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Inhomogeneous elastostatic problem solutions constructed from stress-associated homogeneous solutions |
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| Authors: | M. Fraldi |
| Affiliation: | a Dipartimento di Scienza delle Costruzioni, Facoltà di Ingegneria, Universitá di Napoli “Federico II”, Italy b The New York Center for Biomedical Engineering, New York, USA c Departments of Biomedical and Mechanical Engineering, School of Engineering of the City College, New York, USA d Graduate School of the City University, New York, USA |
| Abstract: | In this paper, we present a theorem that provides solutions for anisotropic and inhomogeneous elastostatic problems by using the known solution of an associated anisotropic and homogeneous problem if the associated problem has a stress state with a zero eigenvalue everywhere in the domain of the problem. The fundamental property on which this stress-associated solution (SAS) theorem is built is the coaxiality of the eigenvector associated with the zero stress eigenvalue in the homogeneous problem and the gradient of the scalar function ? characterizing the inhomogeneous character of the inhomogeneous problem. It is shown that most of the solutions of anisotropic elastic problems presented in the literature have this property and, therefore, it is possible to use the SAS theorem to construct new exact solutions for inhomogeneous problems, as well as to find—using the SAS theorem—solutions for the shape intrinsic and angularly inhomogeneous problems. |
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