Topology optimization of plate/shell structures with respect to eigenfrequencies using a biologically inspired algorithm

In this article, a novel approach is presented to perform topology optimization in a simple and explicit way. The method capitalizes on the use of a bio-inspired algorithm to represent topology, leading to more flexible optimization solutions along with explicit structure representation. To avoid remeshing upon design changes, a special treatment called the enhanced stiffness transformation approach (ESTA) is introduced to transform the stiffness and mass matrices of the growing stiffener into a set of equivalent stiffness and mass matrices. In this way, stiffeners are separated from the finite element mesh and can grow in an arbitrary direction to form an optimized layout solution. Notably, this approach incorporates more geometric information into topology optimization, which improves the clarity of stiffener layouts. Finally, the effectiveness of the proposed method is illustrated with two examples of maximum eigenfrequency design of plate/shell structures.