Matrix-Based Shape Sensitivity Analysis for Linear Strain Energy of Triangular Thin Shell Elements

This study presents an approach to analytical shape sensitivity analysis of linear strain energy in shell structures modeled using thin shell elements. By using the Kirchhoff-Love plate theory and extending conventional finite element methods, the strain energy variations in shell structures due to shape changes are rigorously analyzed in a discrete manner. Sensitivity formulations are sequentially derived by the chain rule, and the procedure to obtain the derivatives of mechanical and geometric properties related to strain energy is explained step by step, ensuring reproducibility and straightforward implementation. Numerical examples include verification of structural analysis results using a benchmark structure and measurement of efficiency and accuracy of our sensitivity analysis implementation compared to the finite difference method. The results with these examples demonstrate the superiority of explicitly computing gradients using the proposed approach, underscoring its potential to advance the optimal design and structural analysis of shell elements.