初应力位形上附加变形线性理论的局限性及二次理论

初应力位形上附加变形线性理论的发展和应用受到附加变形微小性和零应力本构方程属超弹性固体的限制。尝试突破这种限制而建立一般理论。为此从连续介质力学理论出发,首先应用增量Lagrange 应力描写初应力位形上附加变形的控制方程和边界条件,然后利用量级分析的方法给出线性理论的适用范围和一个实用的改进方案棗二次理论,最后给出计算例对比二者的差异。结果表明二次理论成功的突破了线性理论的局限性而具有更大的适用范围和更高的精确性。

THE LIMITATIONS OF LINAER THEORY AND IMPROVED QUADRATIC THEORY FOR SUPERPOSING ADDITIONAL DEFORMATION UPON THE CONFIGURATION WITH INITIAL STRESSES

The linear theory of superposing additional deformation upon the configuration with initial stresses must satisfy two preconditions-the infinitesimal of the additional deformation and the hyperelasticity of the material. This paper attempts to eliminate the two preconditions and provides a more general theory. To this end, the paper starts from the continuum mechanics. The controlling equations and boundary conditions are described with the increment Lagragian stresses. The applicability of the linear theory and an improvement of the linear theory—the development of a quadratic theory by use of the order-of-magnitude analysis are examined. An example is given to compare the quadratic theory and the linear theory. Computational results of the example clearly show that the quadratic theory is applicable under few limits and can lead to a more rational solution.