Response sensitivity analysis for plastic plane problems based on direct differentiation method

Response sensitivity analysis is of significant value to solve various inverse problems in engineering practice using gradient-based optimization algorithms. In the context of finite element (FE) method, an efficient, accurate and general sensitivity analysis approach, namely the direct differentiation method (DDM), has been developed and extended to various element and material models. However, the DDM has not been addressed for the response sensitivity of plastic plane problems (i.e., plane stress and plane strain problems), in spite of their wide applications in practice. This paper bridges this gap by extending the DDM based response sensitivity algorithm to general plastic plane problems, which is solved by taking advantage of general three dimensional (3D) constitutive models. The newly developed DDM-based sensitivity analysis algorithm is implemented in the open source finite element framework (OpenSees) and verified using two realistic application examples of plane problems, i.e., a concrete dam and a steel shear wall. The efficiency and accuracy of the DDM are verified by using the forward finite difference method.