Fu Bao-lian. Energy Theorems for Solving Equations of Deflections[J]. Applied Mathematics and Mechanics, 1981, 2(6): 697-707.
 Citation: Fu Bao-lian. Energy Theorems for Solving Equations of Deflections[J]. Applied Mathematics and Mechanics, 1981, 2(6): 697-707.

# Energy Theorems for Solving Equations of Deflections

• Publish Date: 1981-12-15
• In this paper the unit-dummy-load method is generalized on the basis of Castigliano's Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.
•  [1] Лейбензон,Л.С.,Варuачuонные меmобы Реuенuя Забач Теорuu Уnруосmu,Издателъство Академин наук СССР,Москва(1951).(中译本,叶开沅,卢文达.《弹性力学问题的变分解法》,科学出版社,1958). [2] 胡海昌,《变分法和结构设计——弹性力学的变分原理和它们的应用》(待出版). [3] Timoshenko,S.and Woinowsky-Krieger,Theory of Plate and Shells,second edition(1959). [4] Langhaar,Henry L.,Energy Methods in Applied Mechanics,(1969). [5] Timoshenko,S.,Strength of Materials,Part Ⅰ.

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