Numerical solution of 2D elastostatic problems formulated by potential functions |
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Authors: | JL Morales JA Moreno F Alhama |
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Institution: | 1. Department of Structures and Construction, Universidad Politécnica de Cartagena (UPCT), Campus Muralla del Mar, ETSII, 30202 Cartagena, Spain;2. Department of Mechanical Engineering, Universidad Politécnica de Cartagena (UPCT), Campus Muralla del Mar, ETSII, 30202 Cartagena, Spain;3. Department of Applied Physics, Universidad Politécnica de Cartagena (UPCT), Campus Muralla del Mar, ETSII, 30202 Cartagena, Spain |
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Abstract: | 2D linear elastostatic problems formulated in Cartesian coordinates by potential functions are numerically solved by network simulation method which allows an easy implementation of the complex boundary conditions inherent to this type of formulation. Four potential solutions are studied as governing equations: the general Papkovich–Neuber formulation, which is defined by a scalar potential plus a vector potential of two components, and the three simplified derived formulations obtained by deleting one of the three original functions (the scalar or one of the vector components). Application of this method to a rectangular plate subjected to mixed boundary conditions is presented. To prove the reliability and accurate of the proposed numerical method, as well as to demonstrate the suitability of the different potential formulations, numerical solutions are compared with those coming from the classical Navier formulation. |
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Keywords: | Papkovich&ndash Neuber representation Potential displacements Linear elasticity Network simulation method |
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