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- W1619300835 abstract "This chapter investigates the method of potentials to generate solutions to elasticity problems. Several different potential techniques have been developed in order to solve problems within both displacement and stress formulations. Methods related to the displacement formulation include the scalar and vector potentials from the Helmholtz decomposition, Galerkin vector, and Papkovich–Neuber functions. These schemes provide general solution forms for Navier's equations. Potentials used in the stress formulation are those related to the Maxwell and Morera stress functions, and these lead to Airy and other common stress functions that have already been used for the solution of particular elasticity problems. These stress functions normally satisfy the equilibrium equations identically and when combined with the compatibility relations they yield a simpler and more tractable system of equations. For either displacement or stress formulations, these solution schemes bring up the question: are all solutions of elasticity expressible by the particular potential representation? This issue is normally referred to as the completeness of the representations. For many cases these approaches are useful to solve particular three-dimensional elasticity problems, and we will investigate several such solutions. Some potential methods are also particularly useful in formulating and solving dynamic elasticity problems involving wave propagation." @default.
- W1619300835 created "2016-06-24" @default.
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- W1619300835 date "2009-01-01" @default.
- W1619300835 modified "2023-09-27" @default.
- W1619300835 title "Displacement Potentials and Stress Functions" @default.
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- W1619300835 doi "https://doi.org/10.1016/b978-0-12-374446-3.50017-0" @default.
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