On rigid and infinitesimal rigid displacements in three-dimensional elasticity
On rigid and infinitesimal rigid displacements in three-dimensional elasticity
复制标题
关于三维弹性中的刚性和无穷小刚性位移
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
Cristinel Mardare
中科院分区：
文献类型：
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作者：
P. G. Ciarlet;Cristinel Mardare
设Ω是ℝ3的开连通子集，Θ是从Ω到ℝ3的浸入.首先证明了由开集Θ(Ω的所有刚性位移构成的集合(即保持度量)是空间H1(Ω)的类的6维子流形.然后证明了由同一集合Θ(Ω的所有无穷小刚体位移构成的向量空间只是该子流形原点处的切线空间。这样，三维线性化弹性力学中常见的“无穷小刚体位移引理”得到了正确的表述。
Let Ω be an open connected subset of ℝ3 and let Θ be an immersion from Ω into ℝ3. It is first established that the set formed by all rigid displacements, i.e. that preserve the metric, of the open set Θ(Ω) is a submanifold of dimension 6 and of class of the space H1(Ω). It is then shown that the vector space formed by all the infinitesimal rigid displacements of the same set Θ(Ω) is nothing but the tangent space at the origin to this submanifold. In this fashion, the familiar "infinitesimal rigid displacement lemma" of three-dimensional linearized elasticity is put in its proper perspective.