四边简支压电热弹性体层合开口壳的精确解

根据压电热弹性体的本构关系和热传导关系的相似性,通过增维方式将热传导关系写进压电热弹性体的本构关系中,直接得到了一个新的增维的压电热弹性体本构关系。依据此增维的本构关系,结合压电热弹性体平衡方程和热平衡方程,成功地导出了压电热弹性体层合开口壳机、电、热耦合问题的齐次状态方程。这类方法大大简化了人们在分析压电热弹性体耦合问题时通常要求解的非齐次微分方程和关于温度的平衡方程和导热方程的二阶微分方程的繁琐方法,同时,齐次状态方程的提出大大减少了数值计算的工作量。

Exact Solution for Laminated Piezothermoelastic Open Cylindrical Shells with Four Simply Supported Edges

Based on the comparability of piezoelectric thermoelasticity and the heat exchange equations,a new augment dimensions constitutive relationship is established by combining the heat exchange equations into the constitutive equations of piezoelectric thermoelasticity.The homogeneous state control equations with mechanic electric heat coupling effect of piezoelectric thermoelastic open shell is derived by uniting the static equilibrium equations,the charge displacement equilibrium equations and thermal flow equilibrium equations.The treatments simplifies greatly the solution programs which are often performed to solving non-homogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship and the workload of numerical computation at same time.