Sensitivity Analysis and Reanalysis of Elastoplastic Plane Stress Problems〔付討論〕

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This paper describes a procedure for shape design sensitivity analysis of elastoplastic structural response in plane stress field using the incremental solution scheme, which is briefed as follows ; (1) State equation in the incremental form is differentiated with respect to design variables. The co-ordinates of nodal points and the thicknesses of elements are considered as the design variables. (2) The increments of sensitivities of nodal displacements with respect to the design variables are derived at every load step. The sensitivities of nodal displacements are evaluated as the sum of their increments. (3) In the differentiation of stiffness matrix and stress components, the differentiation of the stress-strain matrix has to be considered for the plastic element. The method of reanalysis is also shown based on the Taylor Series Expansion Method. Based on a few sample calcuations, it has been found that ; (1) For the sensitivities of the first and the second-order, satisfactory results are obtained for simple calculation models. (2) The results of reanalysis are different from the exact solutions when large changes are imposed on the values of desigu variables. (3) The CPU time to calculate first-order sensitivity is less than 10 % of that for ordinary stress analysis. On the contrary, the CPU time for second-order sensitivity rapidly increases with increase in the number of design variables.
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