筋板结构动力学特性边界元法解析研究

研究加筋薄板结构动力学特性多域合成的边界元建模解析方法。将矩形板沿梁划分为若干个区域,同时把梁的约束等效为作用在薄板区域上的反力,基于板、梁元件的动态基本解,由边界元法推导出带约束反力的梁和薄板的兰量控制方程,并依据耦合边界上的连续条件,运用多域合成的解析方法快速地建立筋板结构的动力学方程。数值算例表明,文中方法不但节省了计算量,而且具有良好的计算精度。     

Dynamics of an axially moving Bernoulli-Euler beam: Spectral element modeling and analysis

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.     

FEM Comparison of Ball and Roller Bullgears

A structural finite element model has been developed for calculating the forces transmitted through the rolling elements (load distribution) in a bullgear assembly. The elastic structural model consists of 3-D beam elements used to approximate the global race deflection and non-linear springs that approximate the combined rolling element/raceway contact deflections. For rollers, an upperbound on the contact stress (assuming linear variation of force along the length of the roller) is estimated by modeling the rollers as pairs of nonlinear springs. The finite element approach iteratively solves the contact forces at each, rolling element. Contact stresses are then calculated from the contact, forces using Hertz contact theory. This approach is applied to analyze two proposed designs of ball and crossed roller bearing, bullgear assemblies used for rotating the radar antenna on top of a ship's mast. The loads analyzed include those arising from wind loading and from out-of-flatness of the inner race of the bearings due to deflection of the mast. The distribution of the load and the maximum contact stresses for the proposed bullgear assemblies are estimated and compared. It is found that the maximum contact stress in the crossed roller bearing is less than that in the ball bearing for both types of loads. Furthermore, the analysis shows that the out-of-flatness loading produces significantly higher stresses than wind loading.     

Limit load solution for electron beam welded joints with single edge weld center crack in tension

Limit loads are widely studied and several limit load solutions are proposed to some typical geometry of weldments.However,there are no limit load solutions exist for the single edge crack weldments in tension(SEC(T)),which is also a typical geometry in fracture analysis.The mis-matching limit load for thick plate with SEC(T) are investigated and the special limit load solutions are proposed based on the available mis-matching limit load solutions and systematic finite element analyses.The real weld configurations are simplified as a strip,and different weld strength mis-matching ratio M,crack depth/width ratio a/W and weld width 2H are in consideration.As a result,it is found that there exists excellent agreement between the limit load solutions and the FE results for almost all the mis-matching ration M,a/W and ligament-to-weld width ratio(W-a)/H.Moreover,useful recommendations are given for evaluating the limit loads of the EBW structure with SEC(T).For the EBW joints with SEC(T),the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal,when M changing from 1.6 to 0.6.When M decreasing to 0.4,the mis-matching limit loads can be obtained assuming that the components are wholly made of base metal only for large value of(W-a)/H.The recommendations may be useful for evaluating the limit loads of the EBW structures with SEC(T).The engineering simplifications are given for assessing the limit loads of electron beam welded structure with SEC(T).     

Thermal buckling analysis of annular FGM plate having variable thickness under thermal load of arbitrary distribution by finite element method

In this paper, a finite element formulation is developed for analyzing the axisymmetric thermal buckling of FGM annular plates of variable thickness subjected to thermal loads generally distributed nonuniformly along the plate radial coordinate. The FGM assumed to be isotropic with material properties graded in the thickness direction according to a simple power-law in terms of the plate thickness coordinate, and has symmetry with respect to the plate midplane. At first, the pre-buckling plane elasticity problem is developed and solved using the finite element method, to determine the distribution of the pre-buckling in-plane forces in terms of the temperature rise distribution. Subsequently, based on Kierchhoff plate theory and using the principle of minimum total potential energy, the weak form of the differential equation governing the plate thermal stability is derived, then by employing the finite element method, the stability equations are solved numerically to evaluate the thermal buckling load factor. Convergence and validation of the presented finite element model are investigated by comparing the numerical results with those available in the literature. Parametric studies are carried out to cover the effects of parameters including thickness-to-radius ratio, taper parameter and boundary conditions on the thermal buckling load factor of the plates.     

考虑剪切变形的复杂刚架结构动力学特性分析

采用谱元法计算分析了复杂刚架结构的动力学响应特性,建立了直杆和Timoshenko梁的局部动力刚度阵,并组装得到了整体刚架结构的动力刚度阵。计算了刚架结构的频响曲线,并与有限元法得到的结果进行了比较,获得了刚架的固有频率和冲击载荷作用下的频域曲线。研究结果表明,谱元法可有效且准确地分析刚架结构的动力学响应特性,尤其适合中高频动态响应特性分析,与有限元方法相比,其精度高且用时短。       

NON-LINEAR DYNAMIC BEHAVIOR OF THERMOELASTIC CIRCULAR PLATE WITH VARYING THICKNESS SUBJECTED TO NON- CONSERVATIVE LOADING

The non-linear dynamic behaviors of thermoelastic circular plate with varying thickness subjected to radially uniformly distributed follower forces are considered. Two coupled non-linear differential equations of motion for this problem are derived in terms of the transverse deflection and radial displacement component of the mid-plane of the plate. Using the Kantorovich averaging method, the differential equation of mode shape of the plate is derived, and the eigenvalue problem is solved by using shooting method. The eigencurves for frequencies and critical loads of the circular plate with unmovable simply supported edge and clamped edge are obtained. The effects of the variation of thickness and temperature on the frequencies and critical loads of the thermoelastic circular plate subjected to radially uniformly distributed follower forces are then discussed.     

匀速旋转弹性薄板分布动载荷时域识别

以典型的基于Kirchhoff假设的匀速旋转弹性薄板为对象,研究其动载荷时域识别技术.首先,从结构动力学的正问题着手,建立弹性薄板在匀速旋转情况下受到分布动载荷时的受迫振动微分方程;然后,选取一种通用厚薄板单元并分析其有限元形式;最后,研究对应的基于广义正交多项式的匀速旋转薄板动载荷时域识别技术.数值算例表明,该时域识别技术精度较高,计算稳定性良好,方法简单有效,适合在工程中应用.     

Vibration analysis of rectangular Mindlin plates with internal line supports using static Timoshenko beam functions

In this paper, the vibration characteristics of rectangular Mindlin plates with internal line supports in one or two directions are studied by using the Rayleigh–Ritz method. The static Timoshenko beam functions are employed as admissible functions, which are composed of a set of transverse deflection functions and a set of rotation-angle functions due to bending. The static Timoshenko beam functions are derived from a point-supported strip of unit width taken from the particular plate under consideration in a direction parallel to the edge of the plate and acted upon by a series of static sinusoidal loads distributed along the length of the strip. It can be seen that the suggested approach is very simple mathematically, and each of the beam functions is only a sine or cosine function plus a polynomial function of not more than the third order. A unified program can be easily prepared, because the changes in boundary conditions, number and locations of internal line supports and thickness ratio of the plate will result in a corresponding change of only the coefficients of the polynomials. Both high accuracy and low computational cost have been verified by convergence and comparison studies. In addition, it can be seen that the admissible functions presented in this paper can also properly describe the discontinuity conditions of the shear forces at the line supports. Therefore, accurate results can be expected for the analysis of dynamic response and internal force distribution of the plate.     

On the load distribution of thin-walled beams subjected to bending with respect to the cross-section distortion

The paper deals with the estimation of the load distribution under which distortion of the cross-sections of thin-walled beams subjected to bending cannot occur. It is assumed that beam walls are hinged along their longitudinal edges. Beams with closed and open rectangular cross-sections, with three or two cells, with two or one axis of symmetry are considered. It is shown that the problem can be treated by two equivalent beams, defined by the shear flow zero points of the beam with rigid cross-section. The beam load must be distributed in the plane of beam walls, proportionally to the cross-section moments of inertia of the equivalent beams. Some illustrative examples are given.     

The study of structural system dynamic problems by recursive estimation method

This paper presents the recursion-relation algorithm to determine the input forces of beam structures and the individual node displacement. The system state equations of the beam structures are based on the average acceleration method, and a dynamic beam matrix equation is constructed by using the finite element method. Implementation of this method involves handling various systems' parameters such as the measurement noise, the modeling error, and the external disturbance. The Kalman filter is used to predict the applied forces and adjusted at each time step according to the measured dynamic response data of structures. The estimator employs a recursive least-squares algorithm to compute the magnitudes of the impulsive loads. The accuracy of the present method is demonstrated by the numerical simulations for loads applied along the axis of a beam on different time frames.     

Dynamic instability analysis of stiffened shell panels subjected to partial edge loading along the edges

The dynamic instability characteristics of stiffened shell panels subjected to partial in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effects of parameters like loading type and shell geometry are considered in the dynamic instability analysis of stiffened panels subjected to non-uniform in-plane harmonic loads along the boundaries. The tension buckling aspect of the stiffened panels are also considered and the dynamic stability behavior due to tensile in-plane edge loading is studied for the concentrated load.     

Dynamic behavior of plastic circular plates with polygonal apertures

Using a model of a rigidly plastic body, a procedure has been developed permitting calculation of limiting loads and residual damageability of circular plates with a regular polygonal aperture if dynamic loads of explosion type distributed uniformly act on them. Both contours are supported by hinges or fixed. It is shown that three mechanisms of plate deformation are possible depending on the load level. For each of them, defining equations have been obtained and conditions of their realization have been analyzed. Examples of numerical solutions are presented.     

Forced vibration of composite cylindrical helical rods

The dynamic behavior of composite cylindrical helical rods subjected to time-dependent loads is theoretically investigated in the Laplace domain. The governing equations for naturally twisted and curved spatial laminated rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, the anisotropy of the rod material, effect of the rotary inertia, axial and shear deformations are considered in the formulations. The material of the rod is assumed to be homogeneous, linear elastic and anisotropic. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem accurately. The solutions obtained are transformed to the time domain using an appropriate numerical inverse Laplace transform method. The free vibration is then taken into account as a special case of forced vibration. The results obtained in this study are found to be in a good agreement with those available in the literature.     

A three-dimensional finite element method for plate bending

A three-dimensional finite element method is proposed for plate bending. The displacement function is assumed to have a particular form with respect to the thickness variable.The assumed displacement function is substituted into the three-dimensional potential energy functional and a two-dimensional variational problem emerges.The two-dimensional problem is treated by the finite element method and it is seen that for conforming solutions the only requirement is continuity of the basis functions.The method includes transverse shear and thickness effects and may be used for both thin and moderately thick shells.To illustrate the method and to compare it with other results, the problems of a square plate under point and distributed loads and with simply supported and clamped boundary are treated numerically.     

An improved closed-form solution to interfacial stresses in plated beams using a two-stage approach

Shear stress and normal stress in the thickness direction at interfaces (referred to as interfacial shear and transverse normal stresses, respectively, hereafter) have played a significant role in understanding the premature debonding failure of beams strengthened by bonding steel/composite plates at their tension surfaces. Due to the occurrence of dissimilar materials and the abrupt change of cross-section, the stress distribution at plate ends becomes singular and is hence considerably complicated. Extensive experimental and analytical analyses have been undertaken to investigate this problem. Large discrepancies have been found from various studies, particularly from experimental results due to the well-acknowledged difficulty in measuring interfacial stresses. Numerical analyses, e.g. 2-D or 3-D finite-element analysis (FEA), may predict accurate results, but they demand laborious work on meshing and sensitivity analysis. Analytical solutions, in particular those in a closed form, are more desirable by engineering practitioners, as they can be readily incorporated into design equations. This paper reports an improved closed-form solution to interfacial stresses in plated beams using a two-stage approach. In this solution, beams and bonded plates can be further divided into a number of sub-layers to facilitate the inclusion of steel bars or multiple laminae. Thermal effects may also be considered by using equivalent mechanical loads, i.e. equivalent axial loads and end moments. Numerical examples are presented to show interfacial stresses in concrete or cast iron beams bonded with steel or FRP plates under mechanical and/or thermal loads. The effect of including steel reinforcements with various ratios in the RC beam on interfacial stresses is also investigated. Compared with previously published analytical results, this one improves the accuracy of predicting the transverse normal stresses in both adhesive-beam and plate-adhesive interfaces and the solution is in a closed form.     

Rigid-plastic modelling of blast-loaded stiffened plates—Part II: Partial end fixity, rate effects and two-way stiffened plates

A new rigid-plastic analysis of stiffened plates subjected to uniformly distributed blast loads is developed. In this first part of a two-part paper, a uniform one-way stiffened plate with clamped ends is modelled as a singly symmetric beam, comprised of one stiffener and its tributary plating. Rigid-plastic analysis is then applied to this beam using an idealized piecewise linear bending moment-axial force capacity interaction relation or yield curve. Two solutions to the response are developed. The first solution is in closed form and is based on the solution of the resulting linearized differential equations. The second solution is obtained by approximating the response as a sequence of instantaneous mode responses, where the mode shapes are determined by an extremum principle which maximizes the rate of change of the kinetic energy. This latter solution may be extended to cases involving non-rigid boundaries and two-way stiffening and this is done in the second part of this paper. Here, the two solution methods are applied to several examples of one-way stiffened plates subjected to various blast-type pulses. Good agreement is obtained between the present results and those from elastic-plastic beam finite element and finite strip solutions.     

水平定向钻机大梁的瞬态动力学分析

以某型水平定向钻机的关键部件大梁为研究对象,在其三维实体模型的基础上建立了有限元模型,运用ANSYS有限元软件对大梁进行了瞬态分析。通过求解,确定了大梁结构承受随时间变化载荷时的动力响应,为定向钻机结构的改进和动态特性的提高提供了设计依据。     

Use of a generalized beam/spring element to analyze natural vibration of rail track and its application

This paper describes the formulation of a generalized beam/spring track element to obtain the natural vibration characteristics of a railway track modeled as a periodic elastically coupled beam system on a Winkler foundation. The rail/tie beams are described by either the Timoshenko beam theory or the Bernoulli-Euler beam theory. The rail beam is assumed to be discretely coupled to the cross-track ties through the coupling spring elements at the periodic rail/tie intersections. The generalized beam/spring element consists of a rail span beam segment, two adjacent tie beams, the coupling spring elements and the ultimate foundation stiffness. The entire track/beam system is then discretized into an assembly of periodic structural units. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the track substructure unit is formulated to establish the dynamic stiffness matrix of the generalized element. The eigenvalue problem of the track/beam system is solved by employing a comprehensive and efficient numerical routine. Solutions are provided for the natural frequencies of the track and the mode shapes of the rail/tie beams under transversely (cross-track) symmetric vibration. The natural vibration results are used to obtain the dynamic receptance response of a typical field track and to compare them with an existing model and field experimental data.     

动载荷识别的小波级数分解法阶次确定

在基于正交小波级数分解法的分布动载荷识别过程中，由于小波级数阶次的不适当选择，造成载荷识别的不准确或计算量庞大。通过矩阵的谱分解，根据Parseval定理，信号在时域中的总能量和频域中的总能量是相等的，给出了随着阶次的增加而趋于收敛的小波级数系数幅值的包络线，将没有确定解析规律的小波级数系数解析化，得到确定的小波级数阶次与载荷识别相对误差的函数关系。根据实际工程需求的识别误差等级来选取小波级数的阶次，给出了待识别动载荷级数分解时选择阶次的理论依据。计算机仿真分别采用单频、多频、实际载荷信号，试验系统采用冲击载荷加载，验证了该定阶方法的正确性和有效性，结果表明定阶理论适用于不同载荷类型。