共查询到19条相似文献,搜索用时 31 毫秒
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薄壁曲梁的稳定性研究进展 总被引:1,自引:0,他引:1
曲梁是桥梁、建筑、船舶、航空和航天工程中常见的薄壁构件,根据外载荷与主曲率平面的关系,又被称为拱或水平曲梁.随着工程材料的日益发展,如复合材料、功能梯度材料的引入,曲梁的应用范围更加广泛,进一步推进了薄壁曲梁稳定性问题的研究.本文首先对薄壁梁结构的稳定性行为进行了分类.接着简述了薄壁构件的基本假设,对比了近几十年来薄壁曲梁的基本理论,针对复合材料薄壁曲梁,总结了相应的本构关系,并对各理论间存在的分歧进行了归纳.结合最新的薄壁曲梁研究,根据平衡法、能量法和虚位移(虚功)原理推导出控制微分方程,阐述了相应的求解方法,如解析法、半解析法和数值解法.为验证薄壁曲梁理论的准确性,曲梁承载能力试验验证尤为重要,但目前国内外相关研究还很少,亟待发展.最后讨论了现阶段薄壁曲梁研究的局限性和未来发展的方向. 相似文献
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A ‘classical’ theory of beams (i.e., a theory in which the basic kinetic variables are a stress resultant and a stress couple)
undergoing elastic, thermodynamic processes is developed by first deriving exact beamlike (one-dimensional) equations of motion
and a beamlike Second Law (Clausius–Duhem inequality) by descent from three-dimensions. Then what may be considered as the
three basic assumptions of a classical theory are introduced: an assumed form of the First Law (conservation of energy), a
relaxed form of the Second Law, and a general form of the constitutive relations. Throughout, detailed specification of geometry,
kinematics, or constitution is minimized. It is shown how the kinematic Kirchhoff hypothesis may be avoided by first introducing
a mixed-energy density and then imposing a logically more satisfying constitutive Kirchhoff hypothesis.
Mathematics Subject Classifications (2000) 74A15, 74B20, 74K10 相似文献
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This paper revisits the historical aspects of the contributions made into the elastic stability theory from the structural engineering point of view.Extensive quotations are brought in order to substantiate the claims made. It is hoped that the review constitutes a contribution to the identification of the main ideas pertinent to engineering mechanics. 相似文献
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轴压下各向异性开口薄壁杆的非线性共振 总被引:1,自引:0,他引:1
本文推导了轴压下各向异性薄壁直杆的非线性动力学方程组.在推导中计及了杆壁中面的剪切变形,以及开口薄壁杆中剪应力沿厚度变化而造成的Saint-Venant扭矩,但略去了杆壁的弯曲.从这一方程组出发,用渐近方法计算了简谐变化轴向压力作用下薄壁杆共振时幅频曲线,且对各种影响因素,包括Saint-Venant扭矩的影响,作了分析. 相似文献
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A. D. Matveev 《Journal of Applied Mechanics and Technical Physics》2004,45(4):591-597
Mixed formulations of bending problems for homogeneous plates (beams) are proposed, whose essence is that the deformation of a plate (beam) near its fixed boundary is described by the threedimensional elasticity equations, and the remaining part by the conventional equations of plate (beam) bending. At the interface between these regions, the solutions of these equations are joined. The mixed formulation allows one to describe the threedimensional stress state in the neighborhood of the fixed boundaries of plates (beams) and take into account the complex nature of the fixing conditions. Finiteelement implementation is more efficient for the mixed formulations of plate (beam) bending problems than for the wellknown threedimensional formulations. 相似文献
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This paper deals with the asymptotic analysis of the three-dimensional problem for a linearly elastic cantilever having an
open cross-section which is the union of rectangles with sides of order ε and ε
2, as ε goes to zero. Under suitable assumptions on the given loads and for homogeneous and isotropic material, we show that the
three-dimensional problem Γ-converges to the classical one-dimensional Vlassov model for thin-walled beams.
相似文献
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Singularly perturbed systems with structural perturbations are analyzed for stability. New sufficient conditions of asymptotic stability and uniform asymptotic stability are established. The systems in question are widely used in control theory, engineering, etc 相似文献
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Two- and three-dimensional stability problems for a rectangular plate under uniaxial compression are solved by the mesh method. It is shown that the difference between the critical loads obtained in the three- and two-dimensional problems is not greater than 5% for arbitrary fixation conditions and arbitrary length and thickness ratio of the plate 相似文献
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本文推广文献[1、2]结果,对变刚度连续矩形薄板弯曲和稳定计算提出了一个新法则,算例表明此法简明有效。 相似文献
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本文研究单阶和多阶截面杆在集中和分布轴向荷载作用下的弹性稳定计算方法,首次给出了其整体稳定和局部稳定的解析解. 相似文献
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The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates
with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process
helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions
and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting
moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish
at infinity. An example is discussed to illustrate the theory. 相似文献
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对于一般任意支撑的连续梁结构动力稳定性问题,已有的计算方法求解过程都很复杂,给工程设计带来极大的不便.本文提出了一个简化的分析方法,利用现有的商业软件,只需求得连续梁的自然频率及静力屈曲(失稳)荷载,就可容易得到结构的动力失稳区域,当考虑结构阻尼对不稳定区域的影响时,可将阻尼矩阵表达为Rayleigh阻尼的形式.研究结果表明:采用本文计算方法与已有的理论计算方法得到的连续梁主参数共振的不稳定边界非常吻合,而本文计算方法更为简单,计算结果可靠,计算精度高,可满足工程设计的需要. 相似文献
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New conditions of stability in two measures are established for nonlinear impulsive systems with structural perturbations. A list of two measures used in the nonlinear dynamics of pulse systems is presented 相似文献
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弹性地基板的弯曲问题,尤其是自由边板,一直是学者和工程师们所十分关切的问题。本文用无单元法研究双参数弹性地基板的弯曲问题,由最小二乘法和变分原理导出了双参数弹性地基板的无单元法刚度短阵,编制相应的无单元法计算程序,并给出计算实例。结果表明本方法精度良好,可求出任意荷载作用下板中任一点的挠度、转角、弯矩和扭矩,且有广泛的工程应用前景。 相似文献
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采用样条函数构造的位移模式,出了非理想压杆稳定极限承载力及稳定平衡全过程的样条函数分析法。本方法可以考虑任意实际初始缺陷和材料弹塑性加卸载效应的影响。计算表明,本方法精度高,速度快。 相似文献