Generalized Optimality Criteria Method for Topology Optimization

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.

Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

Topological optimization of the fork-end of a knuckle joint

Topology optimization is a mathematical approach that optimizes the layout for the given design constraints such as loading and boundary conditions so that the optimum design obtained performs its function. In different types of loading conditions such as single load or multiple load topological optimization result in the best use of a material for a body in given volume constraints. In topological optimization the structural compliance is minimized while satisfying a constraint on the volume of the structure. This paper represents the topological optimization of the fork-end (double eye) of a knuckle joint with the objective to reduce the mass of an existing fork-end of a knuckle joint of an automobile or locomotive by applying the optimization technique. Reducing the weight of an automobile part will result in the overall weight reduction of a vehicle, thus, its energy consumption demands decrease thereby improving its fuel efficiency. The topological optimization was done using a finite element solver, ANSYS. The ANSYS Parametric Design Language was employed for utilizing the topological optimization capabilities of the commonly used finite element solver ANSYS. Solid92 elements were used to model and mesh the fork end of the knuckle joint in ANSYS. The optimality criteria method was used for topological optimizing the fork end of a knuckle joint.