The full-scale bounds estimation for 2-D bi-modular problem with interval uncertain constitutive parameters is realized by means of sensitivity analysis. An efficient FE model is presented to solve the deterministic 2-D bi-modular problem by complementing a shear modulus identical with the coaxial condition required by the constitutive relationship, and the equations to calculate both the first- and second-order derivatives of displacements with respect to constitutive parameters are derived. When the interval scale of uncertain constitutive parameters is relatively small, two algorithms are developed for the bounds estimation by using the first-/second-order Taylor series approximation and interval arithmetic; when the interval scale is large, a rigorous bounds estimation can be achieved by using the first-order derivatives and a global searching technique. In addition, two second-order Taylor series approximation-based algorithms are proposed to reduce the computational expense in the process of optimization for bounds estimation. With the consideration of expansion order of Taylor series, interval scale of uncertainty, ratio of \(E^-/E^+\), etc., numerical examples are presented to illustrate the accuracy and efficiency of the proposed approach.

通过灵敏度分析实现了具有区间不确定本构参数的二维双模量问题的满量程边界估计。提出了一种有效的有限元模型，通过补充与本构关系所需的同轴条件相同的剪切模量来解决确定性的二维双模问题，并利用方程式计算了位移的一阶和二阶导数。关于本构参数的推导。当不确定性本构参数的区间尺度较小时，采用一阶/二阶泰勒级数逼近和区间算法开发了两种边界估计算法。当间隔比例大时 通过使用一阶导数和全局搜索技术，可以实现严格的边界估计。另外，提出了两种基于二阶泰勒级数逼近的算法，以减少边界估计优化过程中的计算量。考虑泰勒级数的展开阶，不确定性的区间标度，\（E ^-/ E ^ + \）等，通过数值示例来说明所提出方法的准确性和效率。