2ND-ORDER SHAPE DESIGN SENSITIVITY USING P-VERSION FINITE-ELEMENT ANALYSIS

The p-version finite element analysis (FEA) approach is attractive for design sensitivity analysis (DSA) and optimization due to its high ac curacy of analysis results, even with coarse mesh; insensitivity to fi nite element mesh distortion and aspect ratio; and tolerance for large shape design changes during design iterations. A continuum second-ord er shape DSA formulation is derived and implemented using p-version FE A. The second-order shape design sensitivity can be used for reliabili ty based analysis and design optimization by incorporating it with the second-order reliability analysis method (SORM). Both the second-orde r shape DSA formulations with respect to the single and mixed shape de sign parameters are derived for elastic solids using the material deri vative concept. Both the direct differentiation and hybrid methods are presented in this paper. A shape DSA is implemented by using an estab lished p-version FEA code, STRESS CHECK. Two numerical examples, a con necting rod and bracket, are presented to demonstrate the feasibility and accuracy of the proposed seond-order shape DSA approach.