Calculation of Design Shape Sensitivity in Solid Mechanics Through a Novel Hybrid Method Using CVM and DSM

In this study, a novel hybrid method was presented by considering the strengths and weaknesses of the two methods of the direct sensitivity method (DSM) and the complex variables method (CVM) and combining them to calculate shape sensitivity. The most of methods available are highly dependent on the values of step size variation related to the type of the problem. To validate the proposed method, some examples were analyzed by using the written finite element code. The comparison of results at solved problems indicated the independency of the proposed method from step size and only need to select an arbitrary small step size and the rounding error is negligible. It is a sign of its high computational performance which converges to reliable, stable, and high-precision results and saves calculation time compared to the other methods. The other advantages of the proposed method are the low volume of occupied memory and simplicity of implementation and its application in a wide range of engineering problems having simple and complicated equations.