ANALYTICAL ANALYSIS OF INTERFACIAL STRESSES IN FRP-RC HYBRID BEAMS WITH TIME-DEPENDENT DEFORMATIONS OF RC BEAM

In this paper, the effect of time-dependent deformations (such as shrinkage and creep) on the interfacial stresses between an RC beam and FRP plate is presented. For this end, a closed-form solution for such stresses in externally FRP plated RC beams including creep and shrinkage effects is presented. The developed model is formulated to predict the interfacial stresses at time ‘t’, in which the RC beams have been already subjected to creep and shrinkage effects. The adherend shear deformations have been included in the present theoretical analysis by assuming a parabolic shear stress through the thickness of the RC beam and the FRP panel. Contrary to some existing studies, the assumption that both RC beam and FRP panel have the same curvature is not used in the present investigation. This research is helpful for the understanding on mechanical behavior of the interface and design of the FRP-RC hybrid structures.     

基于最小加速度原理分析点阵材料夹芯梁的弹塑性动力响应

以Lee的有限变形弹塑性连续体的最小加速度原理为基础,结合有限差分法建立了两端铰支轴向不可移的四棱锥夹芯梁受到横向均布冲击载荷时的动力学控制方程,并且考虑了横向剪切效应.通过对简支梁进行弹塑性动力响应数值计算和分析,证明了四棱锥夹芯梁的抗冲击性能明显优于相同质量的实心梁,芯层杆元与面板的夹角对夹芯梁的抗冲击能力有显著影响.所得结果对点阵材料夹芯梁的设计和优化有参考价值.     

冲击荷载与火灾联合作用下SFRC梁的力学行为

为了探究冲击荷载与火灾联合作用下钢纤维混凝土(steel fiber reinforced concrete, SFRC)梁的力学性能，联合应用高性能落锤试验系统、四点弯曲实验装置与装配式电炉开展了4根SFRC梁的冲击实验与高温恒载实验，观察了其破坏模式并记录了跨中位移和钢筋应变的时程曲线，探讨了冲击损伤SFRC梁的抗火性能。此外，在实验研究的基础上，考虑材料的应变率强化效应及温度软化效应，建立数值模型，首先对梁进行冲击加载模拟，并以冲击模拟结果为初始状态，采用热-力“顺序”耦合方法，对冲击加载与高温恒载联合作用下SFRC梁的力学行为进行了三维宏观有限元数值模拟。同时，考虑混凝土内部结构非均质性的影响，采用类似步骤，开展了细观模拟。宏/细观模拟结果与实验结果的良好吻合验证了本文数值方法的合理性与有效性，并体现了细观方法的优越性。研究发现，冲击能量较小时，SFRC梁在冲击荷载作用下，尽管局部混凝土开裂，梁整体残余变形较小，抗火性能有一定程度的下降；随着钢纤维掺量增大，混凝土基体抗剪强度增大，SFRC梁在冲击荷载作用下的开裂形态由弯剪裂缝并存向以弯曲裂缝为主转变；冲击损伤SFRC梁在高温恒载作用下裂缝分布较为集中，且发生脆性破坏。     

外包钢-砼组合梁纯扭作用下抗扭刚度的实验及数值模拟

为了研究新型外包钢-砼T形截面组合梁在纯扭作用下的变形性能,设计了5根不同配箍率的的足尺悬臂组合梁。通过对5根悬臂梁的抗扭性能的实验研究,得到了组合梁的扭矩-扭率关系曲线。利用有限元分析软件ANSYS,对组合梁的抗扭性能进行了非线性有限元分析,得到了混凝土与外包钢在极限阶段的应力云图。根据实验以及有限元结果分析了组合梁在整个加载过程中扭转刚度的变化。基于现行砼结构设计规范,提出了组合梁从开裂到极限阶段抗扭刚度的计算公式,可供组合梁受扭设计参考。把有限元模型和公式的计算结果与实验结果进行比较,三者吻合较好。     

Shear deformation effect in non-linear analysis of composite beams of variable cross section

In this paper the non-linear analysis of a composite Timoshenko beam with arbitrary variable cross section undergoing moderate large deflections under general boundary conditions is presented employing the analog equation method (AEM), a BEM-based method. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson's ratio and are firmly bonded together. The beam is subjected in an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, the axial displacement and to two stress functions and solved using the AEM. Application of the boundary element technique yields a system of non-linear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples are worked out to illustrate the efficiency, the accuracy, the range of applications of the developed method and the influence of the shear deformation effect.     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part II: applications and validation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. In Part I the governing equations of the aforementioned problem have been derived, leading to the formulation of five boundary value problems with respect to the transverse displacements, to the axial displacement and to two stress functions. These problems are numerically solved using the Analog Equation Method, a BEM based method. In this Part II, numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. Thus, the results obtained from the proposed method are presented as compared with those from both analytical and numerical research efforts from the literature. More specifically, the shear deformation effect in nonlinear free vibration analysis, the influence of geometric nonlinearities in forced vibration analysis, the shear deformation effect in nonlinear forced vibration analysis, the nonlinear dynamic analysis of Timoshenko beams subjected to arbitrary axial and transverse in both directions loading, the free vibration analysis of Timoshenko beams with very flexible boundary conditions and the stability under axial loading (Mathieu problem) are presented and discussed through examples of practical interest.

     

Nonlinear dynamic analysis of Timoshenko beams by BEM. Part I: Theory and numerical implementation

In this two-part contribution, a boundary element method is developed for the nonlinear dynamic analysis of beams of arbitrary doubly symmetric simply or multiply connected constant cross section, undergoing moderate large displacements and small deformations under general boundary conditions, taking into account the effects of shear deformation and rotary inertia. Part I is devoted to the theoretical developments and their numerical implementation and Part II discusses analytical and numerical results obtained from both analytical or numerical research efforts from the literature and the proposed method. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading and bending moments in both directions as well as to axial loading. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, to the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a nonlinear coupled system of equations of motion. The solution of this system is accomplished iteratively by employing the average acceleration method in combination with the modified Newton–Raphson method. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. The proposed model takes into account the coupling effects of bending and shear deformations along the member, as well as the shear forces along the span induced by the applied axial loading.

     

Large deformations of nonlinear viscoelastic and multi-responsive beams

This study presents analyses of deformations in nonlinear viscoelastic beams that experience large displacements and rotations due to mechanical, thermal, and electrical stimuli. The studied beams are relatively thin so that the effect of the transverse shear deformation is neglected, and the stretch along the transverse axis of the beams is also ignored. It is assumed that the plane that is perpendicular to the longitudinal axis of the undeformed beam remains plane during the deformations. The nonlinear kinematics of the finite strain beam theory presented by Reissner [27] is adopted, and a nonlinear viscoelastic constitutive relation based on a quasi-linear viscoelastic (QLV) model is considered for the beams. Deformation in beams due to mechanical, thermal, and electric field inputs are incorporated through the use of time integral functions, by separating the time-dependent function and nonlinear measures of field variables. The nonlinear measures are formulated by including higher order terms of the field variables, i.e. strain, temperature, and electric field. Responses of beams under mechanical, thermal, and electrical stimuli are illustrated and the effects of nonlinear constitutive relations on the overall deformations of the beams are highlighted.     

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.     

考虑收缩徐变影响的新旧混凝土叠合梁非线性分析实用方法

界面存在粘结滑移的新旧混凝土叠合梁是一种重要的工程梁.以叠合面上的变形协调条件为计算条件,推导出叠合梁以轴力表达的非线性微分方程.求解该微分方程,得到截面协同工作系数理论表达式.通过该截面协同工作系数,建立了能够准确反映新旧混凝土叠合梁承载力与变形的非线性实用分析方法,使得Bernoulli假定与截面协同工作系数达到了统一,并与已有解析解进行了对比分析,发现计算精度满足工程需求,说明了该分析方法的实用性.     

A new super convergent thin walled composite beam element for analysis of box beam structures

In this paper, a new composite thin wall beam element of arbitrary cross-section with open or closed contour is developed. The formulation incorporates the effect of elastic coupling, restrained warping, transverse shear deformation associated with thin walled composite structures. A first order shear deformation theory is considered with the beam deformation expressed in terms of axial, spanwise and chordwise bending, corresponding shears and twist. The formulated locking free element uses higher order interpolating polynomial obtained by solving static part of the coupled governing differential equations. The formulated element has super convergent properties as it gives the exact elemental stiffness matrix. Static and free vibration analyses are performed for various beam configuration and compared with experimental and numerical results available in current literature. Good correlation is observed in all cases with extremely small system size. The formulated element is used to study the wave propagation behavior in box beams subjected to high frequency loading such as impact. Simultaneous existence of various propagating modes are graphically captured. Here the effect of transverse shear on wave propagation characteristics in axial and transverse directions are investigated for different ply layup sequences.     

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress–strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.     

ANALYSIS OF COMPOSITE LAMINATE BEAMS USING COUPLING CROSS-SECTION FINITE ELEMENT METHOD

Beams and plates manufactured from laminates of composite materials have distinct advantages in a significant number of applications. However, the anisotropy arising from these materials adds a significant degree of complexity, and thus time, to the stress and deformation analyses of such components, even using numerical approaches such as finite elements. The analysis of composite laminate beams subjected to uniform extension, bending, and/or twisting loads was performed by a novel implementation of the usual finite element method. Due to the symmetric features of the deformations, only a thin slice of the beam to be analysed needs to be modelled. Conventional three-dimensional solid finite elements were used for the structural discretization. The accurate deformation relationships were formulated and implemented through the coupling of nodal translational degrees of freedom in the numerical analysis. A sample solution for a rectangular composite laminate beam is presented to show the validity and accuracy of the proposed method.     

Buckling of delaminated bi-layer beam-columns

An improved analytical model is presented to analyze the delamination buckling of a bi-layer beam-column with a through-the-width delamination. Both the transverse shear deformation and local delamination tip deformations are taken into consideration, and two delaminated sub-layers as well as two substrates in the intact (un-delaminated) regions are modeled as individual Timoshenko beams. A deformable interface is introduced to establish the continuity condition between the two substrates in the intact regions. Consequently, a flexible joint is formed at the delamination tip, and it is different from the conventional rigid joint given in most of studies in the literature, in which the local delamination tip deformations are completely ignored. In contrast to the local delamination buckling in our previous study (Qiao et al., 2010), the present model accounts for the global deformations of the intact region in the delaminated composite beam-column, thus capable of capturing the buckling mode shape transitions from the global, to global–local coexistent, and to local buckling for asymmetric delamination as the interface delamination increases. Good agreement of the present analytical solutions with the full 2-D elastic finite element analysis demonstrates the local deformation effects around the delamination tip and verifies the accuracy of the present model. Parametric studies are conducted to investigate the effects of loading eccentricity, delaminated sub-layer thickness ratio, and interface compliance on the critical buckling load for the delaminated composite beam-column. Transitions of buckling modes from the global to local delamination buckling are also disclosed as the thickness of one sub-layer reduces from the thick sub-layer to a thin film. The developed delamination buckling solution facilitates the design analysis and optimization of laminated composite structures, and it can be used with confidence in buckling analysis of delaminated composite structures.     

经典梁热过屈曲问题的解析解

基于非线性经典梁理论,建立了控制轴向和横向变形的基本方程,将两个非线性方程化简为一个关于横向挠度的四阶非线性积分-微分方程。对于本文所考虑的三类边界条件,该方程与相应的边界条件构成了微分特征值问题;直接求解该问题,得到热过屈曲构形的解析解,该解是外加热载荷的函数。为考察热载荷以及边界条件的影响,根据得到的解析解给出了一些数值算例,讨论了梁过屈曲行为的性质。本文得到的解析解可用于验证或改进各类近似理论和数值方法。     

Radial oscillations of nonhomogeneous,thick-walled cylindrical and spherical shells subjected to finite deformations

The infinitesimal breathing motions of long cylindrical tubes and hollow spherical shells of arbitrary wall thickness subjected to a finite deformation field caused by uniform internal and/or external pressures are investigated. A neo-Hookean material with a material constant varying continuously along the radial direction is used. The shell is first subjected to finite static deformations and is then exposed to a secondary dynamic displacement field. Based on the theory of small deformations superposed on large deformations, closed form expressions are obtained for the frequency of small oscillations about the highly prestressed state. Frequency versus initial deformation parameter curves are given for several nohomogeneity functions and for various wall thicknesses.     

A BEM solution to transverse shear loading of composite beams

In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of composite beams of arbitrary constant cross-section. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson’s ratio and are firmly bonded together. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross-section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear centre of the cross-section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson’s ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ‘exact’ elastic beam theory is remarkable.     

钢－混凝土组合梁非线性有限元分析

提出了部分剪力连接钢-混凝土组合梁非线性有限元分析的简化模型，该模型同时考虑了钢、混凝土材料的非线性本构关系和剪力连接件的滑移非线性对组合梁刚度和强度的影响，推导了考虑滑移的剪力连接件单元刚度矩阵。利用该模型计算了连续组合梁的极限荷载、挠度、应力以及滑移，与已有的理论计算结果和实验结果吻合，证明本方法分析钢-混凝土组合梁非线性的可靠性和实用性。     

An investigation into the stresses in double-lap adhesive joints with laminated composite adherends

The mechanics of double-lap joints with unidirectional ([0₁₆]) and quasi-isotropic ([0/90/?45/45]_2S) composite adherends under tensile loading are investigated experimentally using moiré interferometry, numerically with a finite element method and analytically through a one-dimensional closed-form solution. Full-field moiré interferometry was employed to determine in-plane deformations of the edge surface of the joint overlaps. A linear-elastic two-dimensional finite element model was developed for comparison with the experimental results and to provide deformation and stress distributions for the joints. Shear-lag solutions, with and without the inclusion of shear deformations of the adherend, were applied to the prediction of the adhesive shear stress distributions. These stress distributions and mechanics of the joints are discussed in detail using the results obtained from experimental, numerical and theoretical analyses.     

Response and Damage Tolerance of Composite Sandwich Structures under Low Velocity Impact

The deformation and failure response of composite sandwich beams and panels under low velocity impact was reviewed and discussed. Sandwich facesheet materials discussed are unidirectional and woven carbon/epoxy, and woven glass/vinylester composite laminates; sandwich core materials investigated include four types of closed cell PVC foams of various densities, and balsa wood. Sandwich beams were tested in an instrumented drop tower system under various energy levels, where load and strain histories and failure modes were recorded for the various types of beams. Peak loads predicted by spring-mass and energy balance models were in satisfactory agreement with experimental measurements. Failure patterns depend strongly on the impact energy levels and core properties. Failure modes observed include core indentation/cracking, facesheet buckling, delamination within the facesheet, and debonding between the facesheet and core. In the case of sandwich panels, it was shown that static and impact loads of the same magnitude produce very similar far-field deformations. The induced damage is localized and is lower for impact loading than for an equivalent static loading. The load history, predicted by a model based on the sinusoidal shape of the impact load pulse, was in agreement with experimental results. A finite element model was implemented to capture the full response of the panel indentation. The investigation of post impact behavior of sandwich structures shows that, although impact damage may not be readily visible, its effects on the residual mechanical properties of the structure can be quite detrimental.