论文标题
非线性磁弹性固醇的变分原理及其对应关系
Variational principles of nonlinear magnetoelastostatics and their correspondences
论文作者
论文摘要
我们使用涉及机械变形和代表磁成分的独立场的几种变分配方来得出非线性磁弹性固化器的方程。还讨论了等效性，使用Legendre Transform和Maxwell方程的属性之间的某些边界积分或恒定积分。对于所有五个变异原理，也为增量场陈述了第二个基于变异的分叉方程。当在身体周围的无限空间上定义总势能时，我们发现在能量原理中包含某些项，与外部施加的磁场相关，会导致麦克斯韦应力张量和相关边界条件的略有变化。另一方面，当磁场中包含的能量仅限于有限体积时，我们发现讨论的配方与物理实体的相关表达之间存在对应关系。鉴于文献中研究的问题中的一组边界数据和外部应用控制的性质，以及在建模中采用的各种变异原理的多样化列表，我们的分析强调了各种原理和未知领域的选择，因此也满足了与其他选择的一致性。
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo certain boundary integrals or constant integrals, between these formulations using the Legendre transform and properties of Maxwell's equations. The second variation based bifurcation equations are stated for the incremental fields as well for all five variational principles. When the total potential energy is defined over the infinite space surrounding the body, we find that the inclusion of certain term in the energy principle, associated with the externally applied magnetic field, leads to slight changes in the Maxwell stress tensor and associated boundary conditions. On the other hand, when the energy contained in the magnetic field is restricted to finite volumes, we find that there is a correspondence between the discussed formulations and associated expressions of physical entities. In view of a diverse set of boundary data and nature of externally applied controls in the problems studied in the literature, along with a equally diverse list of variational principles employed in modeling, our analysis emphasizes care in the choice of variational principle and unknown fields so that consistency with other choices is also satisfied.
