Methods for topology optimization using a membership variable

A method of designing a structure by computer-implemented topology optimization, the method comprising:

• establishing, by one or more processors, a plurality of design points within a design domain;
• establishing, by the one or more processors:
• at least a first membership field and a second membership field, wherein the first membership field is associated with membership within a first component of the structure and the second membership field is associated within membership within a second component of the structure;
• at least a first density field and a second density field;
• and
• at least a first orientation field and a second orientation field, wherein values of the first orientation field and the second orientation field correspond to an orientation angle of an element;
• assigning, for each individual design point of the plurality of design points, values for the first membership field, the second membership field, the first density field, the second density field, the first orientation field and the second orientation field;
• projecting the values onto a simulation model after multiplying the values of the orientation fields and the density fields by the values of the membership fields;
• and
• achieving convergence of an objective function for a design variable by iteratively executing a topology optimization of the simulation model using the values, wherein:
• convergence results in design of the structure, and
• 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 such that a shape of the first component and a shape of the second component are determined based on the one or more membership fields.

A method of designing a structure by computer-implemented topology optimization, the method comprising:

• establishing, by one or more processors, a plurality of design points within a design domain;
• establishing, by the one or more processors:
• a common membership and density field, wherein values of the common membership and density field are associated with membership within one or more components of the structure and density values within the structure;
• and
• at least a first orientation field and a second orientation field, wherein values of the first orientation field and the second orientation field correspond to an orientation angle of an element;
• assigning, for each individual design point of the plurality of design points, values for the common membership and density field, the first orientation field and the second orientation field;
• projecting the values onto a simulation model after multiplying the values of the orientation fields by the values of the common membership and density field;
• and
• achieving convergence of an objective function for a design variable by iteratively executing a topology optimization of the simulation model using the values, wherein:
• convergence results in design of the structure, and
• each design point of the plurality of design points is a member of no component or one of the one or more components such that a shape of a first component and a shape of a second component are determined based on the one or more membership fields.