A modified level set method for topology optimization of sparsely-filled and slender structures

Abstract In structural optimization, the level set method is known as a well-established approach for shape and topology optimization. However, special care must be taken, if design domains are sparsely-filled slender. Using steepest descent-type methods, slender structure optimizations tend to instabilities loss of cohesion. A sole step size control or selection more complex initial designs only help occasionally overcome these issues do not describe universal solution. this paper, instead updating function by solving Hamilton–Jacobi partial differential equation, an adapted algorithm update utilized, which allows efficient stable optimization structures. Including different adaptations, replaces unacceptable modifying both pseudo-time Lagrange multiplier. Besides, adjustments incorporated in normal velocity formulation avoid achieve smoother convergence. Furthermore, adding filtering-like adaptation terms scheme, even case very structures, able perform with appropriate convergence speed. This procedure applied compliance minimization problems The stability process shown 2D numerical examples. solid isotropic material penalization (SIMP) used alternative validate result quality presented method. Finally, simple extension 3D addressed, example briefly discussed.