An engineering constraint method for continuum structural topology optimization

Jianfeng Zhu,Xiaokai Chen

doi:10.1177/1687814017743387

Abstract

Manufacturing and machining property are the most important features of structures. The product with good processing property is not only to decrease its costs but also to increase its efficiency. It is very difficult to design and machine because of the complicated results of topology optimization. This study introduces a heuristic approach using an engineering constraint in topology optimization sensitivity process. With this special method, the result of topology optimization can meet the structural design requirement. Several numerical examples were provided to show that the positive influence of new engineering constraint method on the reasonable results of topology optimization was significant. It was a good way to control the material distribution of continuum structural topology optimization using this method.

Highlights

Compliance optimizationMinima compliance of the Messerschmidt– Bolkow–Blohm (MBB) beam is a standard topic, and the mathematical equation of the optimization is defined in the following
Manufacturing and machining property are the most important features of structures
Since early research by Bendsøe and Kikuchi,[1] topology optimization is recognized as an important technique to figure out the optimal structure layout within the given design domain

Summary

Compliance optimization

Minima compliance of the Messerschmidt– Bolkow–Blohm (MBB) beam is a standard topic, and the mathematical equation of the optimization is defined in the following. 0 xe 1 where C is defined as objective denotes compliance; ue is the element displacement vector; k0 represents the element stiffness matrix; xe is the design variable; N is the number of all design variables; U, F, and K are the displacement, load, and the global structure stiffness, respectively; V is the original volume; V(x) is optimal volume; and f is the global volume fraction. Ee is the element Young’s modulus according to its density xe that is modified by SIMP approach and is described in the following formulation. The new modified SIMP method has many outstanding capabilities to implement the extensional filters in topology optimization.[15]

Sensitivity filtering method

Engineering constraint method

Numerical examples

Symmetry problem

Pattern repetition problem

Iteration steps