To perform inverse analysis of structures in plastic behavior, well established analysis scheme, calculation of sensitivity of response variables with regard to design variables, and an algorithm for optimization of object function with regard to design variables are required. In this paper, rate constitutive equation of plastic problem is integrated by generalized mid-point rule and governing equation in variational form is linearized with consistent tangent moduli which is linearized form of integrated constitutive equation. The iterative solution scheme with consistent tangent moduli preserves the asymptonic quadratic convergence characteristic of Newton's method. Object function is defined in the form of square of difference between measured response variables and analyzed response variables. Optimization of object function with regard to design variables is nonlinear optimization problem with constraints. RQP(Recursive Quadratic Programming), an optimization algorithm which can be directly applied to optimization problem with equality and inequality constraint, is used in this paper. To optimize object function with regard to design variables by RQP, first and second order sensitivity of response variables with regard to design variables is required. First order sensitivity can be calculated by direct differentiation of consistent tangent moduli. Since it is impossible to derive exact second order sensitivity of response variables in plasticity problem, Gauss-Newton method which approximate hessian of object function with only first order sensitivity of response variables is used. To validate the proposed inverse analysis scheme, three case studies are performed in this paper. In this paper, single-step inverse analysis using final excavation step data as input data as well as multi-step inverse analysis using all the excavation step data as input data is developed, and each result from them is compared.
consistent tangent moduli, direct differentiation, object function, first order sensitivity, second order sensitivity, RQP(Recursive Quadratic Programming), Gauss-Newton method |