The semi-analytical method (SAM) has been reported serious accuracies in sensitivity analysis of structural elements such as frame, beam, plate elements because the finite difference method (FDM) used in the SAM is sensitive to the step size. The proposed semi-analytical complex variable method (SACVM) adopts the complex variable method (CVM) to avoid the accuracy problem and maintain the computational efficiency of the SAM. Various methods have been developed to improve the accuracy of the SAM in linear structural problems. However, a few methods address this accuracy problem for nonlinear cases. The paper applies the SACVM to a geometrical nonlinear Euler-Bernoulli beam to obtain the accurate sensitivity of finite element response. As an example application, the SACVM sensitivities are used to compute the reliability index of a defined limit state function for the nonlinear beam. The results reveal that the SACVM can always compute response sensitivity and system reliability consistently, accurately and efficiently. The method is also computationally efficient as it employs a semi-analytical approach. The SACVM is easily applicable and only requires minor modifications to existing finite element codes, therefore it has great application in practical problems.

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