Toyota Motor Engineering & Manufacturing North America, Inc.

University of Michigan

Kazuhiro Saitou

Tsuyoshi Nomura

Yuqing Zhou

Methods are provided for designing a structure with developable surfaces using a surface developability constraint. The surface developability constraint is developed based on the discovery of a sufficient condition for surface piecewise developability, namely surface normal directions lie on a small, finite number of planes. Automated methods and algorithms may include providing a design domain and a characteristic function of a material in the design domain to be optimized. The methods include defining a nodal density of the material, and determining surface normal directions of a plurality of planes. A density gradient that describes the surface normal directions is then determined. The methods include performing a topology optimization process on the design domain using a surface developability constraint that is based, at least in part, on the characteristic function. A geometric domain is then created for the structure using results from the topology optimization.

Surface developability constraint for density-based topology optimization

Methods for multi-component topology optimization for composite structures are disclosed. In one embodiment, a method of designing a structure by computer-implemented topology optimization includes establishing a plurality of design points within a design domain and establishing at least a first orientation field and a second orientation field. The method further includes assigning values for the one or more membership fields, the one or more density fields, the first orientation field and the second orientation field, and projecting the values onto a simulation model. The method includes achieving convergence of an objective function for a design variable by iteratively executing a topology optimization of the simulation model using the values. Each design point of the plurality of design points is a member of no component or a member of one of the first component and the second component.

Methods for topology optimization using a membership variable

Methods for combinatorial choice in topology optimization are disclosed. In one embodiment, a method of performing combinatorial choice in a non-linear programming problem for designing a structure includes establishing, by one or more processors, a set of K variables, wherein the set of K variables defines an K-dimensional unit cube in a normal coordinate system. The K-dimensional unit cube includes a plurality of desired vertices representing a plurality of desired combinations that satisfy a constraint and a plurality of undesired vertices representing a plurality of undesired combinations that do not satisfy the constraint. The method further includes transforming the K-dimensional unit cube into a transformed shape in a transformed coordinate system using a shape function. Values of the set of K variables cannot have a combination represented by the plurality of undesired combinations.

Growing community of inventors

Ann Arbor, MI, United States of America

Kazuhiro Saitou