Shape sensitivity analysis of finite element models is useful for structural optimization and design modifications. Within numerical design optimization, semi-analytical method for sensitivity analysis is frequently applied to estimate the derivative of an objective function with respect to the design variables. Generally numerical sensitivity analysis widely suffers from severe error due to the perturbation size and find a method which is not sensitive to the perturbation size is topics under study. Complex variable methods for sensitivity analysis have some potential advantages over other methods. For first order sensitivities using the complex variable method, the implementation is straightforward, only requiring a perturbation of the finite element mesh along the imaginary axis. This paper uses a complex variable and combine it with discrete sensitivity analysis, thus present new method to obtain derivatives for linear structure. The advantage of this method are quickly, accuracy and its simple implementation. The methodologies are demonstrated using two dimensional finite element models of linear elasticity problems with known analytical solutions. Obtained sensitivity derivatives are compared to the exact solution and also finite difference solutions and show that the proposed method is effective and can predict the stable and accurate sensitivity results.

Keywords: Discrete sensitivity method (DSM), complex variable method (CVM), semi-analytical method, Finite Element Method (FEM)

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