Analytical solutions of simply supported magnetoelectroelastic circular plate under uniform loads

INTRODUCTIONInelasticity ,theproblemofasimplysup portedcircularplatesubjectedtouniformloadsisaclassicone .Timoshenkoetal.(1970 )pre sentedasolutionforanisotropiccircularplate .Dingetal.(2 0 0 0 ;2 0 0 1)obtainedtheanalyti calthree dimensionalsolutionforat…     

Pure bending of simply supported circular plate of transversely isotropic functionally graded material

INTRODUCTION In recent years, functionally graded materials (FGMs) have attracted more and more attention. Due to their continuously varying material properties in space on the macroscopic scale, FGMs, therefore, are usually superior to conventional fiber-matrix materi-als in mechanical behavior, especially for perform-ance under thermal loading. Now FGMs have been widely used in various fields including electronics, chemistry, optics, biomedicine, etc. Heretofore, volumes of literatu…     

简支工字梁在偏心荷载下空间失稳问题的计算

在薄壁杆件空间弹性失稳势能的变分方程中，应用附加弯矩与扭矩及其所对应的失稳位移的曲率与扭率的增量来表达其外力失稳势能。该微分方程通过分部积分法应用位移及应力自然边界条件，得出各阶微分方程的迦辽金法的方程组来进行计算，从而简便解决了偏心荷载下简支工字梁的空间失稳问题。     

Analytical solutions for a uniformly loaded circular plate with clamped edges

INTRODUCTION The problem of circular plates subjected to auniform load is one of the classical problems in elas-ticity theory,which also is encountered frequently inpractice.Timoshenko and Goodier(1970)presented athree-dimensional solution for uniformly loaded iso-tropic circular plates with simply supported edges.Analytical solutions of isotropic circular plates witheither clamped or simply supported edges subjectedto a uniform load,which were derived based on thinplate theory with Kirch…     

Three-dimensional analysis of a thick FGM rectangular plate in thermal environment

The thermal behavior of a thick transversely isotropic FGM rectangular plate was investigated within the scope of three-dimensional elasticity. Noticing many FGMs may have temperature-dependent properties, the material constants were further considered as functions of temperature. A solution method based on state-space formulations with a laminate approximate model was proposed. For a thin plate, the method was clarified by comparison with the thin plate theory. The influences of material inhomogeneity and temperature-dependent characteristics were finally discussed, through numerical examples. Project (No. 10002016) supported by National Natural Science Foundation of China     

深埋圆形富水隧道应力与位移的弹塑性解

研究目的：推导获得深埋圆形富水隧道应力场与位移场分布的弹塑性解析解。创新要点：皋于弹性力学厚壁圆筒受均布压力的拉姆解答和Mohr—Coulomb屈服条件,推导了考虑渗流作用和应力释放时含衬砌深埋隧道的弹塑性解,并采用FLAC3D有限差分程序验证了其正确性。研究方法：通过理论分析建立考虑渗流作用和应力释放的含衬砌深埋圆形隧道的解析模型（图1）,然后推导了基于Mohr-Coulomb屈服准则的隧道同岩与衬砌渗流场、位移场和应力场计算的弹塑性解析公式,并通过数值模拟程序（图2）验证了推导公式的正确性。重要结论：基于前人研究皋础,推导获得了深埋富水隧道应力与位移场分布的理论解析解,并通过数值模拟方法验证了其正确性。该解析解一方面可以用于深埋高水头隧道的预设计,如预测隧道周围的水压力、应力场和位移场分布规律,另一方面可用于校核大型复杂数值模型的正确性。     

Three-dimensional analysis of a thick FGM rectangular plate in thermal environment

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Nonlinear vibration of circular plate with variable thickness

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Analytical study on the dynamic displacement response of a curved track subjected to moving loads

A closed-form out-of-plane dynamic displacement response of a curved track subjected to moving loads was pro- posed. The track structure was modeled as a planar curved Timoshenko beam periodically supported by the double-layer spring-damping elements. The general dynamic displacement response induced by the moving loads along the curve on the elastic semi-infinite space was firstly obtained in the frequency domain, according to the Duhamel integral and the dynamic reciprocity theorem. In the case of the periodic curved track structure subjected to moving loads, the dynamic displacement equation was simplified into a form of summation within the basic track cell instead of the integral. The transfer function for the curved track was expressed in the form of a transfer matrix. Single and series moving loads were involved in the calculation program. For the verification of the analytical model, the mid-span vertical deflection of a simply support curved beam subjected to moving load was recalculated and compared with the same case in the reference. The research results indicate that： under the same moving loads, the displacement response of the curved track decreases slightly with the increasing track radius, and the displacement response of the curved track with the radius greater than or equal to 600 m is almost equivalent to the displacement response of the straight track; the frequency spectrum of the curved track is more abundant than that of the straight track, which may result in more wheel-rail resonance and rail corrugation in the curved lines.     

复杂边界厚矩形板在静水压力作用下的弯曲

应用功的互等法（RTM）求解基于Reissner理论厚矩形板的弯曲问题,给出了对边简支另两边固定边界条件下厚矩形板在静水压力作用下弯曲的封闭解析解,并给出了该种情况下的曲线图.     

Preliminary Report on the Theory of Elastic Circular Plate with no Kirchhoff-Love Assumptions

lTheThree-DimensionalEquationsnsofAxisymmetricElasticCircularPlatesOnthebasisofthegeneraltheoryofthepreviouspaperl'],whichabandonsKirchhoff-Loveassumptionsl"'1intheclassicaltheory,thispaperestablishesafirst-orderapproximationtheoryofelastic'circularplates…     

3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials

The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically.