两级敏度分析求解双弹性模量桁架结构反问题

利用光滑函数和有限元技术，建立了求解双弹性模量桁架结构正问题的数值模型，可方便推导刚度对位移、位移对弹性模量的敏度计算公式。在此基础上，提出了基于两级敏度分析求解双弹性模量桁架结构反问题的数值模型，正问题与反问题分别采用Newton-Raphson与Gauss-Newton算法进行求解，数值验证给出了令人满意的结果，并考虑了数据噪音的影响。

SOLVING INVERSE BIMODULAR PROBLEMS OF TRUSS STRUCTURES VIA TWO-LEVEL SENSITIVITY ANALYSIS

A new smooth elastic bimodular constitutive relationship is presented,therefore the sensitivity of stiffness matrix with respect to displacement and the sensitivity of displacement with respect to elastic modulus can be obtained conveniently.A FEM and sensitivity analysis based numerical model is developed to solve direct problems of truss structures with dual extensional/compressive modulus,and Newton-Raphson algorithm is employed in the solution process.By utilizing the solutions of direct problems,a two level sensitivity analysis based algorithm is presented for the identification of bimodulus,Gauss-Newton algorithm is used in the identification.Numerical verification with noisy data is provided with satisfactory results.