变分原理在有限变形压电热弹性体中的应用

Application of Variational Principles in the Field of Thermo-piezoelectric Elastomers with Finite Deformation

  • 摘要: 为了对有限变形压电热弹性动力学基本方程进行有限元数值计算,首先建立相关的分区变分原理和广义分区变分原理.在考虑到有限变形弹性体的热力学效应和压电效应后,将弹性体动力学分区变分原理推广到有限变形压电热弹性体,建立了3类变量的有限变形压电热弹性动力学分区变分原理.在有限变形压电热弹性动力学分区变分原理中进一步引入拉格朗日乘子并加以识别的方法,得到了6类变量的有限变形压电热弹性动力学分区广义变分原理.

     

    Abstract: To apply finite element methods in the numerical calculation of basic equations of finite deformation thermopiezoelectric elastodynamics, it is first necessary that relevant regionwise variational principles and regionwise generalized variational principles are set up. Taking thermodynamic and piezoelectric domino effects in elastomers into account, elastic regionwise variational principles are extended into the field of finite deformation piezoelectric thermoelastomers to establish three-field finite deformation thermopiezoelectric elastodynamic regionwise variational principles, on introducing Lagrangian multipliers and distinguishing them in the finite deformation thermopiezoelectric elastodynamic regionwise variational principles, six-field finite deformation thermopiezoelectric elastodynamic regionwise generalized variational principles are finally obtained.

     

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