耦合热弹性平面问题的有限元法基本方程

本文在耦合热弹性问题变分原理的基础上,导出非定常温度场热弹性平面问题的有限元法基本方程.推导中,弹性平面划分为三节点三角形单元,时间过程划分为时间元,时间元中各变量(节点的位移和温度)随时间作线性变化.得出以各节点在每个瞬时(时间元的端点)的位移和温度为待定值的两组耦合的线性代数方程组,即基本方程.

The Fundamental Equations in Finite-Element Method of Coupled Thermo-elastic Plane Problem

The fundamental equations in finite element method for unsteady temperature field elastic plane proble m are derived on the bases of variational principle of coupled thermoelastic problems,In these derivations,elastic plane is divided into three nodes triangular elements,and time interval is divided into linear time elements,in which all the variables,including displacements and temperatures at various nodal points,are varied linearly with time,Two coupled sets of linear algebraic equations of all the unknown displacements and temperatures at every nodal point in every instant(i,e,the terminal values of time elements) are obtained.They are the fundamental equations of the said problem.