曲線座標系における応力関数

概要

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In this note we intended to obtain three types of stress functions for the equation of elasto-statics, which was described in general curvilinear coordinate system. Let Ω be an open subset of R^n(n⪈2), f_j (j=1, …, n) a body force, which is sufficiently smooth. It is well known that the covariant displacements uj satisfy the following equation in Ω: [numerical formula] where g^<ks> stands for the contravariant metric tensor, m and G the elastic constants and we denote by (・)|_k the covariant derivative with respect to the k-th variable. Then we get the following three representations for the solution of eq.(^*): (a) [numerical formula] (b) [numerical formula] (c) [numerical formula] where u^i means the contravariant solution of eq.(^*) and ∈^<αβi> stands for the e-system. In the cartesian coordinates, the formulas (a), (b), (c) above coincide with Galerkin, Neuber-Papkovich and Boussinesq's formula, respectively.
明治大学の論文