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A threedimensional transient piezothermoelastic solution is developed for a simplesupported combined plate.


Aiming at calculating the vibrating fundamental frequency of specialshaped, elastic simplesupported rectangleplates, in the inplane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region.


Mapping analysis of vibrating fundamental frequency for simplesupported elastic rectangleplates with concentrated mass


Conformal analysis of fundamental frequency of vibration of simplesupported elastic ellipseplates with concentrated substance




 Two methods for analyzing caissonbeams are introduced in this paper.One is the wellknown 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 caissonbeams are introduced in this paper.One is the wellknown 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。  The paper deals with a new approach of the limit analysts of conical shells subjected to internal uniform pressure. On the basis of carryingcapacity from membrane theory, a rational correction is made for the bending effect according to the nature ofactual supporting condition. If the characteristic number of shell is sufficiently small, very simple formulae are obtained for the carrying capacity in the case of unmovable simple support as well as in the case of fixed support. The comparison with experimental... The paper deals with a new approach of the limit analysts of conical shells subjected to internal uniform pressure. On the basis of carryingcapacity from membrane theory, a rational correction is made for the bending effect according to the nature ofactual supporting condition. If the characteristic number of shell is sufficiently small, very simple formulae are obtained for the carrying capacity in the case of unmovable simple support as well as in the case of fixed support. The comparison with experimental data gives satisfactory result. The formula of the carryingcapacity is:where pinternal pressure, ayield limit stress, hthickness of shell, aradius of shellbottom, rhalf of vertex angle, , a= 1.45 of 1.65 according to casesof unmovable simple support or clamped support on the bottom of shell respectively.  本文研究了锥壳在受均布内压作用时极限分析的一个途径.以薄膜理论的极限载荷为基础,考虑了锥壳的实际支承条件而进行了弯曲效应的修正.同时,利用薄壳的特征值作为小参数,得到了非常简单的理论近似公式 其中σ_T为材料屈服极限,h为壳厚,α为底周半径,r为半锥角;α=1.45或1.65,分别相当于底周支承情况为不可移简支或为嵌固的情况.同实验资料进行比较,理论结果同实验数据符合情况良好.  This paper deals with the calculation or deflections and internal forces of shallow spherical shells under external uniform pressure by means of finite element method. Comparing with the well known approximate formula that of the boundary effect superposing to membrance solution, the cause producing a considerable error in the formula had been fond for an example of shallow spherical shell clamped on square bottom, Consequently, a modified fornmla has been proposed by producting a sum of infinite geometric progression.... This paper deals with the calculation or deflections and internal forces of shallow spherical shells under external uniform pressure by means of finite element method. Comparing with the well known approximate formula that of the boundary effect superposing to membrance solution, the cause producing a considerable error in the formula had been fond for an example of shallow spherical shell clamped on square bottom, Consequently, a modified fornmla has been proposed by producting a sum of infinite geometric progression. Results obtained in this paper for the above example are identical to that obtained by finite difference method. Additionally, for the singularity at corners or shallow spherical shells simple supported on hexagonal bottom, successive and automatic computation in fine mesh has been made using a transformation of similitude.  本文用有限元法对地下球扁壳的挠变与内力进行了分析与计算。文中以一 个四边固定的方底球扁壳为例，和通常的简单边界效应叠加无矩解的近似公式 作了比较，指出这个公式产生较大误差的原因；由此本文提出了乘以一个无穷 等比级数之和的修正公式。对于这个例子，本文结果与用差分法［３］所得结果完 全吻合。本文还采用相似变换，对正六角形底、周边简支球扁壳的奇异性角区 进行了逐次自动加密计算。   << 更多相关文摘 
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