高层束筒建筑板块法理论

本文给出了正交异性板在多种平面应力边界条件下的应力分布解析表达式，由此提出了多筒高层框筒（或剪力墙筒体）内力与位移计算的正变异性板板块法理论．该方法是基于力法体系及形变协调条件的半解析法，可方便地应用于多筒筒体或多室梯形箱梁等折板结构分析。     

Determination of stresses in slightly orthotropic plates using off-axis horizontally polarized ultrasonic shear waves

Many structural materials display a slight orthotropy when they are rolled into plate form. A theory is developed for propagation of horizontally polarized ultrasonic shear waves in the planes of (orthotropic) material symmetry of these plates. The waves propagate at an angle θ to the plate normal. If E represents a measure of the shear stress field, then pure-mode waves can be propagated if both cos² θ and sin² θ E; the polarization directions are the material symmetry axes.

The theory can be applied to ultrasonic stress measurements. The (normalized) velocity difference (acoustic birefringence) between two pure-mode SH-waves propagating in orthogonal material symmetry planes is related to stresses in the plate, and to the (initial) birefringence in the unstressed state. By making measurements of birefringence at two or more values of θ, the dependence upon the initial birefringence can be removed and information about the stresses obtained.     

Complexity results in graph reconstruction

We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c?1 of deletion:

(1)

, , , and .

(2)

For all k?2, and .

(3)

For all k?2, .

(4)

.

(5)

For all k?2, .

For many of these results, even the c=1 case was not previously known.Similar to the definition of reconstruction numbers vrn_∃(G) [F. Harary, M. Plantholt, The graph reconstruction number, J. Graph Theory 9 (1985) 451-454] and ern_∃(G) (see [J. Lauri, R. Scapellato Topics in Graph Automorphism and Reconstruction, London Mathematical Society, Cambridge University Press, Cambridge, 2003, p. 120]), we introduce two new graph parameters, vrn_∀(G) and ern_∀(G), and give an example of a family {G_n}_n?4 of graphs on n vertices for which vrn_∃(G_n)<vrn_∀(G_n). For every k?2 and n?1, we show that there exists a collection of k graphs on (2^k-1+1)n+k vertices with 2ⁿ 1-vertex-preimages, i.e., one has families of graph collections whose number of 1-vertex-preimages is huge relative to the size of the graphs involved.     

Use of off-axis SH-waves to map out three-dimensional stresses in orthotropic plates

An acoustical birefringence method is proposed to measure thickness-varying stresses in slightly orthotropic plates. In this method, off-axis SH-waves at various angles of incidence are propagated in the body's planes of material symmetry, and pass through a common point. The weighted sum of times-of-flight of waves propagating in one plane is subtracted from the corresponding sum in the orthogonal plane. To a first approximation, this difference is the local birefringence at the common point and as such can be related to components of the stress tensor there.The ability of the method to map out simple stress concentrations was tested analytically. Reasonably good spatial resolution was obtained, but the method underestimated the magnitudes.     

四边固定正交各向异性矩形板的非线性弯曲问题

本文利用“两变量法”［１］和“混和摄动法”［２］研究了正交各向异性矩形板在非均布横向载荷作用下的非线性弯曲问题，在四边固定条件下，得到了一致有效渐近解．     

均布载荷作用下正交各向异性一端固支一端简支梁的解析解

构造了一个应力函数，用Ariy应力函数逆解法给出了受均布载荷作用的正交各向异性矩形梁在一端固支一端简支条件下平面应力问题的解析解．采用的2种不同固支边界条件与Timoshenko and Goodier在1970年中所采用的方法相同，并给出了数值算例．     

静载荷作用下正交各向异性旋转扁壳的非线性自由振动

本文用加权残值法和Lindstedt－Poincare摄动法研究了圆柱型正交各向异性扁薄球壳和锥壳在均布静载荷作用下的轴对称非线性自由振动问题，得到了其非线性固有频率和振幅间的特征关系，并讨论了静载荷及壳体的几何参数和材料参数对其振动特性的影响。     

Nonlinear vibration analysis of viscoelastic plates based on a refined Timoshenko theory

Nonlinear vibrations of viscoelastic orthotropic and isotropic shells are mathematically modeled using a geometrically nonlinear Timoshenko theory. Nonlinear problems are solved by using the Bubnov-Galerkin method and a numerical method based on quadrature formulas. Results obtained from different theories are compared and analyzed. For each problem, the Bubnov-Galerkin method is tested for convergence. The influence of the viscoelasticity and inhomogeneity of materials on the vibrations of plates is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 120–131, May 2006.     

NONLINEAR THEORY OF MULTILAYER SANDWICH SHELLS AND ITS APPLICATION (Ⅱ)──FUNDAMENTAL EQUATIONS FOR ORTHOTROPIC SHALLOW SHELLS

This paper applied the simplified theory for multilayer sandwich shells undergoing moderate/small rotations in Ref. [1] to shallow shells. The equilibrium equations and boundary conditions of large deflection of orthotropic and the special case, isotropic shells, are presented.     

Influence of orthotropy parameters on the stress state of hollow cylinders with elliptic cross-section

An approach based on the use of discrete Fourier series is employed to analyze the stress state of orthotropic and transversely isotropic elliptical hollow cylinders __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 82–90, December 2007.