环肋柱壳大挠度弹塑性屈曲临界压力计算式。讨论了开口角、周向相当波数和初始几何缺陷对临界压力的影响。计算结果表明,开口角对结构弹塑性屈曲的临界压力影响很小,而周向相当波数是影响临界压力的主要因素。     

Advanced analysis of multi-span suspension bridges

In this paper, an efficient analysis method considering both geometric and material nonlinearities is proposed for predicting the ultimate strength and behavior of multi-span suspension bridges. The geometric nonlinearities of the cable members due to sag effects are captured using the catenary element, while the geometric nonlinearities of the beam-column members due to second-order effects are captured using the stability functions. The material nonlinearities of the cable and beam-column members are considered using elastic–plastic hinge and refined plastic hinge models, respectively. A simple initial shape analysis method is presented to determine the deformed shape and initial cable tension of the bridge under dead loads. Numerical examples are presented to verify the accuracy and efficiency of the proposed method. In addition, a case study on a four-span suspension bridge is carried out to show the capability of the proposed method in estimating the strength and behavior of very large scale structures.     

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.     

Nonlinear analysis of composite beams with concrete-encased steel truss

Composite beams constituted by a concrete-encased steel truss welded to a continuous steel plate are analyzed using a nonlinear finite element formulation based on Newmark's classical model. The web member of the steel truss is made by deformed or structural steel rebars and behaves like a deformable shear connection. In order to avoid slip locking, finite elements based on second-order interpolation of longitudinal displacements and flexural rotations are employed. Simply supported composite beams subjected to a uniformly distributed transverse load are considered. The bending capacity is evaluated for short up to long spans, taking the nonlinear behavior of concrete, steel and shear connection into account. The effects of the shear connection ductility are put in evidence, showing that, for short spans, the interfacial stress transfer resulting from the yielding of connection may be penalizing. In fact, the high slip gradient arising in sections near the supports may lead to a premature concrete failure. In this case, the exact solution to the linear elastic problem for steel–concrete composite beams can be used for design purposes.     

Torsion in thin-walled cold-formed steel beams

Thin-walled cold-formed steel members have wide applications in building structures. They can be used as individual structural framing members or as panels and decks. In general, cold-formed steel beams have open sections where centroid and shear center do not coincide. When a transverse load is applied away from the shear center it causes torque. Because of the open nature of the sections, torsion induces warping in the beam. This paper summarizes the research on the behavior of cold-formed steel beams subject to torsion and bending. The attention is focused on beams subject to torque, because of the effect of transverse loads not applied at the shear center. A simple geometric nonlinear analysis method, based on satisfying equilibrium in the deformed configuration, is examined and used to predict the behavior of the beams. Simple geometric analyses, finite element analyses and finite strip analyses are performed and compared with experimental results. The influence of typical support conditions is studied and they are found to produce partial warping restraint at the ends. This effect is accounted for by introducing hypothetical springs. The magnitude of the spring stiffness is assessed for commonly used connections. Other factors that affect the behavior of cold-formed steel members, such as local buckling, are also studied.     

Geometrically non-linear approximations on stability and free vibration of composite beams

Second-order formulations based on moderate rotations are often used in finite element models because this approximation facilitates their implementation. However, in some cases this approximation is not enough to obtain all couplings among bending, twisting and stretching deformations for a beam member. Therefore, a simplified second-order formulation may lead to the subsequent loss of some significant terms in the non-linear strains. Without these terms the beam model may predict inaccurate results when the effect of large rotations is important. The present paper investigates the influence of large rotations on the buckling and free vibration behavior of thin-walled composite beam. To carry out this analysis it is necessary to use a geometrically higher-order non-linear beam theory. A distinctive feature of the present study over others available in the literature is that this beam model incorporates, in a full form, the effects of shear flexibility (bending and warping shear). The numerical results show that second-order formulation overestimates the buckling load and natural frequency values when the effect of large rotation is important, and this effect depends on some factors such as load condition and stacking sequences.     

Lateral buckling analysis of thin-walled laminated composite beams with monosymmetric sections

Lateral buckling of thin-walled composite beams with monosymmetric sections is studied. A general geometrically nonlinear model for thin-walled laminated composites with arbitrary open cross-section and general laminate stacking sequences is given by using systematic variational formulation based on the classical lamination theory. All the stress resultants concerning bar and shell forces are defined, and nonlinear strain tensor is derived. General nonlinear governing equations are given, and the lateral buckling equations are derived by linearizing the nonlinear governing equations. Based on the analytical model, a displacement-based one-dimensional finite element model is developed to formulate the problem. Numerical examples are obtained for thin-walled composite beams with monosymmetric cross-sections and angle-ply laminates. The effects of fiber orientation, location of applied load, modulus ratio, and height-to-span ratio on the lateral buckling load are investigated. The torsion parameter and a newly-defined composite monosymmetry parameter are also investigated for various cases.     

Localized support settlements of thin-walled storage tanks

This paper investigates the influence of support settlements on the out-of-plane displacements of thin-walled cylindrical tanks with a fixed top roof. The shell considered is representative of many steel tanks constructed in Puerto Rico and in the United States, and has a ratio between the diameter and the height of the order of 2.5, with slenderness ratio (radius to thickness) of the order of 1,700. The behavior of the tank is investigated using the finite element computer package ABAQUS by means of a geometrically non-linear algorithm for the analysis and linear elastic material behavior. Results are presented for geometrically linear analysis, geometrically nonlinear analysis and bifurcation buckling analysis. It is shown that the equilibrium path is highly non linear and that the shell displays a plateau for a settlement of the order of half the thickness of the shell. Linear results provide a poor indication of the real displacements in the shell, so that geometric nonlinearity should be included in the analysis for working loads.     

Nonlinear analysis of multi-cell reinforced concrete box girder bridges

A numerical method of analysis is developed to determine the nonlinear response, collapse mechanisms and ultimate failure loads of multi-cell RC (reinforced concrete) box girder bridges under stepwise increasing static loads. Nonlinearities considered are material nonlinearities inherent in RC members such as cracking of the concrete, yielding of the reinforcement and formation of plastic hinges due to shear and flexure. The analytical model, based on a three-dimensional grillage, is developed for multicellular structures of arbitrary plan geometry and constant height. Realistic but simple assumptions for the interaction of internal forces due to flexure, shear and torsion in the cellular structure, as well as idealized trilinear force-deformation characteristics for the individual members comprising the grillage, result in a very economical nonlinear analytical model. The proposed analytical scheme, which is based on a mixed model formulation at the element level, is demonstrated and tested on a series of numerical examples and the analytical results indicate good agreement with experimental results obtained from large scale model tests on RC box girder bridges.