EQUI-STRENGTH DESIGN FOR STATICALLY INDETERMINATE BEAMS

In this paper a method for equi-strength design of statically indeterminate beams ispresented,based on the principle of minimum complementary energy.And an analyticalexpression is derived for the stiffness variation of single or multi-span beams under theapplication of arbitrarily distributed loads.concentrated forces and couples.Illustratedexamples concerning beams with fixed width a(?)iable height or sandwich beams withvariable thickness of outer sheets are also given.The comparison with reported resultsshows the effectiveness of the proposed method.     

Transverse-longitudinal bending of rheonomic rods

In [1, 2], an energy method for the determination of critical buckling times is developed for rods subjected to compression in the conditions of longitudinal bending. In this case, for given compressive loads, the bending moments in the rod cross-sections depend only on the current deflection of the rod axis. In contrast to longitudinal bending, in the case of transverse-longitudinal bending the bending moment in general depends not only on the deflection but also on the axial coordinate and the reaction forces in the supports. Depending on the rod fixing conditions, the problems of transverse-longitudinal bending can be categorized as statically determinate or statically indeterminate. In the latter case, the derivation of equilibrium conditions for a rod segment is complicated by the indefiniteness of the reactions in the rod buckling process. In the current paper, the energy method developed in [1, 2] is extended to a class of statically indeterminate transverse-longitudinal bending problems. To determine the redundant variables, it is proposed to use the principle of minimum of additional dissipation.     

自适应超静定桁架结构强度控制的研究

以超静定桁架结构为背景研究了自适应结构的承载能力,探讨作动器和杆单元的共同工作,用以进行结构分析和控制结构承载能力,后者意指通过作动器的主动变形调控结构的内力分布以获得更加合理的工作状态。     

用拉格朗日函数分析不同模量静不定桁架内力

在外载荷作用下的不同模量静不定桁架平衡问题,是任意有限多个自变量的多元函数在任意有限多个约束条件下的极值问题,对采用拉格朗日乘数法求解此类极值问题进行了数学证明．通过求解不同模量静不定桁架极限载荷的几个算例,阐述拉格朗日乘数法在计算不同模量静不定桁架极限载荷中的应用．研究结果表明：采用拉格朗日乘数法求解不同模量静不定桁架极限载荷的通用性较强,用拉格朗日乘数法求解不同模量静不定桁架极限载荷的方法不但克服了常规方法需利用几何关系建立协调方程的缺陷,且具有力学概念清晰直观、计算过程简便、便于工程设计人员在实际中掌握和应用．     

An analytical method for solving internal forces and deformations of bar-system structure in space

In this paper, based on the idea of finite element method, the initial parametric method in bending problem of a beam is extended to analyse the bar-system structure by employing Dirac function and Heaviside step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.     

Discrete element-embedded finite element model for simulation of soft particle motion and deformation

The motion and deformation of soft particles are commonly encountered and important in many applications. A discrete element-embedded finite element model (DEFEM) is proposed to solve soft particle motion and deformation, which combines discrete element and finite element methods. The collisional surface of soft particles is covered by several dynamical embedded discrete elements (EDEs) to model the collisional external forces of the particles. The particle deformation, motion, and rotation are independent of each other in the DEFEM. The deformation and internal forces are simulated using the finite element model, whereas the particle rotation and motion calculations are based on the discrete element model. By inheriting the advantages of existing coupling methods, the contact force and contact search between soft particles are improved with the aid of the EDE. Soft particle packing is simulated using the DEFEM for two cases: particle accumulation along a rectangular straight wall and a wall with an inclined angle. The large particle deformation in the lower layers can be simulated using current methods, where the deformed particle shape is either irregular in the marginal region or nearly hexagonal in the tightly packed central region. This method can also be used to simulate the deformation, motion, and heat transfer of non-spherical soft particles.     

超静定梁?柱的解析解研究

本文采用渐进积分法研究了超静定梁?柱的弯曲问题. 首先建立超静定梁?柱的四阶挠度微分方程, 考虑到边界条件和连续光滑条件, 采用连续分段独立一体化积分法求解得到了挠度的精确解析解. 为了满足工程设计需要, 构造了超静定梁?柱的四阶挠度微分迭代方程, 选取无轴向力作用时超静定梁的挠曲线作为梁的初函数, 将初函数代入梁的四阶挠度微分迭代方程进行积分, 利用边界条件和连续光滑条件确定积分常数, 得到下一次迭代挠度函数, 依次进行迭代积分运算. 计算出了最大挠度、最大转角和最大弯矩等用轴向力放大系数表示的多项式解析函数解. 本文选取了两种边界条件下受分布力作用的超静定梁?柱进行分析, 计算结果表明, 当超静定梁?柱所受的轴向力小于欧拉临界力的1/2时, 迭代六次误差就可以控制在1%以内; 不仅梁?柱最大位移和最大内力的大小随轴向力的增大而增大, 而且其位置也随轴向力的增大而发生迁移. 本文的研究对揭示轴向力对超静定梁?柱变形和内力的影响有重要意义, 为超静定梁?柱的实际设计提供了一定的理论基础.      

求解弹性梁的普遍化方法

介绍了一种求解弹性梁的新方法．该方法利用奇异函数与拉普拉斯变换相结合的方法导出弹性梁弯曲变形的普遍表达式，并利用边界条件确定约束力，对具有任意支承形式、受力状况和阶梯形状的静定或超静定梁具有普适性．     

Statically indeterminate contacts in axially loaded wire strand

This paper is concerned with the analysis of simple wire strands made from one layer of circular wires helically wrapped around a circular straight core wire. The undeformed configuration is the special case in which each of the surrounding helical wires touches its two adjacent neighbouring helical wires as well as touching the core wire. This forms a statically indeterminate contact problem. A simple finite element model is developed to analyse this situation. Numerical results show that contacts can occur simultaneously at all possible contact points when the strand is subjected to extension with both ends fixed against rotation.     

Numerical investigations on the biomechanical compatibility of hip-joint endoprostheses

A computational approach for studies on the biomechanical compatibility of hip implants based on detailed three-dimensional finite element models is presented. With the anticipation for a meaningful computational prediction of bone behavior under endoprosthetic treatment a general modeling approach taking into account the model generation from radiological data and the recovery of statically equivalent joint loads and muscle forces from a best fit between simulated and measured bone mass density distribution was developed. Computational results for three different endoprostheses systems are presented and compared with clinical studies. The potential for aiding the development process of new prosthesis designs regarding their biomechanical compatibility is demonstrated.     

转换矩阵在非线性材料杆系分析中的应用

证明了在杆系中,力的转换矩阵与位移的转换矩阵互为转置矩阵,当静不定非线性杆系静力平衡方程确定,而变形协调条件难以确定时,利用转置矩阵可以方便求得静不定非线性杆系的内力及有关节点位移.非线性材料杆系应力-应变关系 σ=Bε1/n中的幂n=2时,非线性材料静不定桁架有可能存在两个解;而采用常规方法求解静不定非线性杆系内力时...     

自适应超静定桁架强度控制能力的提高

利用作动器的调节功能和超静定桁架的内力耦合特性,提高了自适应超静定桁架结构的承载能力,获得了更加合理的结构工作状态,有效地解决了文[8]中当作动器刚度较小时调控能力受限的问题。计算结果比文[8]模型的结果更令人满意。     

Traveling waves vibrations and buckling of rotating anisotropic shells of revolution by finite elements

A quasi-analytical finite element procedure is developed which can obtain the frequency and buckling eigenvalues of prestressed rotating anisotropic shells of revolution. In addition to the usual centrifugal forces, the rotation effects treated also include the contribution of Coriolis forces. Furthermore, since a nonlinear version of Novoshilov's shell theory is employed to develop the element formulation, the effects of moderately large prestress deflection states can be handled. Due to the generality of solution procedure developed, the axisymmetric prestress states treated can also consist of torque loads. In order to illustrate the procedures capabilities, as well as the significant effects of Coriolis forces, torque prestress and material anisotropy, several numerical experiments are presented.     

大跨悬索桥抖振内力响应分析

基于虚拟激励法和有限元法,在频域建立了一种新的桥梁抖振内力响应分析的随机振动方法。该方法与传统随机振动方法相比具有如下两个特点:(1)单元抖振内力响应同时考虑了保留模态多模态耦合产生的动力效应和保留模态外高频模态产生的拟静力效应;(2)单元抖振内力响应同时考虑了单元杆端位移产生的单元杆端力和单元上分布荷载产生的单元固端力。以香港青马悬索桥为例,分析了保留模态多模态耦合产生的动力效应、高频模态拟静力效应、单元上分布荷载产生的单元固端力及主缆上的抖振荷载等因素对主梁抖振内力响应的贡献。结果表明:保留模态多模态耦合产生的动力效应对主梁抖振内力响应占据主导地位,高频模态拟静力效应、单元上分布荷载产生的单元固端力等因素对主梁抖振内力响应均有一定的影响,主缆上的抖振荷载对主梁侧向抖振内力响应有较大贡献。     

Mechanical Properties of two novel planar lattice structures

Two novel statically indeterminate planar lattice materials are designed: a new Kagome cell (N-Kagome) and a statically indeterminate square cell (SI-square). Their in-plane mechanical properties, such as stiffness, yielding, buckling and collapse mechanisms are investigated by analytical methods. The analytical stiffness is also verified by means of finite element (FE) simulations. In the case of uniaxial loading, effective modulus, yield strength, buckling strength and critical relative density are compared for various lattice structures. At a critical relative density, the collapse mode will change from buckling to yielding. Elastic buckling under macroscopic shear loading is found to have significant influence on failure of lattice structures, especially at low relative densities. Comparison of the analytical bulk and shear moduli with the Hashin–Shtrikman bounds indicates that the mechanical properties of the SI-square honeycomb are relatively close to being optimal. It is found that compared with the other existing stretching-dominated 2D lattice structures, the N-Kagome cell possesses the largest continuous cavities for fixed relative densities and wall thicknesses, which is convenient for oil storage, disposal of heat exchanger, battery deploying and for other functions. And the initial yield strength of the N-Kagome cell is slightly lower than that of the Kagome cell. The SI-square cell has similar high stiffness and strength as the mixed cell while its buckling resistance is about twice than that of the mixed cell.     

Axisymmetric deformations of circular rings made of linear and Neo-Hookean materials under internal and external pressure: A benchmark for finite element codes

The axisymmetric deformations of thick circular rings are investigated. Four materials are explored: linear material, incompressible Neo-Hookean material and Ogden's and Bower's forms of compressible Neo-Hookean material. Radial distributed forces and a displacement-dependent pressure are the external loads. This problem is relatively simple and allows analytical, or semi-analytical, solution; therefore it has been chosen as a benchmark to test commercial finite element software for various material laws at large strains. The solutions obtained with commercial finite element software are almost identical to the present semi-analytical ones, except for the linear material, for which commercial finite element programs give incorrect results.     

Semiclosed-form solution for static nonlinear analysis of extensible cables

The analysis of a cable deforming under statically applied body forces leads to a series of differential equations that are inherently nonlinear due to coupling of geometry and loading. These equations have been solved by nonlinear finite element technique, finite difference formulation, or a two-step shooting method. However, a semiclosed-form solution is presented herein in which the governing differential equations are integrated to yield exact expressions for the unknown cable forces and the parameters defining the geometry of the loaded cable. The formulation presented herein is capable of taking care of the large sag and deformation in the cable without employing any numerical solution procedure.     

带弹簧支撑超静定结构位移的简化计算方法

针对带有弹性支撑的超静定结构的位移计算问题, 对利用虚功原理得到的位移计 算一般公式进行了进一步推导, 提出了该类结构位移的简化计算方法. 文中计算公式表达形 式简洁, 且与一般刚性支撑超静定结构的位移计算方法一致. 通过与有限元分析结果的对比, 证明了该公式的正确性.     

旋转弹性体的有限元线法分析

本文将有限元线法应用于一般荷载作用下的旋转弹性体的分析。文中将任意荷载沿环向展开为Ｆｏｕｒｉｅｒ级数，利用正交性，将问题转变为一系列旋转子午面上二维问题的叠加。文中对任一环向谐波建立了旋转面上的曲线曲边单元，导出了相应的常微分方程体系，并对由柱坐标引起的ｒ＝０处的奇异性问题做了完备合理的处理。文中给出了具有代表性的数值算例，用以展示本法的出色的表现     

High-precision solution to the moving load problem using an improved spectral element method

In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.