轴对称层合圆柱壳混合状态方程的弱形式及其边值问题

从Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ变分原理出发，在柱坐标系中，导出圆柱壳轴对称问题的弱形式混合状态方程和边界条件，联用状态空间法给出强厚度叠层柱壳的解析解，此法使得求解该类问题的形式得以扩大和统一。     

约束阻尼层合板的稳态响应

基于Reddy分层理论推导出约束阻尼层合板的稳态振动方程,得到了约束阻尼层合板的振动频率和损耗因子;分别分析了约束阻尼层合板的粘弹性夹层厚度、模量对固有频率和损耗因子的影响;得到了稳态振动时振幅和频率曲线以及横向应力与面内应力。数值计算结果表明所采用的算法是可靠的。     

Bending of functionally graded piezoelectric rectangular plates

By introducing two displacement functions as well as two stress functions, two independent state equations with variable coefficients are derived from the three-dimensional theory equations of piezoelasticity for transverse isotropy. A laminated approximation is used to transform the state equations to those with constant coefficients in each sub-layer. The bending problem of a functionally graded rectangular plate is then analyzed based on the state equations. Numerical results are presented and the effect of material gradient index is discussed. Supported by the National Natural Sciences Foundation of China (No. 10002016).     

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主要基于三维弹性力学和状态空间法给出了四边简支各向同性矩形层合板自由振动和 强迫振动问题的精确解. 首先基于三维弹性力学建立了层合板的基本方程,利用状态空间法 解决了层合板的自由振动问题,然后根据Lagrange动力学方程求解了层合板受到横向冲击时 的强迫振动响应.     

Analytical solution for axisymmetric problem of thick laminated closed cantilever shells in hamilton system

By giving up any assumptions about displacement models and stress distribution, the mixed state Hamilton equation for the axisymmetric problem of the thick laminated closed cantilever cylindrical shells is established. An identical analytical solution is obtained for the thin, moderately thick and thick laminated closed cantilever cylindrical shells. All equations of elasticity can be satisfied, and all elastic constants can be taken into account. This work is supported by the National Natural Science Foundation of China.     

多层压电材料层合板的精确解

抛弃有关位移和应力的所有假设，直接从三维弹性力学理论的静电学理论，先导出正交各向异性压电材料板的状态方程，由此得到四边简支压电材料板的状态主程，再根据矩阵分析理论，建立了单层压电材料板的上下表面状态量之间的关系，进一步建立了多层压电板上，下表面状态量之间关系式，利用上下表面已知状态量，得到上表面未知状态的求解方程解。通过求解方程组，便得上表面未知状态量，最终可以得到任意位置处状态量，最后，同时给出了四边简支，两层不同压电材料组成，不同纵横比的层合板受正弦分布载荷作用下的精确解，其结果与现有解比较，吻合较好。     

混合状态Hamiltonian元的半解析解和叠层板的计算

本文给出混合状态方程的一种强有力的半离散半解析解法,并给出了矩形域和叠层板的算例,讨论了可能的发展和应用。     

粘弹层合板的稳态振动和层间应力

应用混合分层理论和Ressiner混合变分原理，在板厚方向取二次位移插值函数和三次、四次横向应力插值函数推导出粘弹层合板的动力学方程，得出简支粘弹层合板稳态振动的解。不仅得出与三层弹性板精确的自振频率吻合良好的解，而且对于粘弹层合板，所计算的自振频率和结构损耗因子也与三维结果吻合较好。计算了自由阻尼层合板对应的低阶法向位移响应幅值和层问横向应力的幅值。结果表明，较高的层间横向正应力是低频稳态振动中引起粘弹层合板分层破坏的主要因素，采用适当模量和厚度的粘弹性材料将有效地降低粘弹层合板的层间横向正应力的幅值。     

Deformation of physically nonlinear stochastic composites

The studies of the deformation of physically nonlinear homogeneous and composite materials are systematized. Algorithms to determine the effective elastic properties and stress–strain state of particulate, laminated, fibrous, and laminated fibrous composite materials with physically nonlinear components are outlined, and their deformation patterns are studied. Composites are considered as two-component materials of random structure. Their effective properties are determined using the conditional averaging method. The nonlinear equations that allow for the physical nonlinearity of the components are solved by an iterative method. The relationship between macrostresses and macrostrains is established. Macrostress–macrostrain curves of homogeneous and composite materials are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 7–38, December 2008.     

The exact solution for thick laminated cantilever cylindrical shell

Discarding any assumption regarding displacement or stress models, the state equation for orthotropy is established in a cylindrical system. The exact solution is presented for the statics of thick closed laminated cantilever cylindrical shells. Every equation of elasticity can be satisfied and all the elastic constants are taken into account. Arbitrary precision of a desired order can be obtained. Project supported by the National Natural Science Foundation of China     

非平面应变状态下的叠层厚壁筒

抛弃任何有关位移或应力模式的人为假设，在轴对称情况下，导出正交异性厚壁筒的状态方程。在沿筒轴方向任意分布的轴对称荷载下，给出叠层厚壁筒静力问题的精确解。此解满足所有弹性力学基本方程，包含了全部弹性常数，可满足任意精度要求。数值结果和ＳＡＰ５有限元解进行了对比。     

A NEW STATE SPACE SOLUTION FOR RECTANGULAR THICK LAMINATES WITH CLAMPED EDGES Hu Wenfeng Liu Yihua

通过把固支边上的边界位移函数作为状态变量引入状态方程,得到了含固支边矩形单层与叠层厚板的精确解. 在求解过程中,将非齐次状态方程的求解变为齐次状态方程的求解,省略了求解待定常数的中间过程,使求解过程变得简单. 所得到的解能够严格满足固支边界条件,在同一材料层内不需作分层处理,因而更加精确. 此外,对固支边的应力提出了新的计算方法,能够得到更精确的边界应力. 算例表明,本文解比现有精确解收敛快,与有限元解吻合的更好,尤其是在固支边处体现得更加明显.     

On the Bending, Vibration and Stability of Laminated Rectangular Plates with Transversely Isotropic Layers

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔａｔｉｃｓａｎｄｄｙｎａｍｉｃｓｏｆｒｅｃｔａｎｇｕｌａｒｐｌａｔｅｓｈａｖｅａｌｗａｙｓｂｅｅｎｏｆｐａｒｔｉｃｕｌａｒｒｅｓｅａｒｃｈｉｎｔｅｒｅｓｔｉｎｓｏｌｉｄｍｅｃｈａｎｉｃｓ.Ｉｎｐａｒｔｉｃｕｌａｒ,ｔｈｅｅｍｅｒｇｅｎｃｅｏｆｎｅｗｍａｔｅｒｉａｌｓａｎｄｎｅｗｓｔｒｕｃｔｕｒｅｓｈａｓｂｒｏｕｇｈｔｏｕｔｅｎｄｌｅｓｓｖｉｔａｌｆｏｒｃｅｉｎｔｏｔｈｅｓｔｕｄｙ .Ｉｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｃｌａｓｓｉｃａｌｐｌａｔｅｔｈｅｏｒｙｂ…     

Influence of the Direction of the Principal Anisotropy Axes in a Rectilinearly Orthotropic Material on the Stress State of a Compound Solid of Revolution Subject to Nonaxisymmetric Heating

A technique for analysis of the temperature fields and the stress state of isotropic and orthotropic laminated bodies of revolution under nonaxisymmetric loading is described. The influence of the direction of the principal anisotropy axes in a rectilinearly orthotropic material on the stress state of a three-layer body of revolution under nonaxisymmetric loading is studied     

Exact solution of the thick laminated open cylindrical shells with four clamped edges

ＥＸＡＣＴＳＯＬＵＴＩＯＮＯＦＴＨＥＴＨＩＣＫＬＡＭＩＮＡＴＥＤＯＰＥＮＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＷＩＴＨＦＯＵＲＣＬＡＭＰＥＤＥＤＧＥＳＦａｎＪｉａ－ｒａｎｇ（范家让）（ＨｅｆｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ）ＨｅｆｅｉＤｉ...     

Exact solution for laminated continuous open cylindrical shells

I.Introducti0nNowadays,thecurrenttheoriesofplatesandshe1ls,suchasthetheoriesofReissner's,KirchhoffLove'sandAmbartsumyan'setc,areestablishedons0mehypotheses.Forexample-assumethatthemechanicalquantitiesarethepolynomialsofacertaincoordinatevariable.Itisshown…     

On two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic bimodulus materials

The paper compares two approaches to determining the axisymmetric elastoplastic stress-strain state of laminated shells made of isotropic and transversely isotropic materials with different elastic moduli in tension and compression. The approaches use different nonlinear constitutive equations describing the elastic deformation of the transversally isotropic bimodulus materials. Both approaches employ the theory of deformation along paths of small curvature and the Kirchhoff-Love hypothesis for the whole laminate to describe the deformation of the isotropic materials. The problem is solved by the method of successive approximations. The solutions of specific problems obtained by the two approaches are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 59–69, June 2008.     

Elastoplastic Axisymmetric Stress-Strain State of Laminated Shells Made of Isotropic and Transversely Isotropic Materials with Different Moduli

A method is developed for analysis of the elastoplastic stress-strain state of laminated shells of revolution under axisymmetric loading. The shells are made of isotropic and transversally isotropic materials with different moduli. The method is based on the Kirchhoff-Love hypotheses for the whole laminate, the theory of deformation along paths of small curvature (for isotropic materials), and the theory of elasticity with different tensile and compressive moduli (transversely isotropic materials). The problem is solved by the method of successive approximations. Numerical examples are given __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 88–96, August 2005.     

任意厚度层合开口柱壳的温度应力

基于层合柱壳混合状态方程和边界条件的弱形式,建立了具有固支边的层合开口柱壳的温度应力混合方程,给出了任意厚度层合开口柱壳在温度荷载和机械荷载共同作用下的解析解。     

Transient thermal stress analysis of a functionally graded magneto-electro-thermoelastic strip due to nonuniform surface heating

This article is concerned with the theoretical analysis of the functionally graded magneto-electro-thermoelastic strip due to unsteady and nonuniform surface heating in the width direction. We analyze the transient thermal stress problem for a functionally graded strip constructed of the anisotropic and linear magneto-electro-thermoelastic materials using a laminated composite mode as one of theoretical approximation. The transient two-dimensional temperature is analyzed by the methods of Laplace and finite sine transformations. We obtain the solution for the simply supported and functionally graded magneto-electro-thermoelastic strip under a plane strain state. As an illustration, we carried out numerical calculations for a functionally graded strip composed of piezoelectric BaTiO₃ and magnetostrictive CoFe₂O₄, and examined the behaviors in the transient state for temperature change, stress, electric potential and magnetic potential distributions. Furthermore, the effects of the nonhomogeneity of material on the stresses, electric potential, and magnetic potential are investigated.