Shape preserving design of geometrically nonlinear structures using topology optimization

Subparts of load carrying structures like airplane windows or doors must be isolated from distortions and hence structural optimization needs to take such shape preserving constraints into account. The paper extends the shape preserving topology optimization approach from simple linear load cases into geometrically nonlinear problems with practical significance. Based on an integrated deformation energy function, an improved warpage formulation is proposed to measure the geometrical distortion during large deformations. Structural complementary elastic work is assigned as the objective function. The average distortion calculated as the integrated deformation energy accumulated in the incremental loading process is accordingly constrained to obtain warpage control. In the numerical implementation, an energy interpolation scheme is utilized to alleviate numerical instability in low stiffness regions. An additional loading case avoids isolation phenomena. Optimization results show that shape preserving design is successfully implemented in geometrically nonlinear structures by effectively suppressing local warping deformations.