A Solving Method for a System of Partial Differential Equations With an Application to the Bending Problem of a Thick Plate
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摘要: 提出并证明了一类非齐次线性微分方程组的积分解法,并以求解受激光和横向力联合加载厚板的轴对称弯曲问题作为该方法的应用实例,籍此给出了考虑挤压效应、旋转惯性效应和剪切变形效应时厚板动态弯曲的扰度和转角公式。结果表明运用该定理求解问题具有规范、简明的特点。Abstract: A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved,the mathematical role and physical nature of the theorem is interpreted briefly. As an example,the theorem is applied to solve the problem of thermo-force bending of a thick plate.
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Key words:
- partial differential equations /
- integrating method /
- thick plate /
- thermo-force bending
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[1] 尹益辉,陈裕泽.一类微分方程组的解法及其在圆板热弯曲问题求解中的应用[J].重庆大学学报(自然科学版),1995,18(3):91~96. [2] 尹益辉,陈裕泽.轴对称热载作用厚板的热弹性运动效应分析[J].爆炸与冲击,1994,14(2):119~128. [3] 四川大学数学系编.高等数学(第四册)[M].北京:人民教育出版社,1981,229~278. [4] Couront R,Hillbert D.Methods of Mathematical Physics[M].New York:Interscience Pub,1962,767.
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