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  equation
    The Generalized Equation of Consolidation Theory and Its Application
    固结问题的普遍方程及其应用
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    ANALYSIS OF ELASTIC FOUNDATION BEAM BY STRESS-AREA METHOD AND DEFLECTION EQUATION OF INITIAL PARAMETERS
    用应力面积和初参数挠度方程分析弹性地基梁
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    A Boundary Integral Method for the Elastic and Elastopiastic Bending Analysis of Thin Plates of Arbitrary Plan Form, and Boundary Conditions
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For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation.
      
The Yang-Baxter equation admits two classes of elliptic solutions, the vertex type and the face type.
      
The inverse conductivity problem to the the elliptic equation ${\rm div}((1+(k-1)\chi_D)\nabla u)=0\ {\rm in }\ \Omega$ is considered.
      
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Pointwise fourier inversion: A wave equation approach
      
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Professor Zhmochken chooses cantilever beam as a basic structure for beams on elastic foundations. In his opinion, it is inconvenient to use a simple beam as a basic structure. The calculation of deflection constants is thus involved, and one kind of beam can not be used to represent all kinds of beams on elastic foundations.In this paper the writer tries to use a simple beam with two cantilevers as a basic structure. On the one hand by changing the panel number of cantilevers, one kind of beam may be used to...

Professor Zhmochken chooses cantilever beam as a basic structure for beams on elastic foundations. In his opinion, it is inconvenient to use a simple beam as a basic structure. The calculation of deflection constants is thus involved, and one kind of beam can not be used to represent all kinds of beams on elastic foundations.In this paper the writer tries to use a simple beam with two cantilevers as a basic structure. On the one hand by changing the panel number of cantilevers, one kind of beam may be used to represent all kinds of beams on elastic foundations. On the other hand, the deflection constants computed by the writer are given in the appendix, so the designer may use these constants as easily as he uses Professor Zhmochken's constants. With such a modification the number of normal equations is reduced by two to four.Besides, a method of solving normal equations by utilizing the property of reactive pressures between beams and foundations is suggested. All the normal equations may be solved combinedly by the method of eliminations and successive approximations. Two cycles are usually sufficient for the ordinary purpose.

本文系对苏联学者石氏关於彈性地基梁之理論作了适当的补充。石氏选悬臂梁作为彈性地基梁之輔助結構,本文則选二端附有悬臂之簡支梁。如是,寻求梁与地基之間的反力时,共用於建立法方程的工作,大致与石氏同,而用於求解該項方程的时間,則可大为縮短。

A tabulation method for solving n simultaneous linear equations is given. For the general type, it requires(1/3)n(n-1)(n-2)+(5/2)n(n-1)+n multiplications or divisions. For n three-moment equations, it requires only 6n-5 multiplications or divisions.A slide rule can be used with advantage for working out this tabulation and the small error thus introduced can be corrected, if necessary, by a second tabulation using the coefficients computed in the first.

本文是給出n个联立一次方程准确解的一种列表計算法,对於一般的联立一次方程,本法只要做1/3n(n-1)(n-2)+5/2n(n-1)+n次乘法攻除法,其积或商完全登記在表上,所以便於檢查。应用於解n个三撓矩方程,本法只要做6n-5次乘法或除法。 計算时可用算尺,用算尺計算所产生的小誤差在必要时可用計算校正差表格校正之,这种表格是利用表内已算出的系数作成的。

Two methods for analyzing caisson-beams are introduced in this paper.One is the well-known method of redundant forces. The author has simplified this methed by using couples of redundant forces to set up a typical equation and pointing out the rule that the matrix of the coefficients of simultaneous linear equations which are organized from the expansion of that typical equation. This method can be easily solvd when the number of unknown redundant forces, or that of equations, is less than 3 or 4; but it will...

Two methods for analyzing caisson-beams are introduced in this paper.One is the well-known method of redundant forces. The author has simplified this methed by using couples of redundant forces to set up a typical equation and pointing out the rule that the matrix of the coefficients of simultaneous linear equations which are organized from the expansion of that typical equation. This method can be easily solvd when the number of unknown redundant forces, or that of equations, is less than 3 or 4; but it will be difficult when the number is more than that. In order to solve this difficulty the author suggests another kind of method of which the essential principle is mentioned in the following.Supposing that the distance between the beams is sufficiently short in comparing with their spans, we can set up a partial differential equation for its deffiection W, as we often do in the theory of elasticity. In this way we can solve it with its boundary conditions of simple supporting by sine series. From this we can easily get the formulas of bending moments, shears and twist moments of each beam by partially differentiating the function of deffiection. The result of the calculation proves that it quite agrees with the method of redundant forces when the distance between beams is no longer than 1/5 of their spans.There are some tables given in this raper for practical use.

本文介紹了計算井字梁的兩种方法。 第一种方法是按冗力送来計算的。本文利用了成对的未知力以建立冗力法的典型方程,指明了由典型方程所組成的联立方程中其系数排列的規律,从而簡化了建立方程的过程和減少錯誤的机会。冗力法仅在联立方程的数目不多于3至4时是相当方便的,若未知冗力过多,解算过程便異常繁重。为此,笔者提出了下述的第二种方法。 当梁的間距比梁的跨度为一較小的数值时,可应用彈性力学所常用的方法,建立一个关于井字梁撓度曲面的偏微分方程。以符合簡支边界条件的正弦级数求出撓度后,便可依微分关系求出各梁的弯矩、切力及扭矩。鈇摩辛柯在其著作中(見[3]§37)討論向異性板的弯曲时,亦曾附帶地提及本法的可能性。本文給出了全部計算公式及为实用的目的而制訂了各种数表。計算的結果表明当梁間距不大于跨度的1/5时,本法与冗力法的結果相差無几,而本法在应用上的簡便笑为任何方法所不及。

 
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