TY - JOUR
T1 - A Non-Ersatz Material Approach for the Topology Optimization of Elastic Structures Based on Piecewise Constant Level Set Method
AU - Zhang , Zhengfang
AU - Dong , Yanqiang
AU - Chen , Weifeng
JO - Communications in Computational Physics
VL - 5
SP - 1370
EP - 1389
PY - 2021
DA - 2021/10
SN - 30
DO - http://doi.org/10.4208/cicp.OA-2020-0231
UR - https://global-sci.org/intro/article_detail/cicp/19933.html
KW - Non-ersatz material approach, piecewise constant level set method, linearized elasticity system, sensitivity analysis, penalty gradient algorithm.
AB - <p style="text-align: justify;">The topology optimization of a linearized elasticity system with the area
(volume) constraint is investigated. A non-ersatz material approach is proposed. By
introducing a fixed background domain, the linearized elasticity system is extended
into the background domain by a characteristic function. The piecewise constant level
set (PCLS) method is applied to represent the original material region and the void
region. A quadratic function of PCLS function is proposed to replace the characteristic
function. The functional derivative of the objective functional with respect to PCLS
function is derived, which is zero in the void region and nonzero in the original material region. A penalty gradient algorithm is proposed. Four numerical experiments of
2D and 3D elastic structures with different boundary conditions are presented, illustrating the validity of the proposed algorithm.</p>