计及表面能的应变梯度理论本构参数识别

Constitutive Parameters Identification of Gradient Elasticity Theory with Surface Energy

本文提出利用静态位移信息对一种计及表面能的应变梯度理论本构参数进行识别的求解策略。基于Vardoulakis和Sulem的计及表面能的简单线性应变梯度理论,文献[13]给出了伯努力-欧拉梁弯曲问题的正演解析模型,本文将其反演归结为两个带有不等式约束的非线性规划问题。在此基础上,采用黄金分割一维搜索方法进行求解,给出了数值验证,讨论了信息误差对反演结果的影响。结果显示,这种方法可以用来对应变梯度理论本构参数进行识别,即使在体积和表面能常数非常小的情况下,仍然能够得到满意的结果。

A solution strategy was presented for the constitutive parameters identification of gradient elasticity theory with surface energy via static displacement. Based on the simple gradient elasticity theory with surface energy due to Vardoulakis and Sulem, Chen et al. the analytical solution of direct bending problem of Bernoulli-Euler beams was given. The inverse problem was converted into two problems of nolinear programming with a constrain of inequality. A technique of golden section search was used in optimal solution. Numerical results were presented and the effects of noise data on the results were discussed. The numerical results show that the present method can be used to the constitutive parameters identification of gradient elasticity theory with surface energy. The considerably satisfying results can be obtained, even if the material lengths related to surface and volumetric elastic strain energy is very small.