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In linear elasticity, the equations describing the deformation of an elastic body subject only to surface forces on the boundary are (using index notation) the equilibrium equation: : where is the stress tensor, and the Beltrami-Michell compatibility equations: : A general solution of these equations may be expressed in terms the Beltrami stress tensor. Stress functions are derived as special cases of this Beltrami stress tensor which, although less general, sometimes will yield a more tractable method of solution for the elastic equations. == Beltrami stress functions == It can be shown that a complete solution to the equilibrium equations may be written as : Using index notation: : : + \frac -2\frac | | |- | | | |- | | | |} where is an arbitrary second-rank tensor field that is continuously differentiable at least four times, and is known as the ''Beltrami stress tensor''.〔 Its components are known as Beltrami stress functions. is the Levi-Civita pseudotensor, with all values equal to zero except those in which the indices are not repeated. For a set of non-repeating indices the component value will be +1 for even permutations of the indices, and -1 for odd permutations. And is the Nabla operator 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Stress functions」の詳細全文を読む スポンサード リンク
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