Bi-directional evolutionary topology optimization using element replaceable method

In the present paper, design problems of maximizing the structural stiffness or natural frequency are considered subject to the material volume constraint. A new element replaceable method (ERPM) is proposed for evolutionary topology optimization of structures. Compared with existing versions of evolutionary structural optimization methods, contributions are twofold. On the one hand, a new automatic element deletion/growth procedure is established. The deletion of a finite element means that a solid element is replaced with an orthotropic cellular microstructure (OCM) element. The growth of an element means that an OCM element is replaced with a solid element of full materials. In fact, both operations are interchangeable depending upon how the value of element sensitivity is with respect to the objective function. The OCM design strategy is beneficial in preventing artificial modes for dynamic problems. Besides, the iteration validity is greatly improved with the introduction of a check position (CP) technique. On the other hand, a new checkerboard control algorithm is proposed to work together with the above procedure. After the identification of local checkerboards and detailed structures over the entire design domain, the algorithm will fill or delete elements depending upon the prescribed threshold of sensitivity values. Numerical results show that the ERPM is efficient and a clear and valuable material pattern can be achieved for both static and dynamic problems.