Time-dependent creep and shrinkage analysis of composite beams curved in-plan

This paper develops a numerical formulation for the time-dependent creep and shrinkage analysis of steel–concrete composite beams that are curved in-plan under conditions of service load. The creep behaviour of the concrete is considered by using the viscoelastic Wiechert model, in which the aging effect of the concrete is taken into account. The curved composite beam model that is developed also accounts for the partial shear interaction at the deck-girder interface in the tangential (or longitudinal) direction, as well as in the radial (or horizontal) direction, due to the flexibility of the shear connectors. Models based on the developed formulation are validated by comparisons with sophisticated and computationally intensive ABAQUS shell element models, and with available results reported in the literature. The effects of initial curvature and partial interaction on the time-dependent behaviour of curved composite beams are also illustrated in the examples.     

Optimal design of elastic-plastic stepped beams under dynamic loading

The optimal design of two-stepped elastic-plastic beams under dynamic loads is discussed. Such beam dimensions are sought for which a minimum peak deflection is attained within designs of constant volume. The numerical results achieved are compared with results for elastic and rigid-plastic beams obtained in previous papers by the author.     

轴向可伸缩复合材料悬臂梁的非线性振动研究

以航空领域中可变体机翼的伸缩变形过程为研究对象,对可伸缩悬臂复合材料层合梁的时变非线性振动进行理论研究.建立可伸缩悬臂复合材料层合梁在外载荷作用下的非线性动力学模型;根据时变系数非线性动力学方程研究时变非线性振动特性.分析可伸缩悬臂复合材料层合梁在外伸与收缩变形过程中的非线性动力学特性.从数值结果上看:模型的外伸速度、飞行速度对振动的影响较大,初值对振动的影响较小.     

Analysis of Nonlinear Multibody Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of nonlinear multibody systems involving elastic members made of laminated, anisotropic composite materials. The analysis methodology can be viewed as a three-step procedure. First, the sectional properties of beams made of composite materials are determined based on an asymptotic procedure that involves a two-dimensional finite element analysis of the cross-section. Second, the dynamic response of nonlinear, flexible multibody systems is simulated within the framework of energy-preserving and energy-decaying time-integration schemes that provide unconditional stability for nonlinear systems. Finally, local three-dimensional stresses in the beams are recovered, based on the stress resultants predicted in the previous step. Numerical examples are presented and focus on the behavior of multibody systems involving members with elastic couplings.     

Complex modes based numerical analysis of viscoelastic sandwich plates vibrations

In this paper, a numerical method for linear and nonlinear vibrations analysis of viscoelastic sandwich beams and plates is developed with finite element based solution. This method couples the harmonic balance technique to complex mode Galerkin’s procedure. This results in a scalar nonlinear complex amplitude–frequency relationship involving numerical computation of three coefficients. A general formulation taking into account the frequency dependence of the viscoelastic behaviour allowing to intoduce any viscoelastic law is given. Complex eigenmodes are numerically computed in a general procedure and used as Galerkin’s basis. The free and steady-state vibrations analyses of viscoelastic sandwich beams and plates are investigated for constant and frequency dependent viscoelastic laws and for various boundary conditions. The equivalent frequencies and loss factors as well as forced harmonic response and phase curves are performed. The obtained results show the efficiency of the present approach to large amplitudes vibrations of viscoelastic sandwich structures with nonlinear frequency dependence.     

Finite strip analysis of curved composite girders with incomplete interaction

This paper presents a finite strip analysis of curved composite girders with incomplete interaction. In the present analysis curved composite girder bridges are modelled by curved strip elements for the concrete slab and steel girder and spring elements for the shear connectors. The shear connectors are assumed as a two-dimensional spring element along the nodal line. The proposed method is applied to the analysis of curved box girders, curved plates and curved composite girder bridges with complete and incomplete interaction. Some analytical results obtained by this method are compared with the test results and theoretical values obtained by other methods, and they are in good agreement. Slip behavior of curved composite box girders is also discussed based on the results by the proposed method.     

一种求解混合约束问题的快速完备算法

布尔与数值变量相混合的约束问题有着广泛的应用,但是当约束中的数值变量间存在非线性关系时该问题求解起来十分困难.目前的许多求解方法都是不完备的,即这些方法不能完全肯定某些包含非线性数值表达式的约束是否能够成立.针对这种问题,提出了数值与区间分析相结合进行数值约束求解的方法.已经实现了一个基于此方法的原型工具.实验结果表明,该方法能够有效、快速、完备地求解非线性混合约束问题.     

Large deflections of cantilever beams of nonlinear materials

This paper deals with the large deflections (finite) of thin cantilever beams of nonlinear materials, subjected to a concentrated load at the free end. The stress-strain relationships of the materials are represented by the Ludwick relation. Because of the large deflections, geometrical nonlinearity arises and, therefore, the analysis is formulated according to the nonlinear bending theory. Consequently, the exact expression of the curvature is used in the moment-curvature relationship. The resulting second-order nonlinear differential equation is solved numerically using fourth-order Runge-Kutta method. For comparison purposes, the differential equation is solved for linear material and the results are compared to the exact solution which uses elliptic integrals. Deflections and rotations along the central axis of beams of nonlinear materials are obtained. The numerical algorithm was performed on the UNIVAC 1110.     

轴向运动梁横向非线性振动模型研究进展

综述了描述轴向运动梁横向非线性振动的两组数学模型的研究进展.在轴向运动梁径向和横向平面非线性振动耦合模型的基础上,总结了两组横向非线性振动模型的推导,以及在自由振动、受迫振动、参激振动工况下两组横向模型的近似解析比较的研究进展.在直接数值离散方法的基础上,总结了两组横向模型在各种工况下对平面耦合模型近似程度的研究进展.最后提出若干尚待深入研究的问题.     

Analysis of composite beams with partial shear interaction using available modelling techniques: A comparative study

This paper presents a comparison of available numerical structural analysis formulations for composite beams with partial shear interaction, which include the finite difference method, the finite element method, the direct stiffness method and the exact analytical model, and these formulations are briefly presented. The first two of these formulations lead to a numerical solution that requires a spatial discretisation to be implemented, while the direct stiffness method does not require this discretisation. Using the solution of the exact analytical model as a benchmark reference, the accuracy of the three numerical techniques is tested for the cases of a simply supported beam and a propped cantilever, and a qualitative comparison is carried out to highlight the adequacy and characteristics of these numerical formulations. For the two structural systems considered, the minimum spatial discretisations that need to be adopted to keep the error within an acceptable tolerance are provided for each of the formulations.     

Repeated impact and rebound of an elastic-plastic bar from a rigid surface

The repeated impact, or “bouncing,” of an elastic-plastic rod on a rigid surface, is treated by means of finite element analysis. A computationally convenient substructuring technique is utilized in the analytical treatment to account for the changing kinematic constraints. The time dependence is accounted for by means of a variable time step, direct integration procedure that has been successfully applied to a number of elasto-plastic dynamic response problems. This time integration procedure is at present being employed in a nonlinear crashworthiness study. It has been proven capable of providing an accurate prediction of a variety of multidimensional dynamic elastic-plastic responses. Additionally, the procedure has demonstrated its ability to account for an elastic-plastic dynamic response that includes plastic reflections from boundaries and interaction of plastic wave fronts. The merging of the substructuring technique and numerical time integration procedure has been accomplished. The cases discussed include an unloaded bar traveling at uniform velocity before impact with a rigid barrier, and a bar traveling toward the rigid surface and subject to forces that are applied and removed periodically. Both cases are motivated by questions concerning the elastic-plastic dynamic response of a crashed vehicle. The latter case, which suggests the term “bouncing problem,” has, in addition, applications to problems involving pneumatically driven tools. The response is described, starting with the instant of contact at the impacting end, is followed while elastic/plastic wave propagation extends to the free end, and continues to be treated as elastic/plastic reflections occur and return to the impacting end. Finally, the behavior of the rod as it leaves and possibly returns to the wall is discussed, and the dwell time as a function of elastic and elastic-plastic properties of the material is determined.     

A finite element method for elastic-plastic beams and columns at large deflections

A finite element scheme for the large-displacement analysis of elastic-plastic beams and columns is presented. The proposed method, which assures continuous deflections and continuous slopes at the element junctions, is shown to furnish fairly accurate results with a minimal number of elements. Comparisons are made with existing results for laterally loaded beams on elastic foundations and for elastic columns on bi-linear elastoplastic foundations. The effect of imperfections on the buckling of elastic-plastic columns is also investigated.     

求解布尔与非线性数值约束相混合的约束问题

布尔与数值变量相混合的约束问题有着广泛的应用,但是当约束中的数值变量间存在非线性关系时该问题求解起来十分困难.目前的许多求解方法都是不完备的,即这些方法不能完全肯定某些包含非线性数值表达式的约束是否能够成立.针对这种问题,提出了将非线性数值约束转化为特殊形式的优化问题,采用全局优化算法对其进行求解的方法.已经实现了一个基于此方法的原型工具.实验结果表明,该方法能够有效地求解非线性混合约束问题,并且总能够得到该约束条件是否可满足的结果.     

Modelling of continuous steel–concrete composite beams: computational aspects

Steel–concrete composite members are an interesting option for structural designers, but the reliability of design procedures both in the case of gravity and seismic loads is in continuous development. The issue is very complex, since behaviour of continuous composite beams results from local phenomena of interaction such as partial shear connection and bond.Furthermore, composite beams in buildings generally are not characterised by a full continuity due to the beam to column connections; thus the analysis and the detailing of such parts have a key role in the development of suitable design procedures.In the present paper, some computational aspects related to the modelling of composite flexural members are discussed with reference to continuous and semi-continuous structural systems widely used in practice.     

Deflection of elastic-plastic frames at finite spread of yielding zones

In elastic-perfectly plastic beams and frames finite zones of yielding develop under the collapse load. The classical deflection analysis assumes that the elastic rigidity reduces locally to zero at the yield hinges only. Such an approach underestimates the deflections at collapse.A method is proposed in order to evaluate the displacements of elastic-plastic frames when the actual spread of plastic zones is included in the analysis. In comparison with the classical method the developed technique accounts for the flexural stiffness variation between the hinges and due to the partial yielding of cross-sections. The actual extent of plastic zones depends on the bending moment distribution in the structure.The method contains both the algorithms and program for the deflection evaluation, specified for I-shape cross-sections. The elastic-plastic moment-curvature relations are derived and integrated to obtain additional rotations due to the flexural stiffness variation when the structure transforms in a mechanism. A linear programming program developed earlier is modified to account for the supplementary rotations. The essential features of the method and those of the program application are illustrated purposely in simple examples, showing the order of magnitude of the actual displacements in comparison with the results of the classical deflection analysis of elastic-plastic beams and frames.     

Large deflection electro-mechanical analysis of composite structures bonded with macro-fiber composite actuators considering thermal loads

In this paper, static analysis of laminated composite plates and shells bonded with macro-fiber composite (MFC) actuators under thermo-electro-mechanical loads is considered. Most earlier studies in the literature focused on the effects of MFC actuation power and fiber orientations on shape deformation of composite plates/shells subjected to electrical voltage only. Also most of the earlier studies on MFC-\(\hbox {d}_{33}\) bonded smart structures in literature are performed by commercial softwares like Ansys or Abaqus using the thermal strain equivalent approach to model the piezomechanical coupling. Here, our earlier developed geometrically nonlinear plate and shell finite elements considering finite rotation theory are extended for MFC actuator-bonded composite structures taking into account additionally the response to temperature gradients. An improved Reissner–Mindlin hypothesis is considered to derive the variational formulation, in which a parabolic assumption of transverse shear strains across the thickness is assumed. MFC actuators dominated by the \(\hbox {d}_{33}\) effect (MFC-\(\hbox {d}_{33}\)) with arbitrary fiber orientations are considered. The numerical model is validated with composite beams and plates by comparing the results of simulations with experimental investigations existing in the literature. An angle-ply composite shell structure is studied in detail concerning geometrically nonlinear analysis of bending and twisting deformations under different MFC-\(\hbox {d}_{33}\) fiber orientations under electric loading. Shape control of thermally induced deformations of composite plates and shells is performed using bonded MFC-\(\hbox {d}_{33}\) actuators and the significance of the present geometrically nonlinear model is highlighted.

     

Direct stiffness analysis of a composite beam-column element with partial interaction

This paper presents a stiffness formulation for the analysis of composite steel–concrete beam-columns with partial shear interaction (PI). This formulation is based on the direct stiffness method (DSM). The advantage of the proposed method is that no approximated displacement and/or force fields are introduced in the element derivation, unlike other modelling techniques available in the literature. Some simple structural systems, such as simply supported beams and propped cantilevers, subjected to a point load and to a uniformly distributed load are then considered to validate the accuracy of the results obtained using the proposed formulation against results derived based on closed form solutions; for continuous beams, the results have been validated against those calculated using highly refined mesh of high order finite elements. This has been carried out for different levels of shear connection stiffness to highlight the ability of the proposed method to overcome the curvature locking problems observed in some conventional displacement formulations. The generic applicability of this technique to the analysis of continuous beams is then illustrated, in particular, highlighting its ability to account for material nonlinearities at both service and ultimate conditions.     

Large deflection of clamped skew plates

A theoretical analysis is presented for the large deflection elastic behaviour of clamped, uniformly loaded orthotropic skew plates. The governing nonlinear partial differential equations are transformed into a set of nonlinear algebraic equations. For this purpose a network of discrete points over the domain is considered, and the integral equation of beams along the skew directions is used with appropriate boundary conditions. The resulting nonlinear algebraic equations are then solved by a Newton-Raphson procedure.A convergence study of the solution has been made, and numerical results for a few cases of orthotropy and skew angles are presented in graphical form. The results obtained by this method are compared with available results of other investigators.     

Geometrically exact physics-based modeling and computer animation of highly flexible 1D mechanical systems

This paper presents a geometrically exact beam theory and a corresponding displacement-based finite-element model for modeling, analysis and natural-looking animation of highly flexible beam components of multibody systems undergoing huge static/dynamic rigid-elastic deformations. The beam theory fully accounts for geometric nonlinearities and initial curvatures by using Jaumann strains, concepts of local displacements and orthogonal virtual rotations, and three Euler angles to exactly describe the coordinate transformation between the undeformed and deformed configurations. To demonstrate the accuracy and capability of this nonlinear beam element, nonlinear static and dynamic analysis of two highly flexible beams are performed, including the twisting a circular ring into three small rings and the spinup of a flexible helicopter rotor blade (Graphical abstract). These numerical results reveal that the proposed nonlinear beam element is accurate and versatile for modeling, analysis and 3D rendering and animation of multibody systems with highly flexible beam components.