孔边应力单元与层合板孔边应力精化分析方法研究

 构造了一个满足孔边应力边界条件、层间应力连续条件以及层合板表面应力边界条件的孔边应力单元。并在位移型有限元计算所得位移基础上,提出了一个精确分析孔边应力的有限元方法。首先,运用莫雷阿(G.Morera)应力函数理沦,构造了柱坐标中满足平衡条件的三维应力场的一般表达式,并使之满足前述应力条件。然后,采用上述表达式并利用修正余能原理与拉格朗日乘子法,建立了由已知节点位移分析层合板孔边应力的基本方程。算例表明,所得计算结果与相应解析解或实验结果相符。

A NEW STRESS ELEMENT AND ITS APPLICATION TO THE RE-FINED STRESS CALCULATION NEAR A HOLE

A new stress element near a hole which satisfies both the stress boundary conditions at the hole and at the surface of the laminate and stress continuity condition at the interface is developed. The stress field near the hole can be analyzed exactly on the basis of the displacement field obtained by FEM using the stress element.The new stress element is formulated as follows. The three dimensional stress field satisfying equilibrium equations in cylindrical coordinates and the above-mentioned stress conditions is expressed in G.Morera stress functions. Applying the complementary energy principle and the method of Lagrangian multipliers,the fundamental parameters of the stress element can be found. Some examples of calculation using this stress element show that the results are consistent with the analytical solutions and the experimental results.