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Abstract
In this article, a generalized optimality criteria method is proposed for topology optimization with arbitrary objective function and multiple inequality constraints. This algorithm uses sensitivity information to update both the Lagrange multipliers and design variables. Different from the conventional optimality criteria method, the proposed method does not satisfy constraints at every iteration. Rather, it improves the Lagrange multipliers and design variables such that the optimality criteria are satisfied upon convergence. The main advantages of the proposed method are its capability of handling multiple constraints and computational efficiency. In numerical examples, the proposed method was found to be more than 100 times faster than the optimality criteria method and more than 1000 times faster than the method of moving asymptotes.
Highlights
Unique characteristics of topology optimization are that (a) each iteration of optimization requires expensive finite element simulations, and (b) most optimization problems have a handful of performances and numerous design variables
A new topology optimization algorithm, generalized optimality optimality cricriteria this method (GOCM), was proposed. It is based on thethe conventional criteria teria method (GOCM), was proposed
It is based on the conventional optimality criteria The method (OCM), wherein both Lagrange multiplier and design variables are updated
Summary
Three optimization algorithms have been commonly used: the optimality criteria method [1], the method of moving asymptotes [2], and the sequential linear programming method [3]. The main reason for the popularity of these methods is not from their performance but from their convenience. Unique characteristics of topology optimization are that (a) each iteration of optimization requires expensive finite element simulations, and (b) most optimization problems have a handful of performances (objectives and constraints) and numerous design variables. In the case of the solid isotropic material with penalization (SIMP) method [4], in essence, the number of design variables is the same as the number of finite elements. Optimization algorithms are adopted on the basis of these characteristics
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