Improved sensitivity analysis using a complex variable semi-analytical method

The semi-analytical method (SAM) is a computationally efficient and easy to implement approach often used for the sensitivity analysis of finite element models. However, it is known to exhibit serious inaccuracy for shape sensitivity analysis for structures modeled by beam, frame, plate, or shell elements. In the present paper, we use a semi-analytical approach based on complex variables (SACVM) to compute the sensitivity of finite element models composed of beam and plate elements. The SACVM combines the complex variable method (CVM) with the semi-analytical method (SAM) to obtain the response sensitivity accurately and efficiently. The current approach maintains the computational efficiency of the semi-analytical method but with higher accuracy. In addition, the current approach is insensitive to the choice of step size, a feature that simplifies its use in practical problems. The method is applicable to any structural elements including beam, frame, plate, or shell elements and only requires minor modifications to existing finite element codes.