关于“轴对称圆环壳的一般解”一文的讨论

关于1980年第3期《轴对称圆环壳的一般解》一文中齐次解的衰减指数λ,想指出一点:λ有无穷多个根,其一般形式是λ=±[(β+iγ)+mi),m=0,±1,±2……在文中(2.3)式里C_n有非零解的充分必要条件是其无穷阶的系数行列式Δ(λ)=0.     

The Calculation of Semi-circular Corrugated Tube——An Application of the General Solution of Ring Shell

In this paper, the deformation and stress distribution in semi-circular corrugated tube under axial force are calculated by means of the general solutions of circular ring shell given in previous paper[1].     

The symmetrical deformation of circular membrane under the action of uniformly distributed loads in its central portion

This paper presents the solution of symmetrical deformation of circular membrane under the action of uniformly distributed loads in its central portion. Its limiting case is the solution of circular membrane under concentrated load at the center. This solution is the third solution of the circular membrane problems after the well-known Hencky’s solution.     

The explicit forms of field functions in totrahedron element with 16 and 20 degrees of freedom

In this paper, the explicit forms of field functions in tetrehedron elements with 16 and 20 degrees of freedom are given in terms of volume coordinatesL ₁,L ₂,L ₃,L ₄ of tetrahedron.     

VARIATIONAL PRINCIPLES AND GENERALIZED VARIATIONAL PRINCIPLES IN HYDRODYNAMICS OF VISCOUS FLUIDS

In this paper, the variational principles of hgdrodynamic problems for the incompressibleand compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.     

INVOLUTORY TRANSFORMATIONS AND VARIATIONAL PRINCIPLES WITH MULTI-VAROABLES IN THIN PLATE BENDING PROBLEMS

In this paper. the generalized variational principles of plate bending problems areestablished from their minimum potential energy principle and minimum complementaryenergy principle through the elimination of their constraints by means of the method ofLagrange multipliers. The involutory transformations are also introduced in order toreduce the order of differentiations for the variables in the variation. Furthermore. theseinvolutory tansformations become in fact the addittional constraints in the variation. andadditional Lagrange multipliers may be used in order to remove these additionalconstraints. Thus. various multi-variable variational principles are obtained for the platebending problems. However, it is observed that. not all the constraints of variation can beremoved simply by the ordinary method of linear Lagrange multipliers. In such cases.themethod of high-order Lagrange multipliers are used to remove those constraints left over byordinary linear multiplier method.And consequently. some func     

A NEW ELEMENT FOR THIN PLATE OF BENDING WITH CURVILINEAR BOUNDARY—CURVILINEAR BOUNDARY QUADRILATERAL ELEMENT

This paper presents a curvilinear boundary quadrilateral element for the problem ofthin plate of bending with curvilinear boundary.A coordinate transformation of twodimensions is performed in the calculation of FEM.The introduction of an additionalstiffness matrix based on the generalized variational principles results in high accuracy andless computation time.The numerical results agree with the analytical solution very well.     

亦论广义变分原理与无条件变分原理——就本题答胡海昌先生

本文就胡海昌先生提出的:(1)变分原理的边界(约束)条件算不算约束;(2)关于广义变分原理的命名的争论,进行了详细的答复。     

SUMMATION OF TRIGONOMETRIC SERIES BY FOURIER TRANSFORMS

This paper gives the theorems concerning the summation of trigonometric series Withthe help of Fourier transforms.By means of the known results of Fourier transforms,manydifficult and complex problems of summation of trigonometric series can be solved.Thismethod is a comparatively unusual way to find the summation of trigonometric series.andhas been used to establish the comprehensive table of summation of trigonometric series.Inthis table.10 thousand series are given.and most of them are new.