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Variational principles for the equations of porous piezoelectric ceramics

机译：多孔压电陶瓷方程的变分原理

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摘要

The governing equations of a porous piezoelectric continuum are presented in variational form, though they were well established in differential form. Hamilton's principle is applied to the motions of a regular region of the continuum, and a three-field variational principle is obtained with some constraint conditions. By removing the constraint conditions that are usually undesirable in computation through an involutory transformation, a unified variational principle is presented for the region with a fixed internal surface of discontinuity. The unified principle leads, as its Euler-Lagrange equations, to all the governing equations of the region, including the jump conditions but excluding the initial conditions. Certain special cases and reciprocal variational principles are recorded, arid they are shown to recover some of the earlier ones.
机译：尽管已经很好地建立了微分形式，但多孔压电连续体的控制方程以变化形式表示。将汉密尔顿原理应用于连续体规则区域的运动，并在一定约束条件下获得了三场变分原理。通过不强制变换消除通常在计算中不希望出现的约束条件，为具有固定内表面不连续性的区域提供了统一的变分原理。统一的原理，作为其Euler-Lagrange方程，引向该区域的所有控制方程，包括跳跃条件，但不包括初始条件。记录了某些特殊情况和对等变分原理，并表明它们可以恢复一些早期的情况。

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