应用数学和力学

1988 Vol. 9, No. 4

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Yeh Kai-yuan, Deng Liang-bo

1988, 9(4): 287-295.

Abstract(1473) PDF(546)

Abstract:
In the static and dynamic analysis of composite laminates, a theory for the laminated plates is presented in this paper. Because the deflection W_b which is caused by the classical bending deformation and the deflection W_s which is caused by the shear deformation are divided from the total deflection W in the theory, this makes it easy to solve the governing equations. In addition, this theory is convenient for the discussion and analysis of the effects of transverse shear deformations on bendings, vibrations and stabilities of laminated plates.

The Perturbation-Iterative Method Applied to the Problems of the Large Deflection of the Elastic Circular Thin Plates

Chou Huan-wen, Yin Chuan-yan

1988, 9(4): 297-304.

Abstract(1690) PDF(543)

Abstract:
In this paper, we present a perturbation-iterative method for solving certain boundary value problems encountered in the nonlinear theory of elastic circular thin plates. At the same time, with this method, we strictly prove the convergence of the solutions for the large deflection equations of circular plates subjected to certain distributed loads.

Vibration Analysis of Elliptical Column Partially Submerged in Water

Zhu Yong-yi, Weng Zhi-yuan, Wu Jia-long

1988, 9(4): 305-316.

Abstract(1575) PDF(492)

Abstract:
In this paper, a general analytical method based on Ref. [1] is presented to study the bending vibration of an elliptical column partially submerged in water. Besides, it is pointed out that there is a limitation to the method mentioned in Ref. [2], As a special example, the natural frequencies of circular column submerged in water considering compressibility are calculated, and the extent of compressible effect is given.

Asymptotic Analysis of Stability Problem of Plane Poiseuille Flow for High Reynolds Number

Wang Fa-min, Ng. Tiak Wan

1988, 9(4): 317-326.

Abstract(1637) PDF(498)

Abstract:
A study of the stability of plane Poiseuille flow at higher Reynolds number is made. Within a "triple-deck" structural framework, the qualitative behaviour of the eigenvalue of Orr-Sommerfeld equation is analytically obtained. The corresponding eigenfunction is formulated approximately.

Dynamic Dislocations Solution to Elastoplastic Moving Cracks

Zhao Zhi-su

1988, 9(4): 327-334.

Abstract(1531) PDF(488)

Abstract:
In the range of micro-cosmic, an analogy between linear dislocation arrays and moving cracks is drawn, then elastoplastic moving crack problems are derived by superposition of distribution of dislocations. Various dynamical crack-opened-displacements are derived, which gives an elastoplastic stability criterion of moving cracks. In this paper, modes Ⅰ,Ⅱ,Ⅲ moving crack problems are discussed respectively.

Some Problems for Dynamic Computation of Closed Cylindrical Shell Due to Axial impact Load

Cheng Xiang-sheng

1988, 9(4): 335-339.

Abstract(1787) PDF(420)

Abstract:
The present paper treats some of the problems for dynamic computation of closed cylindrical shell due to an axial impact load, including the calculations of the dynamic stresses and the problems of stability. It analyses the changes of the momen tums and the energy in the impact process, takes into account the effect of the mass of the striking object and the system of the closed cylindrical shell to be struck, turns the distributed mass of the total cylindrical shell into an "equivalent mass" being concentrated on only at one end of the shell by using the way of reduced mass, and accordingly derives the dynamic factor of the closed cylindrical shell under the axial impact load, hence resolves the questions of calculation of the dynamic stresses in the loaded case mentioned above and found out the critical loading.

Theory and Refined Theory of Elasticity for Transversely Isotropic Plates and a New Theory for Thick Plates

Zhong Zheng-hua, Luo Jian-hui

1988, 9(4): 341-354.

Abstract(1947) PDF(621)

Abstract:
A theory of elasticity for the bending of transversely isotropic plates has been developed from the basic equations of elasticity in terms of displacements for transversely isotropic bodies, which takes into account the loads distributed over the surfaces of the plates. Based on this theory, a refined theory of plates which can satisfy three boundary conditions along each edge of the plates and a new theory of thick plates are established. The solution of the refined theory for simply supported polygonal plates has been obtained; and its numerical result is very close to the exact solution of the three-dimensional theory of elasticity. A systematic comparison with the former theories of thick plates shows that the present theory of thick plates is closest to the result of the theory of elasticity.

The Method of Solving Axisymmetric Problems in Elastic Space by Complex Function and Some Examples

Wang Zi-kun

1988, 9(4): 355-363.

Abstract(1847) PDF(580)

Abstract:
This paper proves Love's stress function of space axisymmetric problem can be represented by choosing two generalized analytic functions of complex variates reasonably^[1], and deduces the expressions of the components of stress displacements and boundary conditions in complex function. To present the feasibility of the method here and examining the truth of the formulae founded in this paper, the problem of circular shaft with globular cavity pressed on the side and pulled at the ends is solved by using power series and the result is the same as that solved by other methods. In the end, the problem of a cone sheared by uniform shear stress on the sideface is solved, and the solution of a cone acted on by gravity is given by converting constant body forces into surface forces.

On Second Order Asymptotic Solutions of Axial Symmetrical Problems of r>0 Thin Uniform Circular Toroidal Shells with a Large Parameter a²/R₀h

Chen Guo-dong

1988, 9(4): 365-378.

Abstract(1579) PDF(571)

Abstract:
According to the classital shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a²/R₀h.In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.

Solution for Plane Strain Forward and Backward Extrusions with a Fractional Reduction R=0.5 by the Integration Depending on a Parameter

Zhao De-wen, Zhang Qiang

1988, 9(4): 379-384.

Abstract(1801) PDF(474)

Abstract:
A parameter t is introduced to boundary slip line of rigid regions for plane strain and indirect extrusions with a fractional reduction R=0.5. Integration by substitution has been used along the boundary slip line in order to obtain the extrusion pressure. By the integration depending on a parameter, the following results are obtained, p/2k=1.29 and die pressure is 5.14k for backward extrusion; p/2k=1.29 and pad average pressure is 2.57k for forward extrusion. All the results from this method are the same as those of the conventional solution.