Abstract
A general method giving the perturbation due to the introduction of an inhomogeneity into any initial elastic field is discussed within the framework of plane linear elasticity. Then, the method is applied to obtain the full perturbative solution for the problem of an elliptic inhomogeneity in an infinite plane. Exact formulas for the special cases of void, rigid, and circular inhomogeneity are also worked out and discussed. The obtained results can noticeably simplify the analytic work needed to determine the elastic field in composite or cracked plates.
Riassunto
Nell'ambito della teoria dell'elasticità in mezzi piani e isotropi, si discute un metodo generale per ottenere la perturbazione dovuta all'introduzione di una disomogeneità in un qualsiasi campo elastico preesistente. Il metodo viene poi applicato al caso di una disomogeneità ellittica in un mezzo infinito. Inoltre, si ricavano e si discutono formule esatte che risolono i casi particolari di disomogeneità ellittica vuota oppure rigida, e di disomogeneità circolare. I risultati ottenuti possono semplificare notevolmente l'analisi delle deformazioni piane di lamine composite o con cricche interne.
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Stagni, L. On the elastic field perturbation by inhomogeneities in plane elasticity. Z. angew. Math. Phys. 33, 315–325 (1982). https://doi.org/10.1007/BF00944440
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DOI: https://doi.org/10.1007/BF00944440