Abstract
In this paper the unit-dummy-load method is generalized on the basis of Castigliano's Theorem. On these grounds the general equations 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 equations 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.
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Langhaar, Henry L., Energy Methods in Applied Mechanics, (1969).
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Communicated by Chien Wei-zang.
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Bao-lian, F. Energy theorems for solving equations of deflections. Appl Math Mech 2, 765–777 (1981). https://doi.org/10.1007/BF01897647
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DOI: https://doi.org/10.1007/BF01897647