Shape design sensitivity and optimization using P-version design modeling and finite element analysis

A methodology that supports shape design modeling, structural shape design sensitivity analysis (DSA), and optimization of elastic solids, using p-version finite element analysis (FEA), is developed. The p-version FEA approach is attractive for shape design optimization, due to its high accuracy of analysis results, even with coarse mesh; ease of creation of design and finite element models; consistency between design and finite element models; insensitivity to finite element mesh distortion and aspect ratio; and tolerance for large shape changes during design optimization iterations. A continuum-based DSA method that is applicable to both planar and spatial structures is developed with an established p-version FEA code, STRESS CHECK. A shape design parameterization method that uses the geometric entities of STRESS CHECK is proposed and implemented. In STRESS CHECK, the shape design model is identical to the finite element model, so finite element modeling errors are eliminated. Design optimization is carried out by integrating the shape design parameterization, design velocity field computation; first-order shape design sensitivity computation, STRESS CHECK; and an optimization code, DOT. Examples are run successfully in full-batch mode to demonstrate the feasibility of the proposed integrated optimization method.