应用数学和力学

A Finite Element Analysis for the Temperature Field Produced by a Moving Heat Source

S. N. Atluri, Kuang Zhen-bang

1986, 7(5): 383-400.

Abstract(1670) PDF(482)

Abstract:
Using moving mesh finite element method,we discuss the temperature field produced by a moving heat source with the variable thermal conductivity and with the radioactive and convective boundary conditions in a wide range of the velocity.The temperature-time relationships at various velocities in the static and moving coordinate systems are studied.The steady-state temperature distributions at various velocities in the moving coordinate systems are given.The temperature field produced by the plastic deformation at the process region(a region very near the crack tip) is also studied,and the results show that the highest temperature at the process region is lower than 1000℃ or 1832℉.

Boundary and Angular Layer Behavior in Singular Perturbed Quasilinear Systems

Lin Zong-chi

1986, 7(5): 401-408.

Abstract(1604) PDF(530)

Abstract:
In this paper,using the method of differential inequalities,we study the existence of solutions and their asymptotic behavior,as ε→0⁺ of Dirichlet problem for a second order quasilinear systems Denendine on whether the reduced solution u(t) has or does not have a continuous first-derivative in(a,b),we study two types of asymptotic behavior,thus leading to the phenomena of boundary and angular layers.

On the Compactness of Quasi-Conforming Element Spaces and the Convergence of Quasi-Conforming Element Method

Zhang Hong-qing, Wang Ming

1986, 7(5): 409-423.

Abstract(1669) PDF(436)

Abstract:
In this paper,the compactness of quasi-conforming clement spices and the convergence of quasi-conforming element method are discussed.The well-known rellich compactness theorem is generalized to the sequences of quasi-conforming element spaces with certain properties,and the generalized poincare inequality,the generalized Friedrichs inequality and the generalzed inequality of Poincare-Friedrichs are proved true for them.The error estimates are also given.It is shown that the quasi-conforming element method is convergent if the quasi-conforming element spaces have the approximability and the strong continuity,and satisfy the rank condition of element and pass test IPT.As practical examples,6-parameter,9-parameter,12-parameter,15-parameter,18-parameter and 21-parameter quasi-conforming elements are shown to be convergent,and tlieir.L^2,2(Ω)-errors are O(h_τ)、O(h_τ)、O(h_τ²)、O(h_τ²)、O(h_τ³)and O(h_τ⁴)respectively.

Axisymmetry Problems of Ring Shells under Arbitrary Distributed Loads

Chen Shan-lin

1986, 7(5): 425-434.

Abstract(2045) PDF(823)

Abstract:
Extending Novozhilov's transformation,this paper simplifies successfully the aaisymmetry problems of ring shells under arbitrary distributed loads,and the equation of the problems in complex form which is similar to Novozhilov's is obtained.The particular solution is given.Combining with Chien's general solution of homogeneous equation,this paper gives the general solution for the general symmetry problems of ring shells.Various examples of useful loads and closed ring shells are discussed respectively.

An Algorithm with Randomly Varying Truncation for Adaptive Beam-Formers

Zhu Yun-min

1986, 7(5): 435-442.

Abstract(1558) PDF(450)

Abstract:
A rewxrsive algorithm with randomly varying truncation for adaptive Bram-Formers is proposed.Simple conditions are obtained to guarantee for this algorithm the global convergence almost everywhere.

More Generalized Hybrid Variational Principle and Corresponding Finite Element Model

Chen Wan-ji

1986, 7(5): 443-449.

Abstract(1853) PDF(539)

Abstract:
According to recent studies of the generalized variational principle by Professor Chien Wei-zang,the mere generalized hybrid varialional principle for finite element method is given,from which a new kind of the generalized hybrid element model is established.Using the thin plate bending element with varying thickness as an eaample,we compare various hybrid elements based on different generalized variational principles.

The Effect of Temperature Gradient on the Correlation of Temperature Fluctuations

Ma Bai-kun

1986, 7(5): 451-456.

Abstract(1511) PDF(473)

Abstract:
In this paper we present the experintent results of the space corrclations of temperature fluctuations when there is and is not temperature gradient.From those results we can see clearly that the temperature fluctuation field is isotropic without temperature gradint,and it is obviously anisotropic with temperature gradient.The temperature correlation along the gradient direction β is obviously larger than the vertical to β direction. Our experiment results agree with the theory results of D. W. Dunn and W. H. Reid^[1].

A Uniformly Convergent Difference Scheme for the Singular Perturbation of a Self-adjoint Elliptic Partial Differential Equation

Liu Fa-wang, Zheng Xiao-su

1986, 7(5): 457-465.

Abstract(2019) PDF(517)

Abstract:
In this paper,we consider a self-adjoint elliptic first boundary value problem with a small parameter affecting the highest derivative.In the paper,we set up a new scheme by the asymptotic analysis method,compare asymptotic behavior between the solution of the difference equation and the solution of the differential equation,and show uniform convergence of the new scheme.

An Accurate Solution for the Surface of Elastic Layer under Normal Concentrated Load Acting on a Rigid Horizontal Base

Wen Pi-hua

1986, 7(5): 467-475.

Abstract(1718) PDF(597)

Abstract:
On the basis of referenced^[1],this paper deduces an accurate solution for the surface of elastic layer under normal concentrated load acting on a rigid horizontal base,and gives netmerieal results,which suit civil engineers for reference.

1986 Vol. 7, No. 5