Winkler弹性地基上梁的精化理论

将Cheng精化理论推广到winkler弹性地基上梁的研究当中,对winkler弹性地基上的梁进行了精确的分析,给出其精化理论。首先将板内的位移利用中面上位移及其沿梁厚方向的梯度表示出来,并获得梁内应力张量。再利用winkler弹性地基条件和Lur'e算子方法,获得弹性地基上梁的控制方程。若略去控制方程中的高阶项,与弹性地基上欧拉-伯努利梁的挠度控制方程一致。     

横观各向同性热弹性梁的精化理论

本文从横观各向同性梁的二维问题出发,研究了横观各向同性热弹性梁的精化理论。首先,在不作任何预先假设的条件下,利用横观各向同性热弹性理论和Lur’e算子函数,获得了由梁中线上的物理量表示的位移场和应力场。对热弹性梁上下表面承受非齐次边界条件的情况,推导出梁的近似控制微分方程。再舍去温度项,则横观各向同性热弹性梁的精化理论退化为横观各向同性梁的精化理论。     

弹性力学广义平面应力的精化理论

从Papkovich-Neuber通解出发,导出了弹性力学广义平面应力问题的精化理论控制方程.若取零阶近似表示,方程即为通常弹性力学平面应力问题的平衡方程.对略去h2及以上高阶项的八阶方程给出了通解.     

基于弹性地基梁理论的锚拉支架受力分析

本文应用弹性地基梁理论对锚拉支架中锚杆和拉杆的横向位移、受力状态等进行力学分析，提出一种简化的参数计算方法     

弹性地基双层梁理论下的混凝土路面力学分析

为建立混凝土路面结构受力分析计算模型,以Winkler弹性地基梁模型为基础,推导出了弹性地基双层梁理论的表达式;给定边界条件,利用MATLAB软件获得了无限长弹性地基梁在集中力作用下的挠度表达式。将混凝土路面结构简化为弹性地基上的双层梁,当车辆荷载作用于混凝土路面时,在集中载荷的作用下,建立了面层与基层的微分平衡方程。应用广义“初参数”法,得到了双层梁位移和应力的解析解。通过算例,对面层及基层的变形和应力进行了分析,结果表明:增大面层、基层的轴惯性矩和地基的弹性常数,可以有效地减少面层和基层的变形量,降低最大应力数值,但抗弯刚度对基层和面层的弯矩受力影响不大。最后将结果与ANSYS分析结果进行了比较,佐证了解的可靠性,研究结果可为混凝土路面结构设计提供依据。     

弹性地基梁损伤诊断研究

利用试验得到的振动参数评估结构的破损情况，是当前结构工程学科十分活跃的领域。由于弹性地基梁的振动模态受地基和梁两方面因素的影响，其损伤诊断问题变得十分复杂。本文通过对两靖自由弹性地基梁的灵敏性分析发现弹性地基梁的前两阶自由模态主要与地基有关，利用这一特性构造了两级识别的方法，并引入优化领域寻优能力极强的遗传算法进行识别，找到了令人满意的答案。     

弹性地基上双层叠合梁的解

将双层叠合梁之间的接触状况拟合为一符合Ｇｏｏｄｍａｎ假设的弹性夹层，导出了Ｗｉｎ ｋｌｅｒ弹性地基上双层叠合梁的微分方程组及其解析解．通过引入“广义夹层反应模量”计入了夹层水平和竖向反力引起的梁截面的剪切和拉压形变效应，它有效地提高了计算精度，尤其是在双层梁结构有间断的场合．     

弹性地基梁振动特性的近似分析方法

文中介绍了用模态摄动法分析复杂情况下弹性地基梁动力特性的近似方法。这一方法中可考虑纵向钢筋以及变地基弹性系数对弹性地基梁振动特性的影响，通过算例说明了这一方法的有效性。     

粘弹性地基上弹性梁的自由振动分析

本文将文克尔弹性地基梁模型中的弹簧用粘弹性元件来替代,建立了三元件文克尔粘弹性地基止粘弹性梁的静力和动力本构方程,求出了粘弹性地基上弹性梁的自由振动的级数解。并且对不同的振动情况进行讨论,最后给出了算例及结论。     

考虑尺寸效应板梁的磁弹性屈曲

研究表明,有限尺寸效应是影响板——梁磁弹性稳定性分析精度的主要原因。本文用边界元法分析了板边沿的磁感强度集中,然后用里兹法计算了软铁磁材料悬臂板——梁的临界屈曲磁场。通过和Moon-Pao的理论和实验结果以及Miga的有限元结果比较,表明本方法具有良好的精度,且计算方法简便。     

Analogy between refined beam theories and the Bernoulli-Euler theory

Some refinements of the classical Bernoulli-Euler theory of the bending of beams are shown to be completely analogous to the effects produced by sources of self-stress in the Bernoulli-Euler beam. This is true for deflections, bending moments and shearing forces. They determine rotations, stresses and strains according to the specific refined theory under consideration. Thus, by analogy, differences between the results of various refined theories, having been the object of discussions in recent literature, become accessible to a systematic classification. In an Appendix, this strategy of treating refined theories from the point of view of the classical one is put into the more general context of the Theory of Science.     

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.The project supported by the National Natural Science Foundation of China (10172023)     

横向荷载作用下Winkler地基上有限长梁3次超谐共振分析

基于Winkler地基模型和Euler-Bernoulli梁理论,建立了Winkler地基上有限长梁的非线性运动方程。运用Galerkin方法对运动方程进行一阶模态截断,得到了离散的非线性振动方程,然后利用多尺度法求得了该系统3次超谐共振的幅频响应方程及其位移的一阶近似解。为揭示弹性地基上有限长梁的3次超谐共振响应的特性,分别分析了长细比、弹性模量、基床系数、阻尼、密度等主要参数对该系统3次超谐共振幅频响应曲线的影响,并通过与非共振硬激励情况的对比分析了3次超谐共振对系统实际动力反应的影响。研究结果表明:3次超谐共振响应曲线有跳跃和滞后现象;增大阻尼和基床系数均对3次超谐共振的发生有抑制作用;增大外激励幅值,系统3次超谐共振区域增大;3次超谐共振将增大系统的稳态动力响应幅值和加速度。     

A nonlinear composite beam theory

Presented here is a general theory for the three-dimensional nonlinear dynamics of elastic anisotropic initially straight beams undergoing moderate displacements and rotations. The theory fully accounts for geometric nonlinearities (large rotations and displacements) by using local stress and strain measures and an exact coordinate transformation, which result in nonlinear curvature and strain-displacement expressions that contain the von Karman strains as a special case. Extensionality is included in the formulation, and transverse shear deformations are accounted for by using a third-order theory. Six third-order nonlinear partial-differential equations are derived for describing one extension, two bending, one torsion, and two shearing vibrations of composite beams. They show that laminated beams display linear elastic and nonlinear geometric couplings among all motions. The theory contains, as special cases, the Euler-Bernoulli theory, Timoshenko's beam theory, the third-order shear theory, and the von Karman type nonlinear theory.     

Equilibrium theory for magnetic elastomers and magnetoelastic membranes

A theory for the equilibrium response of magnetoelastic membranes under pressure and applied magnetic fields is formulated on the basis of three-dimensional magnetoelasticity. A variational principle admitted by the three-dimensional theory is used to generate a model for membranes regarded as thin three-dimensional bodies. Minimum energy considerations in the presence of applied magnetic fields are used to motivate a direct theory of magnetoelastic membranes which does not require information about bulk properties. The theory is applicable to conventional elastomers magnetized through infusion with uniformly dispersed ferrous particles.     

A refined bound on the error of Reissner's plate theory

Summary The accuracy of two versions of Reissner's plate theory as compared with three-dimensional elasticity is evaluated. The relative mean square error is shown to consist of two parts: one related to transverse normal rigidity and proportional to the plate thickness squared and the other related to transverse shear rigidity and proportional to the thickness cubed. This refines a previous estimate by Nordgren where both of those parts were proportional to the thickness squared.

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Verbesserte Fehlerschranke für die Reissnersche Plattentheorie

Übersicht Für zwei Varianten der Reissnerschen Plattentheorie werden im Vergleich mit dreidimensionaler Elastizitätstheorie globale Fehlerschranken erhalten. Es wird gezeigt, daß die L ₂-Norm des relativen Fehlers aus zwei Teilen besteht: Einem von der Dehnungssteifigkeit in Dickenrichtung bedingten und dem Quadrat der Plattendicke proportionalen und aus dem zweiten Teil, der von der Schubsteifigkeit der Querschnitte bedingt und der 3. Potenz der Plattendicke proportional ist. Dieses Ergebnis verbessert eine von Nordgren erhaltene Abschätzung in der beide Teile dem Quadrat der Dicke proportional sind.

     

A refined theory of elastic thick plates for extensional deformation

Based on elasticity theory, various two-dimensional (2D) equations and solutions for extensional deformation have been deduced systematically and directly from the three-dimensional (3D) theory of thick rectangular plates by using the Papkovich–Neuber solution and the Lur’e method without ad hoc assumptions. These equations and solutions can be used to construct a refined theory of thick plates for extensional deformation. It is shown that the displacements and stresses of the plate can be represented by the displacements and transverse normal strain of the midplane. In the case of homogeneous boundary conditions, the exact solutions for the plate are derived, and the exact equations consist of three governing differential equations: the biharmonic equation, the shear equation, and the transcendental equation. With the present theory a solution of these can satisfy all the fundamental equations of 3D elasticity. Moreover, the refined theory of thick plate for bending deformation constructed by Cheng is improved, and some physical or mathematical explanations and proof are provided to support our justification. It is important to note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of nonhomogeneous boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order terms with respect to plate thickness. The correctness of the stress assumptions in the classic plane-stress problems is revised. In an example it is shown that the exact or accurate solutions may be obtained by applying the refined theory deduced herein.     

Toward a theory of magnetoelastic interaction in magnetostrictive metals

Physicotechnical Institute of the Russian Academy of Sciences, Izhevsk. Translated from Prikladnaya Mekhanika, Vol. 28, No. 7, pp. 38–43, July, 1992.     

A two variable refined plate theory for orthotropic plate analysis

A new theory, which involves only two unknown functions and yet takes into account shear deformations, is presented for orthotropic plate analysis. Unlike any other theory, the theory presented gives rise to only two governing equations, which are completely uncoupled for static analysis, and are only inertially coupled (i.e., no elastic coupling at all) for dynamic analysis. Number of unknown functions involved is only two, as against three in case of simple shear deformation theories of Mindlin and Reissner. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Well studied examples, available in literature, are solved to validate the theory. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories having more number of unknown functions.