应用数学和力学

A Method for Establishing Generalized Variational Principle

Hsueh Dah-wei

1985, 6(6): 481-488.

Abstract(1704) PDF(570)

Abstract:
A method for establishing generalized variational principle is proposed in this paper. It is based on the analysis of mechanical meaning and it can be applied to problems in which the variational principles are needed but no corresponding variational principle is available. In this paper, the Hu-Washizu's generalized variational principle and the Hu's generalized principle of complementary energy are derived from the mechanical meaning instead of from the generalization of the principle of minimum potenlial energy and the correct proofs of these two generaleed variational principles are given. It is also proved that this is wrong if one beleives that σ_ij, e_ij and ui are independent variables each other based on the reason that these three kinds of variables are all contained in these two generalized variational principles. The condition of using these two variational principles in a correct manner is also explained.

On the Method of Equivalent Inclusions in Elastodynamics and the Scattering Fields of Two Ellipsoidal Inhomogeneities

Li Hao Zhong, Wei-fang, Li Gong-fu

1985, 6(6): 489-498.

Abstract(2165) PDF(565)

Abstract:
Gurtin's variational principle is used to derive the equivalence equalions for general linear elastodynamical problems of multiple inhomogeneities. An approximate expression on scattering field of two ellipsoidal inhomogeneities is obtained by the method of equivalent inclusions. And some numerical examples are presented.

Dynamic Stability and Phase Planar Property for Radial Sector Cyclotrons with N-Folded Symmetry

Luo Shi-yu

1985, 6(6): 499-506.

Abstract(1745) PDF(547)

Abstract:
The particle nonlinear motion equation for a radial sector cyclotron with N-folded symmetry was derived. The betalron oscillations frequency with N=4. 5, 6, 8, 10 and the phase planar properlies before and after v_x=4/3 resonance with N=4, f=0.578 were analyzed, by using numerical method. The dynamic stabililies and nonlinear properties were discussed, the result compared with those of ref. [1] shows that both are consistent when nonlinear terms are neglected.

A New Criterion of Combined Type Crack—The Criterion of Minimum Distance r_min in Plastic Region

Yin Shuang-zeng

1985, 6(6): 507-518.

Abstract(1644) PDF(508)

Abstract:
The existence of the plastic area around the crack tip is an important factor against the cracking. In this plastic region, the crack ing most likely develops in such a direction along which the distance from the existant crack tip to the plastic region edge is the shortest one.

Navier Solution for the Elastic Equilibrium Problems of Rectangular Thin Plates with Variable Thickness in Linear and Nonlinear Theories

Yin Si-ming, Ruan Sheng-huang

1985, 6(6): 519-530.

Abstract(1916) PDF(836)

Abstract:
This paper discusses the elastic equilibrium problems of rectangular thin plates of varying thickness and simply supported on all four sides by linear and nonlinear theory, using the Navier method to seek an approach to the problem, and illustrates the solution with two examples. In conclusion, mention is made of scope of application and the convergency of the solution.

Computational Model of Boundary Integral Equation in Solid Mechanics

Wang Xing-feng, Wang Xing-fa

1985, 6(6): 531-540.

Abstract(1796) PDF(557)

Abstract:
In the first part of the paper, the computational model of boundary integral equation in solid mechanics is presented while in the second part the model is used in the solution of two problems of solid mechanics.

Selection of the Optimum Parameters for Sandwich Construction with Honeycomb Core

Zhou Zhu-lin

1985, 6(6): 541-549.

Abstract(1923) PDF(603)

Abstract:
The minimum weight of sandwich construction which is regarded as objective function has been discussed. Under given constraint condition of the strength or the stiffness, the four optimum parameters of sandwich construction with honeycomb core thickness of the face t_f. thickness of the honeycomb core h_c, thickness of the honeycomb wall t_s, side length of the honeycomb cell c, are evaluated. By using constraint condition of the strength, a equation of high degree is finally solved. In the constraint condition of the stiffness, the constraint optimization problem is treated as inconstraint optimization problem with the method of obtaining extreme value solution by undetermined parameter multiplication. Also, the results are discussed.

The Method of Matrices Conjoint Multiplication for the Problem of Circular Arc Corrugated Diaphragm

Zhou Zhe-wei, Wang Shu

1985, 6(6): 551-566.

Abstract(1783) PDF(519)

Abstract:
The circular are corrugated diaphragins are taken in this paper and structures of several sections of the ring shells and a central cireular plale I matrices and link matrices are derived by using Prof. Chuen Hei-zang's general the ring shell^[1] and perturbation theory of the circular thin plates^[2]. Throngh the meined of matrices conjoint multiplication, the linear exact solution and nonlinear soluaen are obtained. The results agree with that of the experiments presented by W. A. Wildhack^[3].

A Simplified Method for the Construction of the Cubic Spline Function

Tan Fu-qi

1985, 6(6): 567-572.

Abstract(1655) PDF(410)

Abstract:
This paper gives a simplifled method for the construction of the cubic spline function. discusses the related problems, and at last, presents the treatment for its different cases.

1985 Vol. 6, No. 6